def plot5(self):
df1 = pd.read_csv('data/airline_passengers.csv',
index_col='Month',
parse_dates=True)
df1.index.freq = 'MS'
df2 = pd.read_csv('data/DailyTotalFemaleBirths.csv',
index_col='Date',
parse_dates=True)
df2.index.freq = 'D'
df = pd.DataFrame({'a': [13, 5, 11, 12, 9]})
arr = acovf(df['a'])
arr2 = acovf(df['a'], unbiased=True)
arr3 = acf(df['a'])
arr4 = pacf_yw(df['a'], nlags=4, method='mle')
lag_plot(df1['Thousands of Passengers'])
lag_plot(df2['Births'])
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
from statsmodels.tsa.statespace.tools import diff
title = 'Autocorrelation: Daily Female Births'
lags = 40
plot_acf(df2, title=title, lags=lags)
title = 'Autocorrelation: Airline Passengers'
lags = 40
plot_acf(df1, title=title, lags=lags)
plt.interactive(False)
plt.show()
def test_acovf_fft_vs_convolution(demean, unbiased):
np.random.seed(1)
q = np.random.normal(size=100)
F1 = acovf(q, demean=demean, unbiased=unbiased, fft=True)
F2 = acovf(q, demean=demean, unbiased=unbiased, fft=False)
assert_almost_equal(F1, F2, decimal=7)
def test_acovf_fft_vs_convolution(demean, adjusted):
np.random.seed(1)
q = np.random.normal(size=100)
F1 = acovf(q, demean=demean, adjusted=adjusted, fft=True)
F2 = acovf(q, demean=demean, adjusted=adjusted, fft=False)
assert_almost_equal(F1, F2, decimal=7)
def test_acovf2d():
dta = sunspots.load_pandas().data
dta.index = DatetimeIndex(start='1700', end='2009', freq='A')[:309]
del dta["YEAR"]
res = acovf(dta)
assert_equal(res, acovf(dta.values))
X = np.random.random((10,2))
assert_raises(ValueError, acovf, X)
def test_acovf_nlags_missing(acovf_data, unbiased, demean, fft, missing):
acovf_data = acovf_data.copy()
acovf_data[1:3] = np.nan
full = acovf(acovf_data, unbiased=unbiased, demean=demean, fft=fft,
missing=missing)
limited = acovf(acovf_data, unbiased=unbiased, demean=demean, fft=fft,
missing=missing, nlag=10)
assert_allclose(full[:11], limited)
def test_acovf2d():
dta = sunspots.load_pandas().data
dta.index = Index(dates_from_range('1700', '2008'))
del dta["YEAR"]
res = acovf(dta)
assert_equal(res, acovf(dta.values))
X = np.random.random((10,2))
assert_raises(ValueError, acovf, X)
def test_acovf2d():
dta = sunspots.load_pandas().data
dta.index = Index(dates_from_range('1700', '2008'))
del dta["YEAR"]
res = acovf(dta)
assert_equal(res, acovf(dta.values))
X = np.random.random((10, 2))
assert_raises(ValueError, acovf, X)
def test_acovf_nlags_missing(acovf_data, adjusted, demean, fft, missing):
acovf_data = acovf_data.copy()
acovf_data[1:3] = np.nan
full = acovf(acovf_data, adjusted=adjusted, demean=demean, fft=fft,
missing=missing)
limited = acovf(acovf_data, adjusted=adjusted, demean=demean, fft=fft,
missing=missing, nlag=10)
assert_allclose(full[:11], limited)
def test_acovf2d():
dta = sunspots.load_pandas().data
dta.index = DatetimeIndex(start='1700', end='2009', freq='A')
del dta["YEAR"]
res = acovf(dta)
assert_equal(res, acovf(dta.values))
X = np.random.random((10, 2))
assert_raises(ValueError, acovf, X)
def test_acovf2d(reset_randomstate):
dta = sunspots.load_pandas().data
dta.index = date_range(start='1700', end='2009', freq='A')[:309]
del dta["YEAR"]
res = acovf(dta, fft=False)
assert_equal(res, acovf(dta.values, fft=False))
x = np.random.random((10, 2))
with pytest.raises(ValueError):
acovf(x, fft=False)
def test_acovf2d(reset_randomstate):
dta = sunspots.load_pandas().data
dta.index = date_range(start='1700', end='2009', freq='A')[:309]
del dta["YEAR"]
res = acovf(dta, fft=False)
assert_equal(res, acovf(dta.values, fft=False))
x = np.random.random((10, 2))
with pytest.raises(ValueError):
acovf(x, fft=False)
def test_acovf_fft_vs_convolution():
np.random.seed(1)
q = np.random.normal(size=100)
for demean in [True, False]:
for unbiased in [True, False]:
F1 = acovf(q, demean=demean, unbiased=unbiased, fft=True)
F2 = acovf(q, demean=demean, unbiased=unbiased, fft=False)
assert_almost_equal(F1, F2, decimal=7)
def test_acovf_nlags(acovf_data, unbiased, demean, fft, missing):
full = acovf(acovf_data,
unbiased=unbiased,
demean=demean,
fft=fft,
missing=missing)
limited = acovf(acovf_data,
unbiased=unbiased,
demean=demean,
fft=fft,
missing=missing,
nlag=10)
assert_allclose(full[:11], limited)
def levinson_durbin_nitime(s, order=10, isacov=False):
'''Levinson-Durbin recursion for autoregressive processes
'''
#from nitime
## if sxx is not None and type(sxx) == np.ndarray:
## sxx_m = sxx[:order+1]
## else:
## sxx_m = ut.autocov(s)[:order+1]
if isacov:
sxx_m = s
else:
sxx_m = acovf(s)[:order+1] #not tested
phi = np.zeros((order+1, order+1), 'd')
sig = np.zeros(order+1)
# initial points for the recursion
phi[1,1] = sxx_m[1]/sxx_m[0]
sig[1] = sxx_m[0] - phi[1,1]*sxx_m[1]
for k in xrange(2,order+1):
phi[k,k] = (sxx_m[k]-np.dot(phi[1:k,k-1], sxx_m[1:k][::-1]))/sig[k-1]
for j in xrange(1,k):
phi[j,k] = phi[j,k-1] - phi[k,k]*phi[k-j,k-1]
sig[k] = sig[k-1]*(1 - phi[k,k]**2)
sigma_v = sig[-1]; arcoefs = phi[1:,-1]
return sigma_v, arcoefs, pacf, phi #return everything
def levinson_durbin_nitime(s, order=10, isacov=False):
'''Levinson-Durbin recursion for autoregressive processes
'''
#from nitime
## if sxx is not None and type(sxx) == np.ndarray:
## sxx_m = sxx[:order+1]
## else:
## sxx_m = ut.autocov(s)[:order+1]
if isacov:
sxx_m = s
else:
sxx_m = acovf(s)[:order + 1] #not tested
phi = np.zeros((order + 1, order + 1), 'd')
sig = np.zeros(order + 1)
# initial points for the recursion
phi[1, 1] = sxx_m[1] / sxx_m[0]
sig[1] = sxx_m[0] - phi[1, 1] * sxx_m[1]
for k in range(2, order + 1):
phi[k, k] = (sxx_m[k] -
np.dot(phi[1:k, k - 1], sxx_m[1:k][::-1])) / sig[k - 1]
for j in range(1, k):
phi[j, k] = phi[j, k - 1] - phi[k, k] * phi[k - j, k - 1]
sig[k] = sig[k - 1] * (1 - phi[k, k]**2)
sigma_v = sig[-1]
arcoefs = phi[1:, -1]
return sigma_v, arcoefs, pacf, phi #return everything
def DRAWAUTOCOV(x, llim):
ac = acovf(x, unbiased=True, demean=True)
lag = np.arange(len(ac))
fig, sub = plt.subplots()
sub.set_title("Autocovariance", fontdict={"weight": "bold"})
sub.plot(lag, ac, ls="-", c="k")
sub.set_xlabel("Time lag", fontdict={"weight": "bold"})
sub.set_xlim(min(lag), llim)
def test_multivariate_acovf():
_acovf = tools._compute_multivariate_acovf_from_coefficients
# Test for a VAR(1) process. From Lutkepohl (2007), pages 27-28.
# See (2.1.14) for Phi_1, (2.1.33) for Sigma_u, and (2.1.34) for Gamma_0
Sigma_u = np.array([[2.25, 0, 0],
[0, 1.0, 0.5],
[0, 0.5, 0.74]])
Phi_1 = np.array([[0.5, 0, 0],
[0.1, 0.1, 0.3],
[0, 0.2, 0.3]])
Gamma_0 = np.array([[3.0, 0.161, 0.019],
[0.161, 1.172, 0.674],
[0.019, 0.674, 0.954]])
assert_allclose(_acovf([Phi_1], Sigma_u)[0], Gamma_0, atol=1e-3)
# Test for a VAR(2) process. From Lutkepohl (2007), pages 28-29
# See (2.1.40) for Phi_1, Phi_2, (2.1.14) for Sigma_u, and (2.1.42) for
# Gamma_0, Gamma_1
Sigma_u = np.diag([0.09, 0.04])
Phi_1 = np.array([[0.5, 0.1],
[0.4, 0.5]])
Phi_2 = np.array([[0, 0],
[0.25, 0]])
Gamma_0 = np.array([[0.131, 0.066],
[0.066, 0.181]])
Gamma_1 = np.array([[0.072, 0.051],
[0.104, 0.143]])
Gamma_2 = np.array([[0.046, 0.040],
[0.113, 0.108]])
Gamma_3 = np.array([[0.035, 0.031],
[0.093, 0.083]])
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=0),
[Gamma_0], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=1),
[Gamma_0, Gamma_1], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u),
[Gamma_0, Gamma_1], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=2),
[Gamma_0, Gamma_1, Gamma_2], atol=1e-3)
assert_allclose(
_acovf([Phi_1, Phi_2], Sigma_u, maxlag=3),
[Gamma_0, Gamma_1, Gamma_2, Gamma_3], atol=1e-3)
# Test sample acovf in the univariate case against sm.tsa.acovf
x = np.arange(20)*1.0
assert_allclose(
np.squeeze(tools._compute_multivariate_sample_acovf(x, maxlag=4)),
acovf(x, fft=False)[:5])
def find_G_D(data, bootstrap_type, M):
kk = np.arange(-M, M + 1)
acov = acovf(data)[:M + 1]
R_k = np.r_[acov[1:][::-1], acov]
Ghat = np.sum(lam(kk / float(M)) * np.abs(kk) * R_k)
if bootstrap_type == 'Circular':
Dhat = (4 / 3.) * np.sum(lam(kk / float(M)) * R_k)**2
else:
Dhat = 2 * np.sum(lam(kk / float(M)) * R_k)**2
return Ghat, Dhat
def acf_df(dat, mode="correlation", nlags=40):
"""returns acf,aconv,pacf dataframe"""
if mode == "covariance":
vals = sts.acovf(dat) # nlag arg does not exist in v0.9.0
elif mode == "correlation":
vals = sts.acf(dat, nlags=nlags)
elif mode == "pacf":
vals = sts.pacf(dat, nlags=nlags)
else:
raise Exception("wtf")
return pd.DataFrame(np.array([np.array(range(len(vals))), vals]).T,
columns=["lag", "values"])
def get_ar_coef(y, sn, p, add_lag, pad=None):
if add_lag == 'p':
max_lag = p * 2
else:
max_lag = p + add_lag
cov = acovf(y, fft=True)
C_mat = toeplitz(cov[:max_lag], cov[:p]) - sn**2 * np.eye(max_lag, p)
g = lstsq(C_mat, cov[1:max_lag + 1])[0]
if pad:
res = np.zeros(pad)
res[:len(g)] = g
return res
else:
return g
def test_brockwell_davis_example_511():
# Make the series stationary
endog = dowj.diff().iloc[1:]
# Should have 77 observations
assert_equal(len(endog), 77)
# Autocovariances
desired = [0.17992, 0.07590, 0.04885]
assert_allclose(acovf(endog, fft=True, nlag=2), desired, atol=1e-5)
# Yule-Walker
yw, _ = yule_walker(endog, ar_order=1, demean=True)
assert_allclose(yw.ar_params, [0.4219], atol=1e-4)
assert_allclose(yw.sigma2, 0.1479, atol=1e-4)
def stationarity_convergence(phi):
m = 20 # burn in
n = len(phi) - m
if n <= 0:
return 0
na = max(1,int(0.1*n))
nb = max(1,int(0.5*n))
phi_a = phi[(m+n-na):(m+n)]
phi_b= phi[(m):(m+nb)]
phi_b= phi[(m+n-nb):(m+n)]
phi_b_bar = sum(phi_b)/nb
phi_a_bar = sum(phi_a)/na
if len(phi_a) <= 1 or len(phi_b) <= 1:
return 1
v_a = acovf(phi_a)
v_b = acovf(phi_b)
# n gets large and na/n and nb/n stay fixed
z_g = (phi_a_bar - phi_b_bar)/np.sqrt( v_a[0] + v_b[0] )
return z_g
def calc_acf(a_values: Dict[str, np.ndarray]) -> List[np.ndarray]:
"""
Calculate auto-correlation function (ACF)
Args:
a_values: A dict of adjacency matrix with neighbor atom id as keys and arrays
of adjacent boolean (0/1) as values.
Returns:
A list of auto-correlation functions for each neighbor species.
"""
acfs = []
for atom_id, neighbors in a_values.items():
# atom_id_numeric = int(re.search(r"\d+", atom_id).group())
acfs.append(acovf(neighbors, demean=False, unbiased=True, fft=True))
return acfs
def compute_autocorrelation_parameters(record):
'''
Compute Features which are derives from the autocorrelation function with K = 1
'''
record.cor = acovf(record.nn_ints,
unbiased=True,
fft=True,
nlag=None)
record.cor /= record.cor[0]
record.r1 = record.cor[1] # Difference instead of first value?
negatives = [neg[0] for neg in enumerate(record.cor) if neg[1] < 0]
if len(negatives) > 0:
record.m0 = negatives[0]
else:
record.m0 = 0 # Maybe not the best to set an 'undefined' value to 0. Nan?
def hidden_window_summary(self, axis, start, end):
acf = stattools.acf(axis[start:end])
acv = stattools.acovf(axis[start:end])
sqd_error = (axis[start:end] - axis[start:end].mean())**2
return [
self.jitter(axis, start, end),
self.mean_crossing_rate(axis, start, end), axis[start:end].mean(),
axis[start:end].std(), axis[start:end].var(),
axis[start:end].min(), axis[start:end].max(),
acf.mean(),
acf.std(),
acv.mean(),
acv.std(),
skew(axis[start:end]),
kurtosis(axis[start:end]),
math.sqrt(sqd_error.mean())
]
def window_summary(axis, start, end):
acf = stattools.acf(axis[start:end])
acv = stattools.acovf(axis[start:end])
sqd_error = (axis[start:end] - axis[start:end].mean())**2
return [
axis[start:end].mean(),
axis[start:end].std(),
axis[start:end].var(),
axis[start:end].min(),
axis[start:end].max(),
acf.mean(), # mean auto correlation
acf.std(), # standard deviation auto correlation
acv.mean(), # mean auto covariance
acv.std(), # standard deviation auto covariance
skew(axis[start:end]),
kurtosis(axis[start:end]),
math.sqrt(sqd_error.mean())
]
def window_summary(axis, start, end):
acf = stattools.acf(axis[start:end])
acv = stattools.acovf(axis[start:end])
sqd_error = (axis[start:end] - axis[start:end].mean())**2
return [
jitter(axis, start, end), #singal processing
mean_crossing_rate(
axis, start, end), # rate with signal crossing the mean value
axis[start:end].mean(),
axis[start:end].std(),
axis[start:end].var(),
axis[start:end].min(),
axis[start:end].max(),
acf.mean(), # mean auto correlation
acf.std(), # standard deviation auto correlation
acv.mean(), # mean auto covariance
acv.std(), # standard deviation auto covariance
skew(axis[start:end]),
kurtosis(axis[start:end]),
math.sqrt(sqd_error.mean())
]
def window_summary(axis, start, end):
'''
from https://github.com/theumairahmed/User-Identification-and-Classification-From-Walking-Activity/blob/master/Preprocessing.py
'''
acf = stattools.acf(axis[start:end])
acv = stattools.acovf(axis[start:end])
sqd_error = (axis[start:end] - axis[start:end].mean())**2
return [
axis[start:end].mean(),
axis[start:end].std(),
axis[start:end].var(),
axis[start:end].min(),
axis[start:end].max(),
acf.mean(), # mean auto correlation
acf.std(), # standard deviation auto correlation
acv.mean(), # mean auto covariance
acv.std(), # standard deviation auto covariance
skew(axis[start:end]),
kurtosis(axis[start:end]),
math.sqrt(sqd_error.mean())
]
def approx_ar_cov_sum(x):
params, sigma2, order = fit_ar(x)
param_sum = params.sum()
asympt_var = sigma2 / ((1 - param_sum) ** 2)
gammas = acovf(x, nlag=order-1, fft=False)
if (order != 0):
Gamma = 0
for i in range(1, order+1):
for k in range(1, i+1):
Gamma = Gamma + params[i-1] * k * gammas[i-k]
# Gamma is computed using the equation at the bottom of p. 9 in https://arxiv.org/pdf/1804.05975.pdf
# See also https://stats.stackexchange.com/questions/371792/sum-of-autocovariances-for-arp-model/372006#372006
Gamma = 2 * (
Gamma + 0.5 * (asympt_var - gammas[0]) * (params * range(1, order + 1)).sum()
) / (1 - param_sum)
else:
Gamma = 0
return Gamma, asympt_var
def weak_wn_acf(returns, lags=40, alpha=0.95):
n = len(returns)
alpha = 0.95
gamma_0 = acovf(returns)[0]
returns_sq = np.array(returns)**2
sigma_hat_p = (
(1 / n) *
np.array([returns_sq[:n - h] @ returns_sq[h:]
for h in range(1, n)]) / (gamma_0**2))**0.5
upper = sigma_hat_p * norm.ppf(alpha) / (n**0.5)
upper = np.concatenate([[float('NaN')], upper])
lower = -sigma_hat_p * norm.ppf(alpha) / (n**0.5)
lower = np.concatenate([[float('NaN')], lower])
plot_acf(returns, lags=lags, alpha=1 - alpha)
plt.plot(upper[:lags + 1])
plt.plot(lower[:lags + 1])
plt.legend([
'Strong WN CI', 'Auto Correlation', 'Weak WN CI Upper',
'Weak WN CI Lower'
])
plt.show()
kwargs.setdefault('linestyle', 'None')
a, = self.plot(lags, c, **kwargs)
b = None
return lags, c, a, b
arrvs = ar_generator()
##arma = ARIMA()
##res = arma.fit(arrvs[0], 4, 0)
arma = ARIMA(arrvs[0])
res = arma.fit((4, 0, 0))
print(res[0])
acf1 = acf(arrvs[0])
acovf1b = acovf(arrvs[0], unbiased=False)
acf2 = autocorr(arrvs[0])
acf2m = autocorr(arrvs[0] - arrvs[0].mean())
print(acf1[:10])
print(acovf1b[:10])
print(acf2[:10])
print(acf2m[:10])
x = arma_generate_sample([1.0, -0.8], [1.0], 500)
print(acf(x)[:20])
import statsmodels.api as sm
print(sm.regression.yule_walker(x, 10))
import matplotlib.pyplot as plt
#ax = plt.axes()
plt.plot(x)
def test_pandasacovf():
s = Series(lrange(1, 11))
assert_almost_equal(acovf(s), acovf(s.values))
def test_acovf_warns(acovf_data):
with pytest.warns(FutureWarning):
acovf(acovf_data)
arrvs = ar_generator() ##arma = ARIMA() ##res = arma.fit(arrvs[0], 4, 0) arma = ARIMA(arrvs[0]) res = arma.fit((4,0, 0)) print(res[0]) acf1 = acf(arrvs[0]) acovf1b = acovf(arrvs[0], unbiased=False) acf2 = autocorr(arrvs[0]) acf2m = autocorr(arrvs[0]-arrvs[0].mean()) print(acf1[:10]) print(acovf1b[:10]) print(acf2[:10]) print(acf2m[:10]) x = arma_generate_sample([1.0, -0.8], [1.0], 500) print(acf(x)[:20]) import statsmodels.api as sm print(sm.regression.yule_walker(x, 10)) import matplotlib.pyplot as plt #ax = plt.axes()
def durbin_levinson(endog, ar_order=0, demean=True, adjusted=False):
"""
Estimate AR parameters at multiple orders using Durbin-Levinson recursions.
Parameters
----------
endog : array_like or SARIMAXSpecification
Input time series array, assumed to be stationary.
ar_order : int, optional
Autoregressive order. Default is 0.
demean : bool, optional
Whether to estimate and remove the mean from the process prior to
fitting the autoregressive coefficients. Default is True.
adjusted : bool, optional
Whether to use the "adjusted" autocovariance estimator, which uses
n - h degrees of freedom rather than n. This option can result in
a non-positive definite autocovariance matrix. Default is False.
Returns
-------
parameters : list of SARIMAXParams objects
List elements correspond to estimates at different `ar_order`. For
example, parameters[0] is an `SARIMAXParams` instance corresponding to
`ar_order=0`.
other_results : Bunch
Includes one component, `spec`, containing the `SARIMAXSpecification`
instance corresponding to the input arguments.
Notes
-----
The primary reference is [1]_, section 2.5.1.
This procedure assumes that the series is stationary.
References
----------
.. [1] Brockwell, Peter J., and Richard A. Davis. 2016.
Introduction to Time Series and Forecasting. Springer.
"""
max_spec = SARIMAXSpecification(endog, ar_order=ar_order)
endog = max_spec.endog
# Make sure we have a consecutive process
if not max_spec.is_ar_consecutive:
raise ValueError('Durbin-Levinson estimation unavailable for models'
' with seasonal or otherwise non-consecutive AR'
' orders.')
gamma = acovf(endog,
adjusted=adjusted,
fft=True,
demean=demean,
nlag=max_spec.ar_order)
# If no AR component, just a variance computation
if max_spec.ar_order == 0:
ar_params = [None]
sigma2 = [gamma[0]]
# Otherwise, AR model
else:
Phi = np.zeros((max_spec.ar_order, max_spec.ar_order))
v = np.zeros(max_spec.ar_order + 1)
Phi[0, 0] = gamma[1] / gamma[0]
v[0] = gamma[0]
v[1] = v[0] * (1 - Phi[0, 0]**2)
for i in range(1, max_spec.ar_order):
tmp = Phi[i - 1, :i]
Phi[i, i] = (gamma[i + 1] - np.dot(tmp, gamma[i:0:-1])) / v[i]
Phi[i, :i] = (tmp - Phi[i, i] * tmp[::-1])
v[i + 1] = v[i] * (1 - Phi[i, i]**2)
ar_params = [None] + [Phi[i, :i + 1] for i in range(max_spec.ar_order)]
sigma2 = v
# Compute output
out = []
for i in range(max_spec.ar_order + 1):
spec = SARIMAXSpecification(ar_order=i)
p = SARIMAXParams(spec=spec)
if i == 0:
p.params = sigma2[i]
else:
p.params = np.r_[ar_params[i], sigma2[i]]
out.append(p)
# Construct other results
other_results = Bunch({
'spec': spec,
})
return out, other_results
def innovations(endog, ma_order=0, demean=True):
"""
Estimate MA parameters using innovations algorithm.
Parameters
----------
endog : array_like or SARIMAXSpecification
Input time series array, assumed to be stationary.
ma_order : int, optional
Maximum moving average order. Default is 0.
demean : bool, optional
Whether to estimate and remove the mean from the process prior to
fitting the moving average coefficients. Default is True.
Returns
-------
parameters : list of SARIMAXParams objects
List elements correspond to estimates at different `ma_order`. For
example, parameters[0] is an `SARIMAXParams` instance corresponding to
`ma_order=0`.
other_results : Bunch
Includes one component, `spec`, containing the `SARIMAXSpecification`
instance corresponding to the input arguments.
Notes
-----
The primary reference is [1]_, section 5.1.3.
This procedure assumes that the series is stationary.
References
----------
.. [1] Brockwell, Peter J., and Richard A. Davis. 2016.
Introduction to Time Series and Forecasting. Springer.
"""
spec = max_spec = SARIMAXSpecification(endog, ma_order=ma_order)
endog = max_spec.endog
if demean:
endog = endog - endog.mean()
if not max_spec.is_ma_consecutive:
raise ValueError('Innovations estimation unavailable for models with'
' seasonal or otherwise non-consecutive MA orders.')
sample_acovf = acovf(endog, fft=True)
theta, v = innovations_algo(sample_acovf, nobs=max_spec.ma_order + 1)
ma_params = [theta[i, :i] for i in range(1, max_spec.ma_order + 1)]
sigma2 = v
out = []
for i in range(max_spec.ma_order + 1):
spec = SARIMAXSpecification(ma_order=i)
p = SARIMAXParams(spec=spec)
if i == 0:
p.params = sigma2[i]
else:
p.params = np.r_[ma_params[i - 1], sigma2[i]]
out.append(p)
# Construct other results
other_results = Bunch({
'spec': spec,
})
return out, other_results
B[:,:,1] = [[0,0],[0,0],[0,1]]
xhat5, err5 = VARMA(x,B,C)
#print(err5)
#in differences
#VARMA(np.diff(x,axis=0),B,C)
#Note:
# * signal correlate applies same filter to all columns if kernel.shape[1]<K
# e.g. signal.correlate(x0,np.ones((3,1)),'valid')
# * if kernel.shape[1]==K, then `valid` produces a single column
# -> possible to run signal.correlate K times with different filters,
# see the following example, which replicates VAR filter
x0 = np.column_stack([np.arange(T), 2*np.arange(T)])
B[:,:,0] = np.ones((P,K))
B[:,:,1] = np.ones((P,K))
B[1,1,1] = 0
xhat0 = VAR(x0,B)
xcorr00 = signal.correlate(x0,B[:,:,0])#[:,0]
xcorr01 = signal.correlate(x0,B[:,:,1])
print(np.all(signal.correlate(x0,B[:,:,0],'valid')[:-1,0]==xhat0[P:,0]))
print(np.all(signal.correlate(x0,B[:,:,1],'valid')[:-1,0]==xhat0[P:,1]))
#import error
#from movstat import acovf, acf
from statsmodels.tsa.stattools import acovf, acf
aav = acovf(x[:,0])
print(aav[0] == np.var(x[:,0]))
aac = acf(x[:,0])
def test_acovf_error(acovf_data):
with pytest.raises(ValueError):
acovf(acovf_data, nlag=250, fft=False)
def test_acovf_warns(acovf_data):
with pytest.warns(FutureWarning):
acovf(acovf_data)
plt.plot(wm,sdm/sdm[0], '-', wm[maxind], sdm[maxind]/sdm[0], 'o')
else:
plt.plot(wm, sdm, '-', wm[maxind], sdm[maxind], 'o')
plt.title('matplotlib')
if hastalkbox:
sdp, wp = stbs.periodogram(x)
plt.subplot(2,3,3)
if rescale:
plt.plot(wp,sdp/sdp[0])
else:
plt.plot(wp, sdp)
plt.title('stbs.periodogram')
xacov = acovf(x, unbiased=False)
plt.subplot(2,3,4)
plt.plot(xacov)
plt.title('autocovariance')
nr = len(x)#*2/3
#xacovfft = np.fft.fft(xacov[:nr], 2*nr-1)
xacovfft = np.fft.fft(np.correlate(x,x,'full'))
#abs(xacovfft)**2 or equivalently
xacovfft = xacovfft * xacovfft.conj()
plt.subplot(2,3,5)
if rescale:
plt.plot(xacovfft[:nr]/xacovfft[0])
else:
plt.plot(xacovfft[:nr])
def test_acovf_error(acovf_data):
with pytest.raises(ValueError):
acovf(acovf_data, nlag=250, fft=False)
print "T = %i s, t = %3.2f ms"%(T,1000.*newInt)
#try:
bins, lc = binLightCurve(timeSpan[0],timeSpan[0]+T, times, newInt)
lcAve = np.mean(lc)
print "<I> = %4.2f"%lcAve
lcVar = np.power(np.std(lc),2)
print "sigma(I)^2 = %3.3f"%lcVar
lcNorm = lc/lcAve
#plot timestream with T total seconds binned into t=(n+1)*intTime integration time bins
ax1.plot(bins,np.append(lcNorm,lcNorm[-1]),drawstyle='steps-post', label="%i s"%(T))
print "Calculating auto-covariance sequence..."
#acvs = acovf(lc,unbiased=True,demean=True) #* 1.0/(lcVar-lcAve)
acvs = acovf(lc,unbiased=False,demean=False)
#corr,ljb,pvalue = acf(lc,unbiased=True,qstat=True,nlags = T/newInt)
corr,ljb,pvalue = acf(lc,unbiased=False,qstat=True,nlags = T/newInt)
standalone_ljb, standalone_pvalue = acorr_ljungbox(lc)
print "Min(p-value) of acf Ljung-Box test = %f"%np.min(pvalue)
try:
print "Min(p) of acf LB at index %i of %i"%(np.where(pvalue==np.min(pvalue))[0],len(pvalue))
mostCorrLag = np.where(pvalue==np.min(pvalue))[0] * newInt*1000
print "Min(p) of acf LB at lag = %4.3f ms"%mostCorrLag
except TypeError:
print "Min(p) of acf LB at index %i of %i"%(np.where(pvalue==np.min(pvalue))[0][0],len(pvalue))
mostCorrLag = np.where(pvalue==np.min(pvalue))[0][0] * newInt*1000
def test_pandasacovf():
s = Series(range(1, 11))
assert_almost_equal(acovf(s), acovf(s.values))
def test_acovf_nlags(acovf_data, unbiased, demean, fft, missing):
full = acovf(acovf_data, unbiased=unbiased, demean=demean, fft=fft,
missing=missing)
limited = acovf(acovf_data, unbiased=unbiased, demean=demean, fft=fft,
missing=missing, nlag=10)
assert_allclose(full[:11], limited)
def test_pandasacovf():
s = Series(lrange(1, 11))
assert_almost_equal(acovf(s, fft=False), acovf(s.values, fft=False))
plt.figure(1)
plt.clf()
maxm = 15
# 太陽黒点数
with open('sunspot.txt', encoding='utf-8') as f:
data = np.array([float(k) for k in f.readlines()])
# データ数
N = len(data)
# 対数値に変換
#data = np.log10(data)
# 平均を引く
data = data - np.mean(data)
# 自己共分散関数
acovf = stattools.acovf(data)
# acovf = acovf * (N - 1) / N
# 連立方程式を直接解く方法
"""
print("Yule-Walker")
mar, arc_min, sig2_min, AIC_min = yule_walker(N, acovf, maxm)
print('Best model: m=', mar)
# スペクトル
t, logp1 = calc_spectrum(200, arc_min, sig2_min)
"""
# Levinson's algorithm
print()
print("Levinson method")
mar, arc_min, sig2_min, AIC_min = ar.levinson(acovf, N, maxm)
