def _fit_start_params_hr(self, order):
"""
Get starting parameters for fit.
Parameters
----------
order : iterable
(p,q,k) - AR lags, MA lags, and number of exogenous variables
including the constant.
Returns
-------
start_params : array
A first guess at the starting parameters.
Notes
-----
If necessary, fits an AR process with the laglength selected according
to best BIC. Obtain the residuals. Then fit an ARMA(p,q) model via
OLS using these residuals for a first approximation. Uses a separate
OLS regression to find the coefficients of exogenous variables.
References
----------
Hannan, E.J. and Rissanen, J. 1982. "Recursive estimation of mixed
autoregressive-moving average order." `Biometrika`. 69.1.
"""
p,q,k = order
start_params = zeros((p+q+k))
endog = self.endog.copy() # copy because overwritten
exog = self.exog
if k != 0:
ols_params = GLS(endog, exog).fit().params
start_params[:k] = ols_params
endog -= np.dot(exog, ols_params).squeeze()
if q != 0:
if p != 0:
armod = AR(endog).fit(ic='bic', trend='nc')
arcoefs_tmp = armod.params
p_tmp = armod.k_ar
resid = endog[p_tmp:] - np.dot(lagmat(endog, p_tmp,
trim='both'), arcoefs_tmp)
if p < p_tmp + q:
endog_start = p_tmp + q - p
resid_start = 0
else:
endog_start = 0
resid_start = p - p_tmp - q
lag_endog = lagmat(endog, p, 'both')[endog_start:]
lag_resid = lagmat(resid, q, 'both')[resid_start:]
# stack ar lags and resids
X = np.column_stack((lag_endog, lag_resid))
coefs = GLS(endog[max(p_tmp+q,p):], X).fit().params
start_params[k:k+p+q] = coefs
else:
start_params[k+p:k+p+q] = yule_walker(endog, order=q)[0]
if q==0 and p != 0:
arcoefs = yule_walker(endog, order=p)[0]
start_params[k:k+p] = arcoefs
return start_params
def pred_density(self, phi, sigma, y=None, h=8, impact_mat=None):
"""Simulates predictive density..."""
if y is None:
#xest, yest = self.xest, self.yest
xest = lagmat(self.data, maxlag=self._p, trim='backward')
xest = add_constant(xest, prepend=False)
xest = xest[-self._p]
else:
xest, yest = lagmat(y, maxlag=self._p, trim="both", original="sep")
if self._cons is True:
xest = add_constant(xest, prepend=False)
x = xest
nx = x.shape[0]
y = np.zeros((h, self._ny))
if impact_mat == None:
impact_mat = np.ones_like(y)
impact_mat = np.squeeze(impact_mat)
for i in range(0, h):
y[i, :] = x.dot(
phi) + impact_mat[i] * np.random.multivariate_normal(
np.zeros(self._ny), sigma)
if self._p > 0:
x[:(self._ny * (self._p - 1))] = x[(self._ny):(nx -
self._cons)]
x[(self._ny * (self._p - 1)):-1] = y[i, :]
else:
x = y[i, :]
return y
def _fit_start_params_hr(self, order):
"""
Get starting parameters for fit.
Parameters
----------
order : iterable
(p,q,k) - AR lags, MA lags, and number of exogenous variables
including the constant.
Returns
-------
start_params : array
A first guess at the starting parameters.
Notes
-----
If necessary, fits an AR process with the laglength selected according
to best BIC. Obtain the residuals. Then fit an ARMA(p,q) model via
OLS using these residuals for a first approximation. Uses a separate
OLS regression to find the coefficients of exogenous variables.
References
----------
Hannan, E.J. and Rissanen, J. 1982. "Recursive estimation of mixed
autoregressive-moving average order." `Biometrika`. 69.1.
"""
p, q, k = order
start_params = zeros((p + q + k))
endog = self.endog.copy() # copy because overwritten
exog = self.exog
if k != 0:
ols_params = GLS(endog, exog).fit().params
start_params[:k] = ols_params
endog -= np.dot(exog, ols_params).squeeze()
if q != 0:
if p != 0:
armod = AR(endog).fit(ic='bic', trend='nc')
arcoefs_tmp = armod.params
p_tmp = armod.k_ar
resid = endog[p_tmp:] - np.dot(
lagmat(endog, p_tmp, trim='both'), arcoefs_tmp)
if p < p_tmp + q:
endog_start = p_tmp + q - p
resid_start = 0
else:
endog_start = 0
resid_start = p - p_tmp - q
lag_endog = lagmat(endog, p, 'both')[endog_start:]
lag_resid = lagmat(resid, q, 'both')[resid_start:]
# stack ar lags and resids
X = np.column_stack((lag_endog, lag_resid))
coefs = GLS(endog[max(p_tmp + q, p):], X).fit().params
start_params[k:k + p + q] = coefs
else:
start_params[k + p:k + p + q] = yule_walker(endog, order=q)[0]
if q == 0 and p != 0:
arcoefs = yule_walker(endog, order=p)[0]
start_params[k:k + p] = arcoefs
return start_params
def _process_inputs(self, X, E=None, lengths=None):
if self.n_features == 1:
lagged = None
if lengths is None:
lagged = lagmat(X, maxlag=self.n_lags, trim='forward',
original='ex')
else:
lagged = np.zeros((len(X), self.n_lags))
for i, j in iter_from_X_lengths(X, lengths):
lagged[i:j, :] = lagmat(X[i:j], maxlag=self.n_lags,
trim='forward', original='ex')
return {'obs': X.reshape(-1,1),
'lagged': lagged.reshape(-1, self.n_features, self.n_lags)}
else:
lagged = None
lagged = np.zeros((X.shape[0], self.n_features, self.n_lags))
if lengths is None:
tem = lagmat(X, maxlag=self.n_lags, trim='forward',
original='ex')
for sample in range(X.shape[0]):
lagged[sample] = np.reshape\
(tem[sample], (self.n_features, self.n_lags), 'F')
else:
for i, j in iter_from_X_lengths(X, lengths):
lagged[i:j, :] = lagmat(X[i:j], maxlag=self.n_lags,
trim='forward', original='ex')
lagged.reshape(-1, self.n_featurs, self.n_lags)
return {'obs': X, 'lagged': lagged}
def create_dataset(dataset, timestep=1, look_back=1, look_ahead=1):
dataX = lagmat(dataset, maxlag=look_back, trim='both', original='ex')
dataY = lagmat(dataset[look_back:],
maxlag=look_ahead,
trim='backward',
original='ex')
dataX = dataX.reshape(-1, timestep, dataX.shape[1])[:-(look_ahead - 1)]
return np.array(dataX), np.array(dataY[:-(look_ahead - 1)])
def maximum_likelihood_estimation(ts, lags):
"""
Obtain the cointegrating vectors and corresponding eigenvalues
"""
# Make sure we are working with array, convert if necessary
ts = np.asarray(ts)
# Calculate the differences of ts
ts_diff = np.diff(ts, axis=0)
# Calculate lags of ts_diff.
ts_diff_lags = lagmat(ts_diff, lags, trim='both')
# First lag of ts
ts_lag = lagmat(ts, 1, trim='both')
# Trim ts_diff and ts_lag
ts_diff = ts_diff[lags:]
ts_lag = ts_lag[lags:]
# Include intercept in the regressions
ones = np.ones((ts_diff_lags.shape[0], 1))
ts_diff_lags = np.append(ts_diff_lags, ones, axis=1)
# Calculate the residuals of the regressions of diffs and lags
# into ts_diff_lags
inverse = np.linalg.pinv(ts_diff_lags)
u = ts_diff - np.dot(ts_diff_lags, np.dot(inverse, ts_diff))
v = ts_lag - np.dot(ts_diff_lags, np.dot(inverse, ts_lag))
# Covariance matrices of the calculated residuals
t = ts_diff_lags.shape[0]
Svv = np.dot(v.T, v) / t
Suu = np.dot(u.T, u) / t
Suv = np.dot(u.T, v) / t
Svu = Suv.T
# ToDo: check for singular matrices and exit
Svv_inv = np.linalg.inv(Svv)
Suu_inv = np.linalg.inv(Suu)
# Calculate eigenvalues and eigenvectors of the product of covariances
cov_prod = np.dot(Svv_inv, np.dot(Svu, np.dot(Suu_inv, Suv)))
eigenvalues, eigenvectors = np.linalg.eig(cov_prod)
# Use Cholesky decomposition on eigenvectors
evec_Svv_evec = np.dot(eigenvectors.T, np.dot(Svv, eigenvectors))
cholesky_factor = np.linalg.cholesky(evec_Svv_evec)
eigenvectors = np.dot(eigenvectors, np.linalg.inv(cholesky_factor.T))
# Order the eigenvalues and eigenvectors
indices_ordered = np.argsort(eigenvalues)
indices_ordered = np.flipud(indices_ordered)
# Return the calculated values
return eigenvalues[indices_ordered], eigenvectors[:, indices_ordered]
def fit_discrete_state_transition(speed,
is_replay,
penalty=1E-5,
speed_knots=None,
diagonal=None):
"""Estimate the predicted probablity of replay given speed and whether
it was a replay in the previous time step.
p(I_t | I_t-1, v_t-1)
p_I_0, p_I_1 in Long Tao's code
Parameters
----------
speed : ndarray, shape (n_time,)
is_replay : boolean ndarray, shape (n_time,)
speed_knots : ndarray, shape (n_knots,)
Returns
-------
probability_replay : ndarray, shape (n_time, 2)
"""
data = pd.DataFrame({
'is_replay':
is_replay.astype(np.float64),
'lagged_is_replay':
lagmat(is_replay, maxlag=1).astype(np.float64).squeeze(),
'lagged_speed':
lagmat(speed, maxlag=1).squeeze()
}).dropna()
if speed_knots is None:
speed_mid_point = np.nanmedian(speed[speed > 10])
speed_knots = [1., 2., 3., speed_mid_point]
MODEL_FORMULA = (
'is_replay ~ 1 + lagged_is_replay + '
'cr(lagged_speed, knots=speed_knots, constraints="center")')
response, design_matrix = dmatrices(MODEL_FORMULA, data)
penalty = np.ones((design_matrix.shape[1], )) * penalty
penalty[0] = 0.0
fit = penalized_IRLS(design_matrix,
response,
family=FAMILY,
penalty=penalty)
if np.isnan(fit.AIC):
logger.error("Discrete state transition failed to fit properly. "
"Try specifying `speed_knots`")
return partial(predict_probability,
design_matrix=design_matrix,
coefficients=fit.coefficients)
def _process_inputs(self, X, E=None, lengths=None):
# Makes sure inputs have correct shape, generates features
lagged = None
if lengths is None:
lagged = lagmat(X, maxlag=self.n_lags, trim='forward',
original='ex')
else:
lagged = np.zeros((len(X), self.n_lags))
for i, j in iter_from_X_lengths(X, lengths):
lagged[i:j, :] = lagmat(X[i:j], maxlag=self.n_lags,
trim='forward', original='ex')
inputs = {'obs': X.reshape(-1,1),
'lagged': lagged}
return inputs
def pacf_ols(x, nlags=40):
'''Calculate partial autocorrelations
Parameters
----------
x : 1d array
observations of time series for which pacf is calculated
nlags : int
Number of lags for which pacf is returned. Lag 0 is not returned.
Returns
-------
pacf : 1d array
partial autocorrelations, maxlag+1 elements
Notes
-----
This solves a separate OLS estimation for each desired lag.
'''
#TODO: add warnings for Yule-Walker
#NOTE: demeaning and not using a constant gave incorrect answers?
#JP: demeaning should have a better estimate of the constant
#maybe we can compare small sample properties with a MonteCarlo
xlags, x0 = lagmat(x, nlags, original='sep')
#xlags = sm.add_constant(lagmat(x, nlags), prepend=True)
xlags = add_constant(xlags)
pacf = [1.]
for k in range(1, nlags+1):
res = OLS(x0[k:], xlags[k:, :k+1]).fit()
#np.take(xlags[k:], range(1,k+1)+[-1],
pacf.append(res.params[-1])
return np.array(pacf)
def _estimate_df_regression(y, trend, lags):
"""Helper function that estimates the core (A)DF regression
Parameters
----------
y : ndarray
The data for the lag selection
trend : {'nc','c','ct','ctt'}
The trend order
lags : int
The number of lags to include in the ADF regression
Returns
-------
ols_res : OLSResults
A results class object produced by OLS.fit()
Notes
-----
See statsmodels.regression.linear_model.OLS for details on the results
returned
"""
delta_y = diff(y)
rhs = lagmat(delta_y[:, None], lags, trim='both', original='in')
nobs = rhs.shape[0]
lhs = rhs[:, 0].copy() # lag-0 values are lhs, Is copy() necessary?
rhs[:, 0] = y[-nobs - 1:-1] # replace lag 0 with level of y
rhs = _add_column_names(rhs, lags)
if trend != 'nc':
rhs = add_trend(rhs.iloc[:, :lags + 1], trend)
return OLS(lhs, rhs).fit()
def pacf_ols(x, nlags=40):
'''Calculate partial autocorrelations
Parameters
----------
x : 1d array
observations of time series for which pacf is calculated
nlags : int
Number of lags for which pacf is returned. Lag 0 is not returned.
Returns
-------
pacf : 1d array
partial autocorrelations, maxlag+1 elements
Notes
-----
This solves a separate OLS estimation for each desired lag.
'''
#TODO: add warnings for Yule-Walker
#NOTE: demeaning and not using a constant gave incorrect answers?
#JP: demeaning should have a better estimate of the constant
#maybe we can compare small sample properties with a MonteCarlo
xlags, x0 = lagmat(x, nlags, original='sep')
#xlags = sm.add_constant(lagmat(x, nlags), prepend=True)
xlags = add_constant(xlags)
pacf = [1.]
for k in range(1, nlags+1):
res = OLS(x0[k:], xlags[k:, :k+1]).fit()
#np.take(xlags[k:], range(1,k+1)+[-1],
pacf.append(res.params[-1])
return np.array(pacf)
def _estimate_df_regression(y, trend, lags):
"""Helper function that estimates the core (A)DF regression
Parameters
----------
y : array-like, (nobs,)
The data for the lag selection
trend : str, {'nc','c','ct','ctt'}
The trend order
lags : int
The number of lags to include in the ADF regression
Returns
-------
ols_res : OLSResults
A results class object produced by OLS.fit()
Notes
-----
See statsmodels.regression.linear_model.OLS for details on the results
returned
"""
delta_y = diff(y)
rhs = lagmat(delta_y[:, None], lags, trim='both', original='in')
nobs = rhs.shape[0]
lhs = rhs[:, 0].copy() # lag-0 values are lhs, Is copy() necessary?
rhs[:, 0] = y[-nobs - 1:-1] # replace lag 0 with level of y
if trend != 'nc':
rhs = add_trend(rhs[:, :lags + 1], trend)
return OLS(lhs, rhs).fit()
def load_(infile, nLags=1000):
from statsmodels.tsa.tsatools import lagmat
assert infile.endswith('.npy')
X, Y = np.load(infile)
X0 = lagmat(X, nLags, trim='both')
ind = len(X)-len(X0)
return X0, Y[ind:]
def __init__(self, endog, use_exp=True, h=0.1, p=1, q=1, **kwargs):
exog, endog = lagmat(endog,
p,
trim='both',
original='sep',
use_pandas=True)
super().__init__(endog, add_constant(exog), **kwargs)
self.p = p
self.q = q
self.h = h
for plag1 in range(1, p + 1):
self.exog_names.append('phi2%d%d' % (plag1, plag1))
# for plag1 in range(1,p+1):
# for plag2 in range(plag1,p+1):
# self.exog_names.append('phi2%d%d' % (plag1,plag2))
for qlag in range(1, q + 1):
self.exog_names.append('gamma%d' % qlag)
self.exog_names.append('sigma')
# for lag in range(1,max(p,q)+1):
# self.exog_names.append('s%d' % lag)
self.nlinear_terms = self.p + 1
self.nquad_terms = int(self.p * (self.p + 1) / 2)
self.ngamma_terms = self.q
self.ninit_terms = max(self.p, self.q)
def _get_mixed_design_mat_part(seas_part, order, seas_order, m):
"""
Prepares `pP, qQ` parts of the design matrix for SGD.
Parameters
----------
seas_part : array_like
Either the seasonal part that was previosuly calculated with
`_get_seasonal_design_mat_part` for P or for Q.
order : int
Either p or q of SARIMAX.
seas_order : int
Either P or Q of SARIMAX.
m : int
The seasonal period of SARIMAX.
Returns
-------
A matrix shaped (N, P) or (N, Q) that will correspond to the
multiplying terms in SARIMAX's "mixed" parameters i.e. containing both
ordinals and seasonals as a result of multiplicative formulation.
"""
N = seas_part.shape[0]
part = np.empty((N, order * seas_order))
for i in range(seas_order):
part[:, i * order: (i + 1) * order] = lagmat(
seas_part[:, i], maxlag=order
)
return part
def GetADFuller(Y, maxlags=None, regression='c'):
#Y = np.asarray(Y)
Y = Y.T
dy = np.diff(Y)
if dy.ndim == 1:
dy = dy[:, None]
ydall = lagmat(dy, maxlags, trim='both', original='in')
nobs = ydall.shape[0]
ydall[:, 0] = Y[-nobs - 1:-1]
dYshort = dy[-nobs:]
if regression != 'nc':
Z = add_trend(ydall[:, :maxlags + 1], regression)
else:
Z = ydall[:, :maxlags + 1]
resultADFuller = GetOLS(Y=dYshort.T, X=Z.T)
K_dash = 2 * (2 * maxlags + 1)
AIC = np.log(np.absolute(np.linalg.det(
resultADFuller['sigma_hat']))) + 2.0 * K_dash / (
resultADFuller['nobs']) # log(sigma_hat) + 2*K_dash/T
BIC = np.log(np.absolute(np.linalg.det(resultADFuller['sigma_hat']))) + (
K_dash / resultADFuller['nobs']) * np.log(
resultADFuller['nobs']) # log(sigma_hat) + K_dash/T*log(T)
resultADFuller['AIC'] = AIC
resultADFuller['BIC'] = BIC
resultADFuller['adfstat'] = resultADFuller['tvalues'][0, 0]
resultADFuller['maxlag'] = maxlags
return resultADFuller
def train(self, data, **kwargs):
if self.indexer is not None and isinstance(data, pd.DataFrame):
data = self.indexer.get_data(data)
lagdata, ndata = lagmat(data, maxlag=self.order, trim="both", original='sep')
mqt = QuantReg(ndata, lagdata).fit(0.5)
if self.alpha is not None:
uqt = QuantReg(ndata, lagdata).fit(1 - self.alpha)
lqt = QuantReg(ndata, lagdata).fit(self.alpha)
self.mean_qt = [k for k in mqt.params]
if self.alpha is not None:
self.upper_qt = [k for k in uqt.params]
self.lower_qt = [k for k in lqt.params]
if self.dist:
self.dist_qt = []
for alpha in np.arange(0.05,0.5,0.05):
lqt = QuantReg(ndata, lagdata).fit(alpha)
uqt = QuantReg(ndata, lagdata).fit(1 - alpha)
lo_qt = [k for k in lqt.params]
up_qt = [k for k in uqt.params]
self.dist_qt.append([lo_qt, up_qt])
self.shortname = "QAR(" + str(self.order) + ") - " + str(self.alpha)
def lag_func(data,lag,col):
lag = lag
X = lagmat(data["diff"], lag)
lagged = data.copy()
for c in range(1,lag+1):
lagged[col+"%d" % c] = X[:, c-1]
return lagged
def fit_speed_likelihood(speed, is_replay, speed_threshold=4.0):
"""Fits the standard deviation of the change in speed for the replay and
non-replay state.
Parameters
----------
speed : ndarray, shape (n_time,)
is_replay : ndarray, shape (n_time,)
speed_threshold : float, optional
Returns
-------
speed_likelihood : function
"""
is_replay = np.asarray(is_replay).astype(bool)
lagged_speed = lagmat(speed, 1)
lagged_speed[0] = speed[0]
replay_coefficients, replay_scale = fit_speed_model(
speed[is_replay], lagged_speed[is_replay])
no_replay_coefficients, no_replay_scale = fit_speed_model(
speed[~is_replay], lagged_speed[~is_replay])
return partial(speed_likelihood,
replay_coefficients=replay_coefficients,
replay_scale=replay_scale,
no_replay_coefficients=no_replay_coefficients,
no_replay_scale=no_replay_scale,
speed_threshold=speed_threshold)
def selectlag_IC(data, maxlag, penalty):
# Select VAR lag length using information criterion
# preliminaries
n_x = np.size(data, 1)
# compute information criterion for each possible lag length
IC = np.empty((maxlag + 1, 1))
for i in range(1, maxlag + 1):
# set lag length
p = i
# estimate VAR
data_est = data[maxlag - p:, :]
T = np.size(data_est, 0)
T_VAR = T - p
X = lagmat(data_est, p, original='ex')
X = X[p:, :]
Y = data_est[p:, :]
X = np.column_stack((X, np.ones((len(X), 1))))
VAR_coeff = (np.linalg.inv(X.T @ X)) @ (X.T @ Y)
VAR_res = Y - X @ VAR_coeff
# Sigma_u = (VAR_res'*VAR_res)/(T_VAR-n_x*p-1)
Sigma_u = (VAR_res.T @ VAR_res) / T_VAR
# compute information criterion
T = np.size(data, 0) - maxlag
# IC(i) = log(det(Sigma_u)) + i * n_x^2 * 2/T
IC[i] = np.log(np.linalg.det(Sigma_u)) + i * n_x**2 * penalty(T)
lag = np.where(IC == min(IC))
return int(lag[0][0])
def _init_model(self) -> None:
"""Should be called whenever the model is initialized or changed"""
self._reformat_lags()
self._check_specification()
nobs_orig = self._y.shape[0]
if self.constant:
reg_constant = np.ones((nobs_orig, 1), dtype=np.float64)
else:
reg_constant = np.ones((nobs_orig, 0), dtype=np.float64)
if self.lags is not None and nobs_orig > 0:
maxlag = np.max(self.lags)
lag_array = lagmat(self._y, maxlag)
reg_lags = np.empty((nobs_orig, self._lags.shape[1]),
dtype=np.float64)
for i, lags in enumerate(self._lags.T):
reg_lags[:, i] = np.mean(lag_array[:, lags[0]:lags[1]], 1)
else:
reg_lags = np.empty((nobs_orig, 0), dtype=np.float64)
if self._x is not None:
reg_x = self._x
else:
reg_x = np.empty((nobs_orig, 0), dtype=np.float64)
self.regressors = np.hstack((reg_constant, reg_lags, reg_x))
def adf(ts, maxlag=1):
"""
Augmented Dickey-Fuller unit root test
"""
# make sure we are working with an array, convert if necessary
ts = np.asarray(ts)
# Get the dimension of the array
nobs = ts.shape[0]
# Calculate the discrete difference
tsdiff = np.diff(ts)
# Create a 2d array of lags, trim invalid observations on both sides
tsdall = lagmat(tsdiff[:, None], maxlag, trim='both', original='in')
# Get dimension of the array
nobs = tsdall.shape[0]
# replace 0 xdiff with level of x
tsdall[:, 0] = ts[-nobs - 1:-1]
tsdshort = tsdiff[-nobs:]
# Calculate the linear regression using an ordinary least squares model
results = OLS(tsdshort, add_trend(tsdall[:, :maxlag + 1], 'c')).fit()
adfstat = results.tvalues[0]
# Get approx p-value from a precomputed table (from stattools)
pvalue = mackinnonp(adfstat, 'c', N=1)
return pvalue
def __init__(self, endog):
if not isinstance(endog, pd.DataFrame):
endog = pd.DataFrame(endog)
k = endog.shape[1]
augmented = lagmat(endog, 1, trim='both', original='in',
use_pandas=True)
endog = augmented.iloc[:, :k]
exog = add_constant(augmented.iloc[:, k:])
k_states = k * (k + 1)
super().__init__(endog, k_states=k_states)
self.ssm.initialize('known', stationary_cov=np.eye(self.k_states) * 5)
self['design'] = np.zeros((self.k_endog, self.k_states, self.nobs))
for i in range(self.k_endog):
start = i * (self.k_endog + 1)
end = start + self.k_endog + 1
self['design', i, start:end, :] = exog.T
self['transition'] = np.eye(k_states)
self['selection'] = np.eye(k_states)
self._obs_cov_slice = np.s_[:self.k_endog * (self.k_endog + 1) // 2]
self._obs_cov_tril = np.tril_indices(self.k_endog)
self._state_cov_slice = np.s_[-self.k_states:]
self._state_cov_ix = ('state_cov',) + np.diag_indices(self.k_states)
def sample(self, nsim=1000, y=None, flatten_output=False):
if y is None:
y = self.data
ydum, xdum = self._prior.get_pseudo_obs()
xest, yest = lagmat(y, maxlag=self._p, trim="both", original="sep")
if self._cons is True:
xest = add_constant(xest, prepend=False)
#if not (ydum == None).all():
yest = np.vstack((ydum, yest))
xest = np.vstack((xdum, xest))
# This is just a random initialization point....
phihatT = np.linalg.solve(xest.T.dot(xest), xest.T.dot(yest))
S = (yest - xest.dot(phihatT)).T.dot(yest - xest.dot(phihatT))
nu = yest.shape[0] - self._p * self._ny - self._cons * 1
omega = xest.T.dot(xest)
muphi = phihatT
phis, sigmas = NormInvWishart(phihatT, omega, S, nu).rvs(nsim)
if flatten_output:
return np.array([
np.r_[phis[i].flatten(order='F'),
vech(sigmas[i])] for i in range(nsim)
])
else:
return phis, sigmas
return phis, sigmas
def _init_model(self):
"""Should be called whenever the model is initialized or changed"""
self._reformat_lags()
self._check_specification()
nobs_orig = self._y.shape[0]
if self.constant:
reg_constant = ones((nobs_orig, 1), dtype=np.float64)
else:
reg_constant = ones((nobs_orig, 0), dtype=np.float64)
if self.lags is not None and nobs_orig > 0:
maxlag = np.max(self.lags)
lag_array = lagmat(self._y, maxlag)
reg_lags = empty((nobs_orig, self._lags.shape[1]), dtype=np.float64)
for i, lags in enumerate(self._lags.T):
reg_lags[:, i] = np.mean(lag_array[:, lags[0]:lags[1]], 1)
else:
reg_lags = empty((nobs_orig, 0), dtype=np.float64)
if self._x is not None:
reg_x = self._x
else:
reg_x = empty((nobs_orig, 0), dtype=np.float64)
self.regressors = np.hstack((reg_constant, reg_lags, reg_x))
first_obs, last_obs = self._indices
self.regressors = self.regressors[first_obs:last_obs, :]
self._y_adj = self._y[first_obs:last_obs]
def fit_scale(self, leading_indicator, cases, lag=0):
"""
Scaling correction for AR(p) model to fit case counts.
Args:
leading_indicator: Covariate that is a leading indicator for case counts
cases (nd.array): 1-dimensional array containing case counts
offset (int): Offset for window of cases counts you want to correct over
"""
self.lag = lag
leading_mean = np.mean(leading_indicator)
cases_mean = np.mean(cases)
leading_std = np.std(leading_indicator)
cases_std = np.std(cases)
z = leading_indicator[:-lag - 1]
x = cases[lag + 1:]
p = self.p
n = z.shape[0]
self.beta[0] += -leading_mean * cases_std / leading_std + cases_mean
self.beta[1:] *= cases_std / leading_std
Z = np.hstack([tf.ones((n, 1)), lagmat(z, maxlag=p)])[p:]
x_pred = Z @ self.beta.T
self.scale = np.sum(x) / np.sum(x_pred)
def infer_discrete_state_transition_from_training_data(is_non_local,
penalty=1e-5):
data = pd.DataFrame({
'is_non_local':
is_non_local.astype(np.float64),
'lagged_is_non_local':
lagmat(is_non_local, maxlag=1).astype(np.float64).squeeze(),
}).dropna()
MODEL_FORMULA = 'is_non_local ~ 1 + lagged_is_non_local'
response, design_matrix = dmatrices(MODEL_FORMULA, data)
penalty = np.ones((design_matrix.shape[1], )) * penalty
penalty[0] = 0.0
fit = penalized_IRLS(design_matrix,
response,
family=families.Binomial(),
penalty=penalty)
predict_data = {
'lagged_is_non_local': np.asarray([0, 1]),
}
predict_design_matrix = build_design_matrices(
[design_matrix.design_info],
predict_data,
NA_action=NAAction(NA_types=[]))[0]
non_local_probability = families.Binomial().link.inverse(
predict_design_matrix @ np.squeeze(fit.coefficients))
non_local_probability[np.isnan(non_local_probability)] = 0.0
return np.asarray(
[[1 - non_local_probability[0], non_local_probability[0]],
[1 - non_local_probability[1], non_local_probability[1]]])
def my_AR(endog, maxlag, trend=None):
"""
Autoregressive model implementation, aka AR(p)
:param endog: the dependent variables
:param maxlag: maximum number of lags to use
:param trend: 'c': add constant, 'nc' or None: no constant
:return: my_OLS dictionary
See ref: http://statsmodels.sourceforge.net/stable/_modules/statsmodels/tsa/ar_model.html#AR
"""
# Dependent data matrix
Y = endog[maxlag:] # has observations for the fit p lags removed
# Explanatory data matrix
X = lagmat(endog, maxlag, trim='both')
if trend is not None:
X = add_trend(
X, prepend=True,
trend=trend) # prepends puts trend column at the beginning
result = my_OLS(Y, X)
result['maxlag'] = maxlag
# Akaike information criterion using statsmodel def for AR(p) (Lutkephol's definition)
# note this is diff to adfuller's def
result['aic'] = np.log(
result['sigma']) + 2.0 * (1.0 + result['df_model']) / result['nobs']
return result
def VAR_forecast(Vector, VAR_estimates, lag_order, horizon, shock=None):
"""
Inputs the VAR Vector, VAR estimates, the lag order of the model,
the forecast horizon, and the desired first period shock.
Args:
Returns:
"""
# Initial Period shock for IRF.
if shock is None:
shock = np.zeros(len(Vector[0]))
error = np.zeros((len(Vector), len(Vector[0])))
error[0] = shock
# Predictions for Forecast Horizon.
for t in np.arange(0, horizon):
X_hat = Vector
for i in range(1, lag_order):
# X_hat = np.column_stack([X_hat, lag(Vector, i)])
lagged_vector = tsatools.lagmat(Vector, maxlag=1)
X_hat = np.column_stack([X_hat, lagged_vector])
X_hat = sm.add_constant(X_hat)
Y_hat = []
for Eq in VAR_estimates:
Y_hat.append(np.dot(X_hat[-1], VAR_estimates[Eq].params))
Forecast = Y_hat + error[t]
Vector = np.vstack((Vector, Forecast))
return Vector[-horizon:]
def _df_select_lags(y, trend, max_lags, method):
"""
Helper method to determine the best lag length in DF-like regressions
Parameters
----------
y : array-like, (nobs,)
The data for the lag selection exercise
trend : str, {'nc','c','ct','ctt'}
The trend order
max_lags : int
The maximum number of lags to check. This setting affects all
estimation since the sample is adjusted by max_lags when
fitting the models
method : str, {'AIC','BIC','t-stat'}
The method to use when estimating the model
Returns
-------
best_ic : float
The information criteria at the selected lag
best_lag : int
The selected lag
all_res : list
List of OLS results from fitting max_lag + 1 models
Notes
-----
See statsmodels.tsa.tsatools._autolag for details. If max_lags is None, the
default value of 12 * (nobs/100)**(1/4) is used.
"""
nobs = y.shape[0]
delta_y = diff(y)
if max_lags is None:
max_lags = int(ceil(12. * power(nobs / 100., 1 / 4.)))
rhs = lagmat(delta_y[:, None], max_lags, trim='both', original='in')
nobs = rhs.shape[0]
rhs[:, 0] = y[-nobs - 1:-1] # replace 0 with level of y
lhs = delta_y[-nobs:]
if trend != 'nc':
full_rhs = add_trend(rhs, trend, prepend=True)
else:
full_rhs = rhs
start_lag = full_rhs.shape[1] - rhs.shape[1] + 1
ic_best, best_lag, all_res = _autolag(OLS,
lhs,
full_rhs,
start_lag,
max_lags,
method,
regresults=True)
# To get the correct number of lags, subtract the start_lag since
# lags 0,1,...,start_lag-1 were not actual lags, but other variables
best_lag -= start_lag
return ic_best, best_lag, all_res
def _df_select_lags(y, trend, max_lags, method, low_memory=False):
"""
Helper method to determine the best lag length in DF-like regressions
Parameters
----------
y : ndarray
The data for the lag selection exercise
trend : {'nc','c','ct','ctt'}
The trend order
max_lags : int
The maximum number of lags to check. This setting affects all
estimation since the sample is adjusted by max_lags when
fitting the models
method : {'AIC','BIC','t-stat'}
The method to use when estimating the model
low_memory : bool
Flag indicating whether to use the low-memory algorithm for
lag-length selection.
Returns
-------
best_ic : float
The information criteria at the selected lag
best_lag : int
The selected lag
Notes
-----
If max_lags is None, the default value of 12 * (nobs/100)**(1/4) is used.
"""
nobs = y.shape[0]
# This is the absolute maximum number of lags possible,
# only needed to very short time series.
max_max_lags = nobs // 2 - 1
if trend != 'nc':
max_max_lags -= len(trend)
if max_lags is None:
max_lags = int(ceil(12. * power(nobs / 100., 1 / 4.)))
max_lags = max(min(max_lags, max_max_lags), 0)
if low_memory:
out = _autolag_ols_low_memory(y, max_lags, trend, method)
return out
delta_y = diff(y)
rhs = lagmat(delta_y[:, None], max_lags, trim='both', original='in')
nobs = rhs.shape[0]
rhs[:, 0] = y[-nobs - 1:-1] # replace 0 with level of y
lhs = delta_y[-nobs:]
if trend != 'nc':
full_rhs = add_trend(rhs, trend, prepend=True)
else:
full_rhs = rhs
start_lag = full_rhs.shape[1] - rhs.shape[1] + 1
ic_best, best_lag = _autolag_ols(lhs, full_rhs, start_lag, max_lags,
method)
return ic_best, best_lag
def _tsls_arima(self, x, arlags, model):
"""
Two-stage least squares approach for estimating ARIMA(p, 1, 1)
parameters as an alternative to MLE estimation in the case of
solver non-convergence
Parameters
----------
x : array_like
data series
arlags : int
AR(p) order
model : {'c','ct'}
Constant and trend order to include in regression
* 'c' : constant only
* 'ct' : constant and trend
Returns
-------
arparams : int
AR(1) coefficient plus constant
theta : int
MA(1) coefficient
olsfit.resid : ndarray
residuals from second-stage regression
"""
endog = np.diff(x, axis=0)
exog = lagmat(endog, arlags, trim='both')
# add constant if requested
if model == 'ct':
exog = add_constant(exog)
# remove extra terms from front of endog
endog = endog[arlags:]
if arlags > 0:
resids = lagmat(OLS(endog, exog).fit().resid, 1, trim='forward')
else:
resids = lagmat(-endog, 1, trim='forward')
# add negated residuals column to exog as MA(1) term
exog = np.append(exog, -resids, axis=1)
olsfit = OLS(endog, exog).fit()
if model == 'ct':
arparams = olsfit.params[1:(len(olsfit.params) - 1)]
else:
arparams = olsfit.params[0:(len(olsfit.params) - 1)]
theta = olsfit.params[len(olsfit.params) - 1]
return arparams, theta, olsfit.resid
def __init__(self, endog, k_regimes, order, trend='c', exog=None,
exog_tvtp=None, switching_ar=True, switching_trend=True,
switching_exog=False, switching_variance=False,
dates=None, freq=None, missing='none'):
# Properties
self.switching_ar = switching_ar
# Switching options
if self.switching_ar is True or self.switching_ar is False:
self.switching_ar = [self.switching_ar] * order
elif not len(self.switching_ar) == order:
raise ValueError('Invalid iterable passed to `switching_ar`.')
# Initialize the base model
super(MarkovAutoregression, self).__init__(
endog, k_regimes, trend=trend, exog=exog, order=order,
exog_tvtp=exog_tvtp, switching_trend=switching_trend,
switching_exog=switching_exog,
switching_variance=switching_variance, dates=dates, freq=freq,
missing=missing)
# Sanity checks
if self.nobs <= self.order:
raise ValueError('Must have more observations than the order of'
' the autoregression.')
# Autoregressive exog
self.exog_ar = lagmat(endog, self.order)[self.order:]
# Reshape other datasets
self.nobs -= self.order
self.orig_endog = self.endog
self.endog = self.endog[self.order:]
if self._k_exog > 0:
self.orig_exog = self.exog
self.exog = self.exog[self.order:]
# Reset the ModelData datasets
self.data.endog, self.data.exog = (
self.data._convert_endog_exog(self.endog, self.exog))
# Reset indexes, if provided
if self.data.row_labels is not None:
self.data._cache['row_labels'] = (
self.data.row_labels[self.order:])
if self._index is not None:
if self._index_generated:
self._index = self._index[:-self.order]
else:
self._index = self._index[self.order:]
# Parameters
self.parameters['autoregressive'] = self.switching_ar
# Cache an array for holding slices
self._predict_slices = [slice(None, None, None)] * (self.order + 1)
def forecast(self, Phi, Sigma, h=12, y=None, append=True):
if y is None:
y = self.data
y_base = y
y0 = np.ones((self._ny * self._p + self._cons))
y0[:self._ny * self._p] = lagmat(y_base, self._p, 'none')[-self._p]
yfcst = np.zeros((h, self._ny))
for i in range(h):
yfcst[i] = np.dot(y0, Phi)
y = np.vstack((y, yfcst[i]))
if self._cons:
y0[:-self._cons] = lagmat(y, self._p, 'none')[-self._p]
else:
y0 = lagmat(y, self._p, 'none')[-self._p]
return yfcst
def moment_ret(self, theta_ret, theta_vol=None, uarg=None,
zlag=1, **kwargs):
"""Moment conditions (returns) for spectral GMM estimator.
Parameters
----------
theta_ret : (2, ) array
Vector of model parameters. [phi, price_ret]
theta_vol : (3, ) array
Vector of model parameters. [mean, rho, delta]
uarg : (nu, ) array
Grid to evaluate a and b functions
zlag : int
Number of lags to use for the instrument
Returns
-------
moment : (nobs, nmoms) array
Matrix of momcond restrictions
Raises
------
ValueError
"""
if uarg is None:
raise ValueError("uarg is missing!")
vollag, vol = lagmat(self.vol, maxlag=zlag,
original='sep', trim='both')
# Number of observations after truncation
nobs = vol.shape[0]
# Number of moments
nmoms = 2 * uarg.shape[0] * (zlag+1)
# Change class attribute with the current theta
param = ARGparams()
try:
param.update(theta_ret=theta_ret, theta_vol=theta_vol)
except ValueError:
return np.ones((nobs, nmoms))*1e10
# Must be (nobs, nu) array
try:
cfun = self.char_fun_ret(uarg, param)[zlag-1:]
except ValueError:
return np.ones((nobs, nmoms))*1e10
# Must be (nobs, nu) array
error = np.exp(-self.ret[zlag:, np.newaxis] * uarg) - cfun
# Instruments, (nobs, ninstr) array
instr = np.hstack([np.exp(-1j * vollag), np.ones((nobs, 1))])
# Must be (nobs, nmoms) array
moment = error[:, np.newaxis, :] * instr[:, :, np.newaxis]
moment = moment.reshape((nobs, nmoms//2))
# (nobs, 2 * ninstr)
moment = np.hstack([np.real(moment), np.imag(moment)])
return moment
def __init__(self, endog, k_regimes, order, trend='c', exog=None,
exog_tvtp=None, switching_ar=True, switching_trend=True,
switching_exog=False, switching_variance=False,
dates=None, freq=None, missing='none'):
# Properties
self.switching_ar = switching_ar
# Switching options
if self.switching_ar is True or self.switching_ar is False:
self.switching_ar = [self.switching_ar] * order
elif not len(self.switching_ar) == order:
raise ValueError('Invalid iterable passed to `switching_ar`.')
# Initialize the base model
super(MarkovAutoregression, self).__init__(
endog, k_regimes, trend=trend, exog=exog, order=order,
exog_tvtp=exog_tvtp, switching_trend=switching_trend,
switching_exog=switching_exog,
switching_variance=switching_variance, dates=dates, freq=freq,
missing=missing)
# Sanity checks
if self.nobs <= self.order:
raise ValueError('Must have more observations than the order of'
' the autoregression.')
# Autoregressive exog
self.exog_ar = lagmat(endog, self.order)[self.order:]
# Reshape other datasets
self.nobs -= self.order
self.orig_endog = self.endog
self.endog = self.endog[self.order:]
if self._k_exog > 0:
self.orig_exog = self.exog
self.exog = self.exog[self.order:]
# Reset the ModelData datasets
self.data.endog, self.data.exog = (
self.data._convert_endog_exog(self.endog, self.exog))
# Reset indexes, if provided
if self.data.row_labels is not None:
self.data._cache['row_labels'] = (
self.data.row_labels[self.order:])
if self._index is not None:
if self._index_generated:
self._index = self._index[:-self.order]
else:
self._index = self._index[self.order:]
# Parameters
self.parameters['autoregressive'] = self.switching_ar
# Cache an array for holding slices
self._predict_slices = [slice(None, None, None)] * (self.order + 1)
def fit_discrete_state_transition_no_speed(speed,
is_replay,
penalty=1E-5,
speed_knots=None,
diagonal=None):
"""Estimate the predicted probablity of replay and whether
it was a replay in the previous time step.
p(I_t | I_t-1, v_t-1)
p_I_0, p_I_1 in Long Tao's code
Parameters
----------
speed : ndarray, shape (n_time,)
is_replay : boolean ndarray, shape (n_time,)
speed_knots : ndarray, shape (n_knots,)
Returns
-------
probability_replay : ndarray, shape (n_time, 2)
"""
data = pd.DataFrame({
'is_replay':
is_replay.astype(np.float64),
'lagged_is_replay':
lagmat(is_replay, maxlag=1).astype(np.float64).squeeze(),
'lagged_speed':
lagmat(speed, maxlag=1).squeeze()
}).dropna()
MODEL_FORMULA = 'is_replay ~ 1 + lagged_is_replay'
response, design_matrix = dmatrices(MODEL_FORMULA, data)
penalty = np.ones((design_matrix.shape[1], )) * penalty
penalty[0] = 0.0
fit = penalized_IRLS(design_matrix,
response,
family=FAMILY,
penalty=penalty)
return partial(predict_probability,
design_matrix=design_matrix,
coefficients=fit.coefficients)
def _df_select_lags(y, trend, max_lags, method):
"""
Helper method to determine the best lag length in DF-like regressions
Parameters
----------
y : array-like, (nobs,)
The data for the lag selection exercise
trend : str, {'nc','c','ct','ctt'}
The trend order
max_lags : int
The maximum number of lags to check. This setting affects all
estimation since the sample is adjusted by max_lags when
fitting the models
method : str, {'AIC','BIC','t-stat'}
The method to use when estimating the model
Returns
-------
best_ic : float
The information criteria at the selected lag
best_lag : int
The selected lag
all_res : list
List of OLS results from fitting max_lag + 1 models
Notes
-----
See statsmodels.tsa.tsatools._autolag for details. If max_lags is None, the
default value of 12 * (nobs/100)**(1/4) is used.
"""
nobs = y.shape[0]
delta_y = diff(y)
if max_lags is None:
max_lags = int(ceil(12. * power(nobs / 100., 1 / 4.)))
rhs = lagmat(delta_y[:, None], max_lags, trim='both', original='in')
nobs = rhs.shape[0]
rhs[:, 0] = y[-nobs - 1:-1] # replace 0 with level of y
lhs = delta_y[-nobs:]
if trend != 'nc':
full_rhs = add_trend(rhs, trend, prepend=True)
else:
full_rhs = rhs
start_lag = full_rhs.shape[1] - rhs.shape[1] + 1
ic_best, best_lag, all_res = _autolag(OLS, lhs, full_rhs, start_lag,
max_lags, method, regresults=True)
# To get the correct number of lags, subtract the start_lag since
# lags 0,1,...,start_lag-1 were not actual lags, but other variables
best_lag -= start_lag
return ic_best, best_lag, all_res
def _stackX(self, k_ar, trend):
"""
Private method to build the RHS matrix for estimation.
Columns are trend terms then lags.
"""
endog = self.endog
X = lagmat(endog, maxlag=k_ar, trim='both')
k_trend = util.get_trendorder(trend)
if k_trend:
X = add_trend(X, prepend=True, trend=trend)
self.k_trend = k_trend
return X
def _df_select_lags(y, trend, max_lags, method):
"""
Helper method to determine the best lag length in DF-like regressions
Parameters
----------
y : array
The data for the lag selection exercise
trend : {'nc','c','ct','ctt'}
The trend order
max_lags : int
The maximum number of lags to check. This setting affects all
estimation since the sample is adjusted by max_lags when
fitting the models
method : {'AIC','BIC','t-stat'}
The method to use when estimating the model
Returns
-------
best_ic : float
The information criteria at the selected lag
best_lag : int
The selected lag
Notes
-----
If max_lags is None, the default value of 12 * (nobs/100)**(1/4) is used.
"""
nobs = y.shape[0]
delta_y = diff(y)
if max_lags is None:
max_lags = int(ceil(12. * power(nobs / 100., 1 / 4.)))
rhs = lagmat(delta_y[:, None], max_lags, trim='both', original='in')
nobs = rhs.shape[0]
rhs[:, 0] = y[-nobs - 1:-1] # replace 0 with level of y
lhs = delta_y[-nobs:]
if trend != 'nc':
full_rhs = add_trend(rhs, trend, prepend=True)
else:
full_rhs = rhs
start_lag = full_rhs.shape[1] - rhs.shape[1] + 1
ic_best, best_lag = _autolag_ols(lhs, full_rhs, start_lag, max_lags, method)
return ic_best, best_lag
def fit(self, nlags):
'''estimate parameters using ols
Parameters
----------
nlags : integer
number of lags to include in regression, same for all variables
Returns
-------
None, but attaches
arhat : array (nlags, nvar, nvar)
full lag polynomial array
arlhs : array (nlags-1, nvar, nvar)
reduced lag polynomial for left hand side
other statistics as returned by linalg.lstsq : need to be completed
This currently assumes all parameters are estimated without restrictions.
In this case SUR is identical to OLS
estimation results are attached to the class instance
'''
self.nlags = nlags # without current period
nvars = self.nvars
#TODO: ar2s looks like a module variable, bug?
#lmat = lagmat(ar2s, nlags, trim='both', original='in')
lmat = lagmat(self.y, nlags, trim='both', original='in')
self.yred = lmat[:,:nvars]
self.xred = lmat[:,nvars:]
res = np.linalg.lstsq(self.xred, self.yred, rcond=-1)
self.estresults = res
self.arlhs = res[0].reshape(nlags, nvars, nvars)
self.arhat = ar2full(self.arlhs)
self.rss = res[1]
self.xredrank = res[2]
def _em_autoregressive(self, result, betas, tmp=None):
"""
EM step for autoregressive coefficients and variances
"""
if tmp is None:
tmp = np.sqrt(result.smoothed_marginal_probabilities)
resid = np.zeros((self.k_regimes, self.nobs + self.order))
resid[:] = self.orig_endog
if self._k_exog > 0:
for i in range(self.k_regimes):
resid[i] -= np.dot(self.orig_exog, betas[i])
# The difference between this and `_em_exog` is that here we have a
# different endog and exog for each regime
coeffs = np.zeros((self.k_regimes,) + (self.order,))
variance = np.zeros((self.k_regimes,))
exog = np.zeros((self.nobs, self.order))
for i in range(self.k_regimes):
endog = resid[i, self.order:]
exog = lagmat(resid[i], self.order)[self.order:]
tmp_endog = tmp[i] * endog
tmp_exog = tmp[i][:, None] * exog
coeffs[i] = np.dot(np.linalg.pinv(tmp_exog), tmp_endog)
if self.switching_variance:
tmp_resid = endog - np.dot(exog, coeffs[i])
variance[i] = (np.sum(
tmp_resid**2 * result.smoothed_marginal_probabilities[i]) /
np.sum(result.smoothed_marginal_probabilities[i]))
else:
tmp_resid = tmp_endog - np.dot(tmp_exog, coeffs[i])
variance[i] = np.sum(tmp_resid**2)
# Variances
if not self.switching_variance:
variance = variance.sum() / self.nobs
return coeffs, variance
def fnn(data, maxm):
"""
Compute the embedding dimension of a time series data to build the phase space using the false neighbors criterion
data--> time series
maxm--> maximmum embeding dimension
"""
RT=15.0
AT=2
sigmay=np.std(data, ddof=1)
nyr=len(data)
m=maxm
EM=lagmat(data, maxlag=m-1)
EEM=np.asarray([EM[j,:] for j in range(m-1, EM.shape[0])])
embedm=maxm
for k in range(AT,EEM.shape[1]+1):
fnn1=[]
fnn2=[]
Ma=EEM[:,range(k)]
D=dist(Ma)
for i in range(1,EEM.shape[0]-m-k):
#print D.shape
#print(D[i,range(i-1)])
d=D[i,:]
pdnz=np.where(d>0)
dnz=d[pdnz]
Rm=np.min(dnz)
l=np.where(d==Rm)
l=l[0]
l=l[len(l)-1]
if l+m+k-1<nyr:
fnn1.append(np.abs(data[i+m+k-1]-data[l+m+k-1])/Rm)
fnn2.append(np.abs(data[i+m+k-1]-data[l+m+k-1])/sigmay)
Ind1=np.where(np.asarray(fnn1)>RT)
Ind2=np.where(np.asarray(fnn2)>AT)
if len(Ind1[0])/float(len(fnn1))<0.1 and len(Ind2[0])/float(len(fnn2))<0.1:
embedm=k
break
return embedm
[ 0.1, -0.1]]])
a31 = np.r_[np.eye(3)[None,:,:], 0.8*np.eye(3)[None,:,:]]
a32 = np.array([[[ 1. , 0. , 0. ],
[ 0. , 1. , 0. ],
[ 0. , 0. , 1. ]],
[[ 0.8, 0. , 0. ],
[ 0.1, 0.6, 0. ],
[ 0. , 0. , 0.9]]])
########
ut = np.random.randn(1000,2)
ar2s = vargenerate(a22,ut)
#res = np.linalg.lstsq(lagmat(ar2s,1)[:,1:], ar2s)
res = np.linalg.lstsq(lagmat(ar2s,1), ar2s)
bhat = res[0].reshape(1,2,2)
arhat = ar2full(bhat)
#print(maxabs(arhat - a22)
v = _Var(ar2s)
v.fit(1)
v.forecast()
v.forecast(25)[-30:]
ar23 = np.array([[[ 1. , 0. ],
[ 0. , 1. ]],
[[-0.6, 0. ],
def acorr_lm(x, maxlag=None, autolag='AIC', store=False, regresults=False):
'''Lagrange Multiplier tests for autocorrelation
This is a generic Lagrange Multiplier test for autocorrelation. I don't
have a reference for it, but it returns Engle's ARCH test if x is the
squared residual array. A variation on it with additional exogenous
variables is the Breusch-Godfrey autocorrelation test.
Parameters
----------
resid : ndarray, (nobs,)
residuals from an estimation, or time series
maxlag : int
highest lag to use
autolag : None or string
If None, then a fixed number of lags given by maxlag is used.
store : bool
If true then the intermediate results are also returned
Returns
-------
lm : float
Lagrange multiplier test statistic
lmpval : float
p-value for Lagrange multiplier test
fval : float
fstatistic for F test, alternative version of the same test based on
F test for the parameter restriction
fpval : float
pvalue for F test
resstore : instance (optional)
a class instance that holds intermediate results. Only returned if
store=True
See Also
--------
het_arch
acorr_breusch_godfrey
acorr_ljung_box
'''
if regresults:
store = True
x = np.asarray(x)
nobs = x.shape[0]
if maxlag is None:
#for adf from Greene referencing Schwert 1989
maxlag = int(np.ceil(12. * np.power(nobs/100., 1/4.)))#nobs//4 #TODO: check default, or do AIC/BIC
xdiff = np.diff(x)
#
xdall = lagmat(x[:,None], maxlag, trim='both')
nobs = xdall.shape[0]
xdall = np.c_[np.ones((nobs,1)), xdall]
xshort = x[-nobs:]
if store: resstore = ResultsStore()
if autolag:
#search for lag length with highest information criteria
#Note: I use the same number of observations to have comparable IC
results = {}
for mlag in range(1, maxlag+1):
results[mlag] = OLS(xshort, xdall[:,:mlag+1]).fit()
if autolag.lower() == 'aic':
bestic, icbestlag = min((v.aic,k) for k,v in iteritems(results))
elif autolag.lower() == 'bic':
icbest, icbestlag = min((v.bic,k) for k,v in iteritems(results))
else:
raise ValueError("autolag can only be None, 'AIC' or 'BIC'")
#rerun ols with best ic
xdall = lagmat(x[:,None], icbestlag, trim='both')
nobs = xdall.shape[0]
xdall = np.c_[np.ones((nobs,1)), xdall]
xshort = x[-nobs:]
usedlag = icbestlag
if regresults:
resstore.results = results
else:
usedlag = maxlag
resols = OLS(xshort, xdall[:,:usedlag+1]).fit()
fval = resols.fvalue
fpval = resols.f_pvalue
lm = nobs * resols.rsquared
lmpval = stats.chi2.sf(lm, usedlag)
# Note: degrees of freedom for LM test is nvars minus constant = usedlags
#return fval, fpval, lm, lmpval
if store:
resstore.resols = resols
resstore.usedlag = usedlag
return lm, lmpval, fval, fpval, resstore
else:
return lm, lmpval, fval, fpval
def acorr_breusch_godfrey(results, nlags=None, store=False):
'''Breusch Godfrey Lagrange Multiplier tests for residual autocorrelation
Parameters
----------
results : Result instance
Estimation results for which the residuals are tested for serial
correlation
nlags : int
Number of lags to include in the auxiliary regression. (nlags is
highest lag)
store : bool
If store is true, then an additional class instance that contains
intermediate results is returned.
Returns
-------
lm : float
Lagrange multiplier test statistic
lmpval : float
p-value for Lagrange multiplier test
fval : float
fstatistic for F test, alternative version of the same test based on
F test for the parameter restriction
fpval : float
pvalue for F test
resstore : instance (optional)
a class instance that holds intermediate results. Only returned if
store=True
Notes
-----
BG adds lags of residual to exog in the design matrix for the auxiliary
regression with residuals as endog,
see Greene 12.7.1.
References
----------
Greene Econometrics, 5th edition
'''
x = np.asarray(results.resid)
exog_old = results.model.exog
nobs = x.shape[0]
if nlags is None:
#for adf from Greene referencing Schwert 1989
nlags = np.trunc(12. * np.power(nobs/100., 1/4.))#nobs//4 #TODO: check default, or do AIC/BIC
nlags = int(nlags)
x = np.concatenate((np.zeros(nlags), x))
#xdiff = np.diff(x)
#
xdall = lagmat(x[:,None], nlags, trim='both')
nobs = xdall.shape[0]
xdall = np.c_[np.ones((nobs,1)), xdall]
xshort = x[-nobs:]
exog = np.column_stack((exog_old, xdall))
k_vars = exog.shape[1]
if store: resstore = ResultsStore()
resols = OLS(xshort, exog).fit()
ft = resols.f_test(np.eye(nlags, k_vars, k_vars - nlags))
fval = ft.fvalue
fpval = ft.pvalue
fval = np.squeeze(fval)[()] #TODO: fix this in ContrastResults
fpval = np.squeeze(fpval)[()]
lm = nobs * resols.rsquared
lmpval = stats.chi2.sf(lm, nlags)
# Note: degrees of freedom for LM test is nvars minus constant = usedlags
#return fval, fpval, lm, lmpval
if store:
resstore.resols = resols
resstore.usedlag = nlags
return lm, lmpval, fval, fpval, resstore
else:
return lm, lmpval, fval, fpval
def adfuller(x, maxlag=None, regression="c", autolag='AIC',
store=False, regresults=False):
"""
Augmented Dickey-Fuller unit root test
The Augmented Dickey-Fuller test can be used to test for a unit root in a
univariate process in the presence of serial correlation.
Parameters
----------
x : array_like, 1d
data series
maxlag : int
Maximum lag which is included in test, default 12*(nobs/100)^{1/4}
regression : {'c','ct','ctt','nc'}
Constant and trend order to include in regression
* 'c' : constant only (default)
* 'ct' : constant and trend
* 'ctt' : constant, and linear and quadratic trend
* 'nc' : no constant, no trend
autolag : {'AIC', 'BIC', 't-stat', None}
* if None, then maxlag lags are used
* if 'AIC' (default) or 'BIC', then the number of lags is chosen
to minimize the corresponding information criterion
* 't-stat' based choice of maxlag. Starts with maxlag and drops a
lag until the t-statistic on the last lag length is significant
using a 5%-sized test
store : bool
If True, then a result instance is returned additionally to
the adf statistic. Default is False
regresults : bool, optional
If True, the full regression results are returned. Default is False
Returns
-------
adf : float
Test statistic
pvalue : float
MacKinnon's approximate p-value based on MacKinnon (1994, 2010)
usedlag : int
Number of lags used
nobs : int
Number of observations used for the ADF regression and calculation of
the critical values
critical values : dict
Critical values for the test statistic at the 1 %, 5 %, and 10 %
levels. Based on MacKinnon (2010)
icbest : float
The maximized information criterion if autolag is not None.
resstore : ResultStore, optional
A dummy class with results attached as attributes
Notes
-----
The null hypothesis of the Augmented Dickey-Fuller is that there is a unit
root, with the alternative that there is no unit root. If the pvalue is
above a critical size, then we cannot reject that there is a unit root.
The p-values are obtained through regression surface approximation from
MacKinnon 1994, but using the updated 2010 tables. If the p-value is close
to significant, then the critical values should be used to judge whether
to reject the null.
The autolag option and maxlag for it are described in Greene.
Examples
--------
See example notebook
References
----------
.. [1] W. Green. "Econometric Analysis," 5th ed., Pearson, 2003.
.. [2] Hamilton, J.D. "Time Series Analysis". Princeton, 1994.
.. [3] MacKinnon, J.G. 1994. "Approximate asymptotic distribution functions for
unit-root and cointegration tests. `Journal of Business and Economic
Statistics` 12, 167-76.
.. [4] MacKinnon, J.G. 2010. "Critical Values for Cointegration Tests." Queen's
University, Dept of Economics, Working Papers. Available at
http://ideas.repec.org/p/qed/wpaper/1227.html
"""
if regresults:
store = True
trenddict = {None: 'nc', 0: 'c', 1: 'ct', 2: 'ctt'}
if regression is None or isinstance(regression, (int, long)):
regression = trenddict[regression]
regression = regression.lower()
if regression not in ['c', 'nc', 'ct', 'ctt']:
raise ValueError("regression option %s not understood") % regression
x = np.asarray(x)
nobs = x.shape[0]
if maxlag is None:
#from Greene referencing Schwert 1989
maxlag = int(np.ceil(12. * np.power(nobs / 100., 1 / 4.)))
xdiff = np.diff(x)
xdall = lagmat(xdiff[:, None], maxlag, trim='both', original='in')
nobs = xdall.shape[0] # pylint: disable=E1103
xdall[:, 0] = x[-nobs - 1:-1] # replace 0 xdiff with level of x
xdshort = xdiff[-nobs:]
if store:
resstore = ResultsStore()
if autolag:
if regression != 'nc':
fullRHS = add_trend(xdall, regression, prepend=True)
else:
fullRHS = xdall
startlag = fullRHS.shape[1] - xdall.shape[1] + 1 # 1 for level # pylint: disable=E1103
#search for lag length with smallest information criteria
#Note: use the same number of observations to have comparable IC
#aic and bic: smaller is better
if not regresults:
icbest, bestlag = _autolag(OLS, xdshort, fullRHS, startlag,
maxlag, autolag)
else:
icbest, bestlag, alres = _autolag(OLS, xdshort, fullRHS, startlag,
maxlag, autolag,
regresults=regresults)
resstore.autolag_results = alres
bestlag -= startlag # convert to lag not column index
#rerun ols with best autolag
xdall = lagmat(xdiff[:, None], bestlag, trim='both', original='in')
nobs = xdall.shape[0] # pylint: disable=E1103
xdall[:, 0] = x[-nobs - 1:-1] # replace 0 xdiff with level of x
xdshort = xdiff[-nobs:]
usedlag = bestlag
else:
usedlag = maxlag
icbest = None
if regression != 'nc':
resols = OLS(xdshort, add_trend(xdall[:, :usedlag + 1],
regression)).fit()
else:
resols = OLS(xdshort, xdall[:, :usedlag + 1]).fit()
adfstat = resols.tvalues[0]
# adfstat = (resols.params[0]-1.0)/resols.bse[0]
# the "asymptotically correct" z statistic is obtained as
# nobs/(1-np.sum(resols.params[1:-(trendorder+1)])) (resols.params[0] - 1)
# I think this is the statistic that is used for series that are integrated
# for orders higher than I(1), ie., not ADF but cointegration tests.
# Get approx p-value and critical values
pvalue = mackinnonp(adfstat, regression=regression, N=1)
critvalues = mackinnoncrit(N=1, regression=regression, nobs=nobs)
critvalues = {"1%" : critvalues[0], "5%" : critvalues[1],
"10%" : critvalues[2]}
if store:
resstore.resols = resols
resstore.maxlag = maxlag
resstore.usedlag = usedlag
resstore.adfstat = adfstat
resstore.critvalues = critvalues
resstore.nobs = nobs
resstore.H0 = ("The coefficient on the lagged level equals 1 - "
"unit root")
resstore.HA = "The coefficient on the lagged level < 1 - stationary"
resstore.icbest = icbest
resstore._str = 'Augmented Dickey-Fuller Test Results'
return adfstat, pvalue, critvalues, resstore
else:
if not autolag:
return adfstat, pvalue, usedlag, nobs, critvalues
else:
return adfstat, pvalue, usedlag, nobs, critvalues, icbest
def momcond_vol(self, theta_vol, uarg=None, zlag=1):
"""Moment conditions (volatility) for spectral GMM estimator.
Parameters
----------
theta_vol : (3, ) array
Vector of model parameters. [scale, rho, delta]
uarg : (nu, ) array
Grid to evaluate a and b functions
zlag : int
Number of lags to use for the instrument
Returns
-------
moment : (nobs, nmoms) array
Matrix of momcond restrictions
dmoment : (nmoms, nparams) array
Gradient of momcond restrictions. Mean over observations
Raises
------
ValueError
"""
if uarg is None:
raise ValueError("uarg is missing!")
vollag, vol = lagmat(self.vol, maxlag=zlag,
original='sep', trim='both')
prevvol = vollag[:, 0][:, np.newaxis]
# Number of observations after truncation
nobs = vol.shape[0]
# Number of moments
nmoms = 2 * uarg.shape[0] * (zlag+1)
# Number of parameters
nparams = theta_vol.shape[0]
# Change class attribute with the current theta
param = ARGparams()
try:
param.update(theta_vol=theta_vol)
except ValueError:
return np.ones((nobs, nmoms))*1e10, np.ones((nmoms, nparams))*1e10
# Must be (nobs, nu) array
error = np.exp(-vol * uarg) - self.char_fun_vol(uarg, param)[zlag-1:]
# Instruments, (nobs, ninstr) array
instr = np.hstack([np.exp(-1j * vollag), np.ones((nobs, 1))])
# Must be (nobs, nmoms) array
moment = error[:, np.newaxis, :] * instr[:, :, np.newaxis]
moment = moment.reshape((nobs, nmoms//2))
# (nobs, 2 * ninstr)
moment = np.hstack([np.real(moment), np.imag(moment)])
# Initialize derivative matrix
dmoment = np.empty((nmoms, nparams))
for i in range(nparams):
dexparg = - prevvol * self.dafun(uarg, param)[i] \
- np.ones((nobs, 1)) * self.dbfun(uarg, param)[i]
derror = - self.char_fun_vol(uarg, param)[zlag-1:] * dexparg
derrorinstr = derror[:, np.newaxis, :] * instr[:, :, np.newaxis]
derrorinstr = derrorinstr.reshape((nobs, nmoms//2))
derrorinstr = np.hstack([np.real(derrorinstr),
np.imag(derrorinstr)])
dmoment[:, i] = derrorinstr.mean(0)
return moment, dmoment
max_xc = 0
best_shift = 0
for shift in range(-10, 0): #Tune this search range
xc = (numpy.roll(sig1, shift) * sig2).sum()
if xc > max_xc:
max_xc = xc
best_shift = shift
print 'Best shift:', best_shift
"""
If best_shift is at the edges of your search range,
you should expand the search range.
"""
#############################################################################
# create lag matrix for regression
bpmat = tools.lagmat(x,lag, original='in')
etmat = tools.lagmat(z,lag, original='in')
lamat = numpy.column_stack([bpmat,etmat])
#for i in range(len(etmat)):
# lagmat.append(bpmat[i]+etmat[i])
#transpose matrix to determine required length
#run least squared regression
sqrd = numpy.linalg.lstsq(bpmat,y)
sqrdlag = numpy.linalg.lstsq(lamat,y)
wlls = sqrd[0]
lagls = sqrdlag[0]
cumls = numpy.cumsum(wlls)
lagcumls =numpy.cumsum(lagls)
def cointegration_johansen(input_df, lag=1):
"""
For axis: -1 means no deterministic part, 0 means constant term, 1 means constant plus time-trend,
> 1 means higher order polynomial.
:param input_df: the input vectors as a pandas.DataFrame instance
:param lag: number of lagged difference terms used when computing the estimator
:return: returns test statistics data
"""
count_samples, count_dimensions = input_df.shape
input_df = detrend(input_df, type='constant', axis=0)
diff_input_df = numpy.diff(input_df, 1, axis=0)
z = tsatools.lagmat(diff_input_df, lag)
z = z[lag:]
z = detrend(z, type='constant', axis=0)
diff_input_df = diff_input_df[lag:]
diff_input_df = detrend(diff_input_df, type='constant', axis=0)
r0t = residuals(diff_input_df, z)
lx = input_df[:-lag]
lx = lx[1:]
diff_input_df = detrend(lx, type='constant', axis=0)
rkt = residuals(diff_input_df, z)
if rkt is None:
return None
skk = numpy.dot(rkt.T, rkt) / rkt.shape[0]
sk0 = numpy.dot(rkt.T, r0t) / rkt.shape[0]
s00 = numpy.dot(r0t.T, r0t) / r0t.shape[0]
sig = numpy.dot(sk0, numpy.dot(linalg.inv(s00), sk0.T))
eigenvalues, eigenvectors = linalg.eig(numpy.dot(linalg.inv(skk), sig))
# normalizing the eigenvectors such that (du'skk*du) = I
temp = linalg.inv(linalg.cholesky(numpy.dot(eigenvectors.T, numpy.dot(skk, eigenvectors))))
dt = numpy.dot(eigenvectors, temp)
# sorting eigenvalues and vectors
order_decreasing = numpy.flipud(numpy.argsort(eigenvalues))
sorted_eigenvalues = eigenvalues[order_decreasing]
sorted_eigenvectors = dt[:, order_decreasing]
# computing the trace and max eigenvalue statistics
trace_statistics = numpy.zeros(count_dimensions)
eigenvalue_statistics = numpy.zeros(count_dimensions)
critical_values_max_eigenvalue = numpy.zeros((count_dimensions, 3))
critical_values_trace = numpy.zeros((count_dimensions, 3))
iota = numpy.ones(count_dimensions)
t, junk = rkt.shape
for i in range(0, count_dimensions):
tmp = numpy.log(iota - sorted_eigenvalues)[i:]
trace_statistics[i] = -t * numpy.sum(tmp, 0)
eigenvalue_statistics[i] = -t * numpy.log(1 - sorted_eigenvalues[i])
critical_values_max_eigenvalue[i, :] = get_critical_values_max_eigenvalue(count_dimensions - i, time_polynomial_order=0)
critical_values_trace[i, :] = get_critical_values_trace(count_dimensions - i, time_polynomial_order=0)
order_decreasing[i] = i
result = dict()
result['rkt'] = rkt
result['r0t'] = r0t
result['eigenvalues'] = sorted_eigenvalues
result['eigenvectors'] = sorted_eigenvectors
result['trace_statistic'] = trace_statistics # likelihood ratio trace statistic
result['eigenvalue_statistics'] = eigenvalue_statistics # maximum eigenvalue statistic
result['critical_values_trace'] = critical_values_trace
result['critical_values_max_eigenvalue'] = critical_values_max_eigenvalue
result['order_decreasing'] = order_decreasing # indices of eigenvalues in decreasing order
return result
Trans_M2 = curv(delt_M2,P_M2,r) Trans_O1 = curv(delt_O1,P_O1,r) tf=time.clock() print '...Done!',tf-t0, 'seconds' t0=time.clock ########################################################################### # Calculate BP Response Function ########################################################################### ti=time.clock() # measure time of calculation print 'Calculating BP Response function...', t0=time.clock() # create lag matrix for regression bpmat = tools.lagmat(dbp, lag, original='in') etmat = tools.lagmat(ddl, lag, original='in') #lamat combines lag matrices of bp and et lamat = numpy.column_stack([bpmat,etmat]) #for i in range(len(etmat)): # lagmat.append(bpmat[i]+etmat[i]) #transpose matrix to determine required length #run least squared regression sqrd = numpy.linalg.lstsq(bpmat,dwl) #determine lag coefficients of the lag matrix lamat sqrdlag = numpy.linalg.lstsq(lamat,dwl) wlls = sqrd[0] #lagls return the coefficients of the least squares of lamat lagls = sqrdlag[0]
[ 0.1, -0.1]]])
a31 = np.r_[np.eye(3)[None,:,:], 0.8*np.eye(3)[None,:,:]]
a32 = np.array([[[ 1. , 0. , 0. ],
[ 0. , 1. , 0. ],
[ 0. , 0. , 1. ]],
[[ 0.8, 0. , 0. ],
[ 0.1, 0.6, 0. ],
[ 0. , 0. , 0.9]]])
########
ut = np.random.randn(1000,2)
ar2s = vargenerate(a22,ut)
#res = np.linalg.lstsq(lagmat(ar2s,1)[:,1:], ar2s)
res = np.linalg.lstsq(lagmat(ar2s,1), ar2s, rcond=-1)
bhat = res[0].reshape(1,2,2)
arhat = ar2full(bhat)
#print(maxabs(arhat - a22)
v = _Var(ar2s)
v.fit(1)
v.forecast()
v.forecast(25)[-30:]
ar23 = np.array([[[ 1. , 0. ],
[ 0. , 1. ]],
[[-0.6, 0. ],
[ 0.2, -0.6]],
def tideproc(inpfile,bpdata,edata):
delta = 1.1562
p = 7.692E5
###########################################################################
"""
INPUT FILES ARE PUT IN BELOW
"""
lag = 100
tol = 0.05 #percentage of variance in frequency allowed; default is 2%
r = 1 #well radius in inches
Be = 0.10 #barometric efficiency
numb = 2000 # number of values to process
spd = 24 #samples per day hourly sampling = 24
lagt = -6.0 #hours different from UTC (negative indicates west); UT is -7
"""
INPUT FILES END HERE
"""
###########################################################################
#frequencies in cpd
O1 = 0.9295 #principal lunar
K1 = 1.0029 #Lunar Solar
M2 = 1.9324 #principal lunar
S2 = 2.00 #Principal Solar
N2 = 1.8957 #Lunar elliptic
#periods in days
P_M2 = 0.5175
P_O1 = 1.0758
# amplitude factors from Merritt 2004
b_O1 = 0.377
b_P1 = 0.176
b_K1 = 0.531
b_N2 = 0.174
b_M2 = 0.908
b_S2 = 0.423
b_K2 = 0.115
#love numbers and other constants from Agnew 2007
l = 0.0839
k = 0.2980
h = 0.6032
Km = 1.7618 #general lunar coefficient
pi = math.pi #pi
#gravity and earth radius
g = 9.821 #m/s**2
a = 6.3707E6 #m
g_ft = 32.23 #ft
a_ft = 2.0902e7 #ft/s**2
#values to determine porosity from Merritt 2004 pg 56
Beta = 2.32E-8
rho = 62.4
impfile = inpfile
outfile = 'c'+impfile
data = csv.reader(open(impfile, 'rb'), delimiter=",")
dy, u, l, nm, d, wl, t, vert =[], [], [], [], [], [], [], []
yrdty, year, month, day, hours, minutes, seconds, julday = [], [], [], [], [], [], [], []
yrdty2,year2, month2, day2, hours2, minutes2, seconds2, julday2 = [], [], [], [], [], [], [], []
yrdty3,year3, month3, day3, hours3, minutes3, seconds3, julday3 = [], [], [], [], [], [], [], []
# read in bp data
bpdata = bpdata
bdata = csv.reader(open(bpdata, 'rb'), delimiter=",")
v, d2, bp=[], [], []
d3, SG33WDD, PW19S2, PW19M2, MXSWDD = [],[],[],[],[]
etdata = edata
#assign data in csv to arrays
for row in data:
u.append(row)
for row in bdata:
v.append(row)
#pick well name, lat., long., and elevation data out of header of wl file
well_name = u[0][1]
lon = [float(u[5][1])]
latt = [round(float(u[4][1]),3)]
el = [round(float(u[10][1])/3.2808,3)]
#import the bp data
with open(bpdata, 'rb') as tot:
csvreader1 = csv.reader(tot)
for row in skip_first(csvreader1, 3):
d2.append(row[2])
bp.append(float(row[3]))
#import the wl data
with open(impfile, 'rb') as total:
csvreader = csv.reader(total)
for row in skip_first(csvreader, 62):
dy.append(row[0])
nm.append(row[1])
#import supplemental earth tide data
with open(etdata, 'rb') as tos:
csvreader2 = csv.reader(tos)
for row in skip_first(csvreader2,2):
d3.append(row[5])
SG33WDD.append(float(row[6]))
PW19S2.append(row[7])
PW19M2.append(row[8])
MXSWDD.append(row[9])
#import a smaller part of the wl data
for i in range(len(dy)-numb,len(dy)):
d.append(dy[i])
wl.append(nm[i])
#fill in last line of wl data
wl[-1]=wl[-2]
for i in range(len(wl)):
if wl[i] is '':
wl[i]=wl[i-1]
#create a list of latitude, longitude, elevation, and gmt for tidal calculation
lat = latt*len(d)
longit = lon*len(d)
elev = el*len(d)
gmtt = [float(lagt)]*len(d)
# define the various components of the date, represented by d
# dates for wl data
for i in range(len(d)):
yrdty.append(time.strptime(d[i],"%Y-%m-%d %H:%M:%S"))
year.append(int(yrdty[i].tm_year))
month.append(int(yrdty[i].tm_mon))
day.append(int(yrdty[i].tm_mday))
hours.append(int(yrdty[i].tm_hour))
minutes.append(int(yrdty[i].tm_min))
seconds.append(int(0)) #yrdty[i].tm_sec
# dates for bp data
for i in range(len(d2)):
yrdty2.append(time.strptime(d2[i],"%Y-%m-%d %H:%M:%S"))
year2.append(int(yrdty2[i].tm_year))
month2.append(int(yrdty2[i].tm_mon))
day2.append(int(yrdty2[i].tm_mday))
hours2.append(int(yrdty2[i].tm_hour))
minutes2.append(int(yrdty2[i].tm_min))
seconds2.append(int(0)) #yrdty2[i].tm_sec
# dates for bp data
for i in range(len(d3)):
yrdty3.append(time.strptime(d3[i],"%m/%d/%Y %H:%M"))
year3.append(int(yrdty3[i].tm_year))
month3.append(int(yrdty3[i].tm_mon))
day3.append(int(yrdty3[i].tm_mday))
hours3.append(int(yrdty3[i].tm_hour))
minutes3.append(int(yrdty3[i].tm_min))
seconds3.append(int(0)) #yrdty2[i].tm_sec
#julian day calculation
def calc_jday(Y, M, D, h, m, s):
# Y is year, M is month, D is day
# h is hour, m is minute, s is second
# returns decimal day (float)
Months = [0, 31, 61, 92, 122, 153, 184, 214, 245, 275, 306, 337]
if M < 3:
Y = Y-1
M = M+12
JD = math.floor((Y+4712)/4.0)*1461 + ((Y+4712)%4)*365
JD = JD + Months[M-3] + D
JD = JD + (h + (m/60.0) + (s/3600.0)) / 24.0
# corrections-
# 59 accounts for shift of year from 1 Jan to 1 Mar
# -13 accounts for shift between Julian and Gregorian calendars
# -0.5 accounts for shift between noon and prev. midnight
JD = JD + 59 - 13.5
return JD
# create a list of julian dates
for i in range(len(d)):
julday.append(calc_jday(year[i],month[i],day[i],hours[i],minutes[i],seconds[i]))
for i in range(len(d2)):
julday2.append(calc_jday(year2[i],month2[i],day2[i],hours2[i],minutes2[i],seconds2[i]))
for i in range(len(d3)):
julday3.append(calc_jday(year3[i],month3[i],day3[i],hours3[i],minutes3[i],seconds3[i]))
#run tidal function
for i in range(len(d)):
t.append(tamura.tide(int(year[i]), int(month[i]), int(day[i]), int(hours[i]), int(minutes[i]), int(seconds[i]), float(longit[i]), float(lat[i]), float(elev[i]), 0.0, lagt)) #float(gmtt[i])
vert, Grav_tide, WDD_tam, areal, potential, dilation = [], [], [], [], [], []
#determine vertical strain from Agnew 2007
#units are in sec squared, meaning results in mm
# areal determine areal strain from Agnew 2007, units in mm
#dilation from relationship defined using Harrison's code
#WDD is used to recreate output from TSoft
for i in range(len(t)):
areal.append(t[i]*p*1E-5)
potential.append(-318.49681664*t[i] - 0.50889238)
WDD_tam.append(t[i]*(-.99362956469)-7.8749754)
dilation.append(0.381611837*t[i] - 0.000609517)
vert.append(t[i] * 1.692)
Grav_tide.append(-1*t[i])
#convert to excel date-time numeric format
xls_date = []
for i in range(len(d)):
xls_date.append(float(julday[i])-2415018.5)
xls_date2 = []
for i in range(len(d2)):
xls_date2.append(float(julday2[i])-2415018.5)
xls_date3 = []
for i in range(len(d3)):
xls_date3.append(float(julday3[i])-2415018.5)
t_start = xls_date[0]
t_end = xls_date[-1]
t_len = (len(xls_date))
#align bp data with wl data
t1 = numpy.linspace(t_start, t_end, t_len)
bpint = numpy.interp(t1, xls_date2, bp)
etint = numpy.interp(t1, xls_date3, SG33WDD)
xprep, yprep, zprep = [], [], []
#convert text from csv to float values
for i in range(len(julday)):
xprep.append(float(julday[i]))
yprep.append(float(dilation[i]))
zprep.append(float(wl[i]))
#put data into numpy arrays for analysis
xdata = numpy.array(xprep)
ydata = numpy.array(yprep)
zdata = numpy.array(zprep)
bpdata = numpy.array(bpint)
etdata = numpy.array(etint)
bp = bpdata
z = zdata
y = ydata
# tempdata = numpy.array(tempint)
#standarize julian day to start at zero
x0data = xdata - xdata[0]
wl_z = []
mn = numpy.mean(z)
std = numpy.std(z)
for i in range(len(z)):
wl_z.append((z[i]-mn)/std)
bp_z = []
mn = numpy.mean(bp)
std = numpy.std(bp)
for i in range(len(bp)):
bp_z.append((bp[i]-mn)/std)
t_z = []
mn = numpy.mean(y)
std = numpy.std(y)
for i in range(len(y)):
t_z.append((t[i]-mn)/std)
dbp = []
for i in range(len(bp)-1):
dbp.append(bp[i]-bp[i+1])
dwl = []
for i in range(len(z)-1):
dwl.append(z[i]-z[i+1])
dt = []
for i in range(len(y)-1):
dt.append(y[i]-y[i+1])
dbp.append(0)
dwl.append(0)
dt.append(0)
###########################################################################
#
############################################################ Filter Signals
#
###########################################################################
''' these filtered data are not necessary,
but are good for graphical comparison '''
### define filtering function
def filt(frq,tol,data):
#define frequency tolerance range
lowcut = (frq-frq*tol)
highcut = (frq+frq*tol)
#conduct fft
ffta = fft.fft(data)
bp2 = ffta[:]
fftb = fft.fftfreq(len(bp2))
#make every amplitude value 0 that is not in the tolerance range of frequency of interest
#24 adjusts the frequency to cpd
for i in range(len(fftb)):
#spd is samples per day (if hourly = 24)
if (fftb[i]*spd)>highcut or (fftb[i]*spd)<lowcut:
bp2[i]=0
#conduct inverse fft to transpose the filtered frequencies back into time series
crve = fft.ifft(bp2)
yfilt = crve.real
return yfilt
#filter tidal data
yfilt_O1 = filt(O1,tol,ydata)
yfilt_M2 = filt(M2,tol,ydata)
#filter wl data
zfilt_O1 = filt(O1,tol,zdata)
zfilt_M2 = filt(M2,tol,zdata)
zffta = abs(fft.fft(zdata))
zfftb = abs(fft.fftfreq(len(zdata))*spd)
def phasefind(A,frq):
spectrum = fft.fft(A)
freq = fft.fftfreq(len(spectrum))
r = []
#filter = eliminate all values in the wl data fft except the frequencies in the range of interest
for i in range(len(freq)):
#spd is samples per day (if hourly = 24)
if (freq[i]*spd)>(frq-frq*tol) and (freq[i]*spd)<(frq+frq*tol):
r.append(freq[i]*spd)
else:
r.append(0)
#find the place of the max complex value for the filtered frequencies and return the complex number
p = max(enumerate(r), key=itemgetter(1))[0]
pla = spectrum[p]
T5 = cmath.phase(pla)*180/pi
return T5
yphsO1 = phasefind(ydata,O1)
zphsO1 = phasefind(zdata,O1)
phsO1 = zphsO1 - yphsO1
yphsM2 = phasefind(ydata,M2)
zphsM2 = phasefind(zdata,M2)
phsM2 = zphsM2 - yphsM2
# def phase_find(A,B,P):
# period = P
# tmax = len(xdata)*24
# nsamples = len(A)
# # calculate cross correlation of the two signals
# t6 = numpy.linspace(0.0, tmax, nsamples, endpoint=False)
# xcorr = numpy.correlate(A, B)
# # The peak of the cross-correlation gives the shift between the two signals
# # The xcorr array goes from -nsamples to nsamples
# dt6 = numpy.linspace(-t6[-1], t6[-1], 2*nsamples-1)
# recovered_time_shift = dt6[xcorr.argmax()]
#
# # force the phase shift to be in [-pi:pi]
# #recovered_phase_shift = 2*pi*(((0.5 + recovered_time_shift/(period*24)) % 1.0) - 0.5)
# return recovered_time_shift
#
#
# O1_ph= phase_find(ydata,zdata,P_O1)
# M2_ph= phase_find(ydata,zdata,P_M2)
###########################################################################
#
####################################################### Regression Analysis
#
###########################################################################
#define functions used for least squares fitting
def f3(p, x):
#a,b,c = p
m = 2.0 * O1 * pi
y = p[0] + p[1] * (numpy.cos(m*x)) + p[2] * (numpy.sin(m*x))
return y
def f4(p, x):
#a,b,c = p
m =2.0 * M2 * pi
y = p[0] + p[1] * (numpy.cos(m*x)) + p[2] * (numpy.sin(m*x))
return y
#define functions to minimize
def err3(p,y,x):
return y - f3(p,x)
def err4(p,y,x):
return y - f4(p,x)
#conducts regression, then calculates amplitude and phase angle
def lstsq(func,y,x):
#define starting values with x0
x0 = numpy.array([sum(y)/float(len(y)), 0.01, 0.01])
fit ,chks = optimization.leastsq(func, x0, args=(y, x))
amp = math.sqrt((fit[1]**2)+(fit[2]**2)) #amplitude
phi = numpy.arctan(-1*(fit[2],fit[1]))*(180/pi) #phase angle
return amp,phi,fit
#water level signal regression
WLO1 = lstsq(err3,zdata,xdata)
WLM2 = lstsq(err4,zdata,xdata)
#tide signal regression
TdO1 = lstsq(err3,ydata,xdata)
TdM2 = lstsq(err4,ydata,xdata)
#calculate phase shift
phase_sft_O1 = WLO1[1] - TdO1[1]
phase_sft_M2 = WLM2[1] - TdM2[1]
delt_O1 = (phase_sft_O1/(O1*360))*24
delt_M2 = (phase_sft_M2/(M2*360))*24
#determine tidal potential Cutillo and Bredehoeft 2010 pg 5 eq 4
f_O1 = math.sin(float(lat[1])*pi/180)*math.cos(float(lat[1])*pi/180)
f_M2 = 0.5*math.cos(float(lat[1])*pi/180)**2
A2_M2 = g_ft*Km*b_M2*f_M2
A2_O1 = g_ft*Km*b_O1*f_O1
#Calculate ratio of head change to change in potential
dW2_M2 = A2_M2/(WLM2[0])
dW2_O1 = A2_O1/(WLO1[0])
#estimate specific storage Cutillo and Bredehoeft 2010
def SS(rat):
return 6.95690250E-10*rat
Ss_M2 = SS(dW2_M2)
Ss_O1 = SS(dW2_O1)
def curv(Y,P,r):
rc = (r/12.0)*(r/12.0)
Y = Y
X = -1421.15/(0.215746 + Y) - 13.3401 - 0.000000143487*Y**4 - 9.58311E-16*Y**8*math.cos(0.9895 + Y + 1421.08/(0.215746 + Y) + 0.000000143487*Y**4)
T = (X*rc)/P
return T
Trans_M2 = curv(phase_sft_O1,P_M2,r)
Trans_O1 = curv(phase_sft_M2,P_O1,r)
###########################################################################
#
############################################ Calculate BP Response Function
#
###########################################################################
# create lag matrix for regression
bpmat = tools.lagmat(dbp, lag, original='in')
etmat = tools.lagmat(dt, lag, original='in')
#lamat combines lag matrices of bp and et
lamat = numpy.column_stack([bpmat,etmat])
#for i in range(len(etmat)):
# lagmat.append(bpmat[i]+etmat[i])
#transpose matrix to determine required length
#run least squared regression
sqrd = numpy.linalg.lstsq(bpmat,dwl)
#determine lag coefficients of the lag matrix lamat
sqrdlag = numpy.linalg.lstsq(lamat,dwl)
wlls = sqrd[0]
#lagls return the coefficients of the least squares of lamat
lagls = sqrdlag[0]
cumls = numpy.cumsum(wlls)
#returns cumulative coefficients of et and bp (lamat)
lagcumls =numpy.cumsum(lagls)
ymod = numpy.dot(bpmat,wlls)
lagmod = numpy.dot(lamat,lagls)
#resid gives the residual of the bp
resid=[]
for i in range(len(dwl)):
resid.append(dwl[i] - ymod[i])
#alpha returns the lag coefficients associated with bp
alpha = lagls[0:len(lagls)/2]
alpha_cum = numpy.cumsum(alpha)
#gamma returns the lag coefficients associated with ET
gamma = lagls[len(lagls)/2:len(lagls)]
gamma_cum = numpy.cumsum(gamma)
lag_time = []
for i in range(len(xls_date)):
lag_time.append((xls_date[i] - xls_date[0])*24)
######################################### determine slope of late time data
lag_trim1 = lag_time[0:len(cumls)]
lag_time_trim = lag_trim1[len(lag_trim1)-(len(lag_trim1)/2):len(lag_trim1)]
alpha_trim = alpha_cum[len(lag_trim1)-(len(lag_trim1)/2):len(lag_trim1)]
#calculate slope of late-time data
lag_len = len(lag_time_trim)
tran = numpy.array([lag_time_trim, numpy.ones(lag_len)])
reg_late = numpy.linalg.lstsq(tran.T,alpha_trim)[0]
late_line=[]
for i in range(len(lag_trim1)):
late_line.append(reg_late[0] * lag_trim1[i] + reg_late[1]) #regression line
######################################## determine slope of early time data
lag_time_trim2 = lag_trim1[0:len(lag_trim1)-int(round((len(lag_trim1)/1.5),0))]
alpha_trim2 = alpha_cum[0:len(lag_trim1)-int(round((len(lag_trim1)/1.5),0))]
lag_len1 = len(lag_time_trim2)
tran2 = numpy.array([lag_time_trim2, numpy.ones(lag_len1)])
reg_early = numpy.linalg.lstsq(tran2.T,alpha_trim2)[0]
early_line= []
for i in range(len(lag_trim1)):
early_line.append(reg_early[0] * lag_trim1[i] + reg_early[1]) #regression line
aquifer_type = []
if reg_early[0] > 0.001:
aquifer_type = 'borehole storage'
elif reg_early[0] < -0.001:
aquifer_type = 'unconfined conditions'
else:
aquifer_type = 'confined conditions'
###########################################################################
#
################################################################ Make Plots
#
###########################################################################
fig_1_lab = well_name + ' bp response function'
fig_2_lab = well_name + ' signal processing'
plt.figure(fig_1_lab)
plt.suptitle(fig_1_lab, x= 0.2, y=.99, fontsize='small')
plt.subplot(2,1,1)
#plt.plot(lag_time[0:len(cumls)],cumls, label='b.p. alone')
plt.plot(lag_time[0:len(cumls)],alpha_cum,"o", label='b.p. when \n considering e.t.')
# plt.plot(lag_time[0:len(cumls)],gamma_cum, label='e.t.')
plt.plot(lag_trim1, late_line, 'r-', label='late reg.')
plt.plot(lag_trim1, early_line, 'g-', label='early reg.')
plt.xlabel('lag (hr)')
plt.ylabel('cumulative response function')
plt.legend(loc=4,fontsize='small')
plt.subplot(2,1,2)
plt.plot(lag_time,dwl, label='wl', lw=2)
plt.plot(lag_time,ymod, label='wl modeled w bp')
plt.plot(lag_time,lagmod, 'r--', label='wl modeled w bp&et')
plt.legend(loc=4,fontsize='small')
plt.xlim(0,lag)
plt.ylabel('change (ft)')
plt.xlabel('time (hrs)')
plt.tight_layout()
plt.savefig('l'+ os.path.splitext(impfile)[0]+'.pdf')
plt.figure(fig_2_lab)
plt.suptitle(fig_2_lab, x=0.2, fontsize='small')
plt.title(os.path.splitext(impfile)[0])
plt.subplot(4,1,1)
plt.xcorr(yfilt_O1,zfilt_O1,maxlags=10)
plt.ylim(-1.1,1.1)
plt.tick_params(labelsize=8)
plt.xlabel('lag (hrs)',fontsize='small')
plt.ylabel('lag (hrs)',fontsize='small')
plt.title('Cross Correl O1',fontsize='small')
plt.subplot(4,1,2)
plt.xcorr(yfilt_M2,zfilt_M2,maxlags=10)
plt.ylim(-1.1,1.1)
plt.tick_params(labelsize=8)
plt.xlabel('lag (hrs)',fontsize='small')
plt.ylabel('lag (hrs)',fontsize='small')
plt.title('Cross Correl M2',fontsize='small')
plt.subplot(4,1,3)
plt.plot(zfftb,zffta)
plt.tick_params(labelsize=8)
plt.xlabel('frequency (cpd)',fontsize='small')
plt.ylabel('amplitude')
plt.title('WL fft',fontsize='small')
plt.xlim(0,4)
plt.ylim(0,30)
plt.subplot(4,1,4)
plt.plot(x0data,zdata, 'b')
plt.tick_params(labelsize=8)
plt.xlabel('julian days',fontsize='small')
plt.ylabel('water level (ft)',fontsize='small')
plt.twinx()
plt.plot(x0data,f3(WLO1[2],x0data), 'r')
plt.plot(x0data,f4(WLM2[2],x0data), 'g')
plt.tick_params(labelsize=8)
plt.xlim(0,10)
plt.ylabel('tidal strain (ppb)',fontsize='small')
plt.tick_params(labelsize=8)
plt.tight_layout()
plt.title('Regression Fit',fontsize='small')
plt.savefig('f'+ os.path.splitext(impfile)[0]+'.pdf')
plt.close()
###########################################################################
#Write output to files
###########################################################################
# create row of data for compiled output file info.csv
myCSVrow = [os.path.splitext(inpfile)[0],well_name, A2_O1, A2_M2, phase_sft_O1, phase_sft_M2, delt_O1,
delt_M2, Trans_M2, Trans_O1, Ss_O1, Ss_M2, WLO1[1], TdO1[1], WLM2[1], TdM2[1],
WLO1[0], TdO1[0], WLM2[0], TdM2[0], WLO1[2][1], TdO1[2][1], WLM2[2][1],
TdM2[2][1], WLO1[2][2], TdO1[2][2], WLM2[2][2], TdM2[2][2], reg_late[1], reg_early[0], aquifer_type, phsO1, phsM2]
# add data row to compiled output file
compfile = open('info.csv', 'a')
writer = csv.writer(compfile)
writer.writerow(myCSVrow)
compfile.close()
#export tidal data to individual (well specific) output file
with open(outfile, "wb") as f:
filewriter = csv.writer(f, delimiter=',')
#write header
header = ['xl_time','date_time','V_ugal','vert_mm','areal_mm','WDD_tam','potential','dilation_ppb','wl_ft','dbp','dwl','resid','bp','Tsoft_SG23']
filewriter.writerow(header)
for row in range(0,1):
for i in range(len(d)):
#you can add more columns here
filewriter.writerow([xls_date[i],d[i],Grav_tide[i],vert[i],areal[i],WDD_tam[i],potential[i],
dilation[i],wl[i],dbp[i],dwl[i],resid[i],bp[i],etint[i]])
