def _estimate_svar(self,
start_params,
lags,
maxiter,
maxfun,
trend='c',
solver="nm",
override=False):
"""
lags : int
trend : string or None
As per above
"""
k_trend = util.get_trendorder(trend)
y = self.endog
z = util.get_var_endog(y, lags, trend=trend)
y_sample = y[lags:]
# Lutkepohl p75, about 5x faster than stated formula
var_params = np.linalg.lstsq(z, y_sample)[0]
resid = y_sample - np.dot(z, var_params)
# Unbiased estimate of covariance matrix $\Sigma_u$ of the white noise
# process $u$
# equivalent definition
# .. math:: \frac{1}{T - Kp - 1} Y^\prime (I_T - Z (Z^\prime Z)^{-1}
# Z^\prime) Y
# Ref: Lutkepohl p.75
# df_resid right now is T - Kp - 1, which is a suggested correction
avobs = len(y_sample)
df_resid = avobs - (self.neqs * lags + k_trend)
sse = np.dot(resid.T, resid)
#TODO: should give users the option to use a dof correction or not
omega = sse / df_resid
self.sigma_u = omega
A, B = self._solve_AB(start_params,
override=override,
solver=solver,
maxiter=maxiter,
maxfun=maxfun)
A_mask = self.A_mask
B_mask = self.B_mask
return SVARResults(y,
z,
var_params,
omega,
lags,
names=self.endog_names,
trend=trend,
dates=self._data.dates,
model=self,
A=A,
B=B,
A_mask=A_mask,
B_mask=B_mask)
def __init__(self, endog, endog_lagged, params, sigma_u, lag_order,
model=None, trend='c', names=None, dates=None):
self.model = model
self.y = self.endog = endog #keep alias for now
self.ys_lagged = self.endog_lagged = endog_lagged #keep alias for now
self.dates = dates
self.n_totobs, neqs = self.y.shape
self.nobs = self.n_totobs - lag_order
k_trend = util.get_trendorder(trend)
if k_trend > 0: # make this the polynomial trend order
trendorder = k_trend - 1
else:
trendorder = None
self.k_trend = k_trend
self.trendorder = trendorder
#TODO: deprecate coef_names
self.coef_names = self.exog_names = util.make_lag_names(names,
lag_order, k_trend)
self.params = params
# Initialize VARProcess parent class
# construct coefficient matrices
# Each matrix needs to be transposed
reshaped = self.params[self.k_trend:]
reshaped = reshaped.reshape((lag_order, neqs, neqs))
# Need to transpose each coefficient matrix
intercept = self.params[0]
coefs = reshaped.swapaxes(1, 2).copy()
super(VARResults, self).__init__(coefs, intercept, sigma_u, names=names)
def __init__(self,
endog,
endog_lagged,
params,
sigma_u,
lag_order,
A=None,
B=None,
A_mask=None,
B_mask=None,
model=None,
trend='c',
names=None,
dates=None):
self.model = model
self.y = self.endog = endog #keep alias for now
self.ys_lagged = self.endog_lagged = endog_lagged #keep alias for now
self.dates = dates
self.n_totobs, self.neqs = self.y.shape
self.nobs = self.n_totobs - lag_order
k_trend = util.get_trendorder(trend)
if k_trend > 0: # make this the polynomial trend order
trendorder = k_trend - 1
else:
trendorder = None
self.k_trend = k_trend
self.trendorder = trendorder
self.coef_names = util.make_lag_names(names, lag_order, k_trend)
self.params = params
self.sigma_u = sigma_u
# Each matrix needs to be transposed
reshaped = self.params[self.k_trend:]
reshaped = reshaped.reshape((lag_order, self.neqs, self.neqs))
# Need to transpose each coefficient matrix
intercept = self.params[0]
coefs = reshaped.swapaxes(1, 2).copy()
#SVAR components
#TODO: if you define these here, you don't also have to define
#them in SVAR process, but I left them for now -ss
self.A = A
self.B = B
self.A_mask = A_mask
self.B_mask = B_mask
super(SVARResults, self).__init__(coefs,
intercept,
sigma_u,
A,
B,
names=names)
def test_get_trendorder():
results = {
'c' : 1,
'nc' : 0,
'ct' : 2,
'ctt' : 3
}
for t, trendorder in results.iteritems():
assert(util.get_trendorder(t) == trendorder)
def fit(self, maxlags=None, method='ols', ic=None, trend='c',
verbose=False):
"""
Fit the VAR model
Parameters
----------
maxlags : int
Maximum number of lags to check for order selection, defaults to
12 * (nobs/100.)**(1./4), see select_order function
method : {'ols'}
Estimation method to use
ic : {'aic', 'fpe', 'hqic', 'bic', None}
Information criterion to use for VAR order selection.
aic : Akaike
fpe : Final prediction error
hqic : Hannan-Quinn
bic : Bayesian a.k.a. Schwarz
verbose : bool, default False
Print order selection output to the screen
trend, str {"c", "ct", "ctt", "nc"}
"c" - add constant
"ct" - constant and trend
"ctt" - constant, linear and quadratic trend
"nc" - co constant, no trend
Note that these are prepended to the columns of the dataset.
Notes
-----
Lutkepohl pp. 146-153
Returns
-------
est : VARResults
"""
lags = maxlags
if ic is not None:
selections = self.select_order(maxlags=maxlags, verbose=verbose)
if ic not in selections:
raise Exception("%s not recognized, must be among %s"
% (ic, sorted(selections)))
lags = selections[ic]
if verbose:
print 'Using %d based on %s criterion' % (lags, ic)
else:
if lags is None:
lags = 1
k_trend = util.get_trendorder(trend)
self.exog_names = util.make_lag_names(self.endog_names, lags, k_trend)
self.nobs = len(self.endog) - lags
return self._estimate_var(lags, trend=trend)
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 _estimate_svar(self, start_params, lags, maxiter, maxfun,
trend='c', solver="nm", override=False):
"""
lags : int
trend : string or None
As per above
"""
k_trend = util.get_trendorder(trend)
y = self.endog
z = util.get_var_endog(y, lags, trend=trend)
y_sample = y[lags:]
# Lutkepohl p75, about 5x faster than stated formula
var_params = np.linalg.lstsq(z, y_sample)[0]
resid = y_sample - np.dot(z, var_params)
# Unbiased estimate of covariance matrix $\Sigma_u$ of the white noise
# process $u$
# equivalent definition
# .. math:: \frac{1}{T - Kp - 1} Y^\prime (I_T - Z (Z^\prime Z)^{-1}
# Z^\prime) Y
# Ref: Lutkepohl p.75
# df_resid right now is T - Kp - 1, which is a suggested correction
avobs = len(y_sample)
df_resid = avobs - (self.neqs * lags + k_trend)
sse = np.dot(resid.T, resid)
#TODO: should give users the option to use a dof correction or not
omega = sse / df_resid
self.sigma_u = omega
A, B = self._solve_AB(start_params, override=override,
solver=solver,
maxiter=maxiter,
maxfun=maxfun)
A_mask = self.A_mask
B_mask = self.B_mask
return SVARResults(y, z, var_params, omega, lags,
names=self.endog_names, trend=trend,
dates=self._data.dates, model=self,
A=A, B=B, A_mask=A_mask, B_mask=B_mask)
def _estimate_var(self, lags, offset=0, trend='c'):
"""
lags : int
offset : int
Periods to drop from beginning-- for order selection so it's an
apples-to-apples comparison
trend : string or None
As per above
"""
# have to do this again because select_order doesn't call fit
self.k_trend = k_trend = util.get_trendorder(trend)
if offset < 0: # pragma: no cover
raise ValueError('offset must be >= 0')
y = self.y[offset:]
z = util.get_var_endog(y, lags, trend=trend)
y_sample = y[lags:]
# Lutkepohl p75, about 5x faster than stated formula
params = np.linalg.lstsq(z, y_sample)[0]
resid = y_sample - np.dot(z, params)
# Unbiased estimate of covariance matrix $\Sigma_u$ of the white noise
# process $u$
# equivalent definition
# .. math:: \frac{1}{T - Kp - 1} Y^\prime (I_T - Z (Z^\prime Z)^{-1}
# Z^\prime) Y
# Ref: Lutkepohl p.75
# df_resid right now is T - Kp - 1, which is a suggested correction
avobs = len(y_sample)
df_resid = avobs - (self.neqs * lags + k_trend)
sse = np.dot(resid.T, resid)
omega = sse / df_resid
varfit = VARResults(y, z, params, omega, lags, names=self.endog_names,
trend=trend, dates=self._data.dates, model=self)
return VARResultsWrapper(varfit)
def __init__(self, endog, endog_lagged, params, sigma_u, lag_order,
A=None, B=None, A_mask=None, B_mask=None, model=None,
trend='c', names=None, dates=None):
self.model = model
self.y = self.endog = endog #keep alias for now
self.ys_lagged = self.endog_lagged = endog_lagged #keep alias for now
self.dates = dates
self.n_totobs, self.neqs = self.y.shape
self.nobs = self.n_totobs - lag_order
k_trend = util.get_trendorder(trend)
if k_trend > 0: # make this the polynomial trend order
trendorder = k_trend - 1
else:
trendorder = None
self.k_trend = k_trend
self.trendorder = trendorder
self.coef_names = util.make_lag_names(names, lag_order, k_trend)
self.params = params
self.sigma_u = sigma_u
# Each matrix needs to be transposed
reshaped = self.params[self.k_trend:]
reshaped = reshaped.reshape((lag_order, self.neqs, self.neqs))
# Need to transpose each coefficient matrix
intercept = self.params[0]
coefs = reshaped.swapaxes(1, 2).copy()
#SVAR components
#TODO: if you define these here, you don't also have to define
#them in SVAR process, but I left them for now -ss
self.A = A
self.B = B
self.A_mask = A_mask
self.B_mask = B_mask
super(SVARResults, self).__init__(coefs, intercept, sigma_u, A,
B, names=names)
def predict(self, params, start=None, end=None, lags=1, trend='c'):
"""
Returns in-sample predictions or forecasts
"""
start = self._get_predict_start(start, lags)
end, out_of_sample = self._get_predict_end(end)
if end < start:
raise ValueError("end is before start")
if end == start + out_of_sample:
return np.array([])
k_trend = util.get_trendorder(trend)
k = self.neqs
k_ar = lags
predictedvalues = np.zeros((end + 1 - start + out_of_sample, k))
if k_trend != 0:
intercept = params[:k_trend]
predictedvalues += intercept
y = self.y
X = util.get_var_endog(y, lags, trend=trend)
fittedvalues = np.dot(X, params)
fv_start = start - k_ar
pv_end = min(len(predictedvalues), len(fittedvalues) - fv_start)
fv_end = min(len(fittedvalues), end-k_ar+1)
predictedvalues[:pv_end] = fittedvalues[fv_start:fv_end]
if not out_of_sample:
return predictedvalues
# fit out of sample
y = y[-k_ar:]
coefs = params[k_trend:].reshape((k_ar, k, k)).swapaxes(1,2)
predictedvalues[pv_end:] = forecast(y, coefs, intercept, out_of_sample)
return predictedvalues
