def acovf_explicit(ar, ma, nobs):
'''add correlation of MA representation explicitely
'''
ir = arma_impulse_response(ar, ma)
acovfexpl = [np.dot(ir[:nobs-t], ir[t:nobs]) for t in range(10)]
return acovfexpl
def detectAO(model, alpha=0.05, robust=True):
""" Adapted from R's TSA library detectAO.
This function serves to detect whether there is any AO.
It implements the test statistic lambda_{1,t} proposed by Chang,
Chen and Tiao (1988).
"""
d = np.maximum(model.loglikelihood_burn, model.nobs_diffuse)
resid = model.filter_results.standardized_forecasts_error[0]
n_resid = len(resid)
pi_weights = arma_impulse_response(ar=-model.polynomial_ma,
ma=-model.polynomial_ar,
leads=n_resid)
rho2 = 1 / np.cumsum(pi_weights**2)
k = np.zeros(2 * len(resid) - 1)
k[-len(resid):] = resid[::-1]
omega = lfilter(b=pi_weights, a=np.ones(1), x=k)[n_resid - 1:] * rho2
if robust:
sigma = np.sqrt(np.pi / 2) * np.nanmean(np.abs(resid))
else:
sigma = np.sqrt(model.params['sigma2'])
lambda2T = (omega / (sigma * np.sqrt(rho2)))[::-1]
cutoff = norm.ppf(1 - alpha / (2 * len(lambda2T)))
out = (np.abs(lambda2T) > cutoff)
ind = np.array(np.where(out)).squeeze()
lambda2 = lambda2T[out].squeeze()
return lambda2, ind
def acovf_explicit(ar, ma, nobs):
'''add correlation of MA representation explicitely
'''
ir = arma_impulse_response(ar, ma)
acovfexpl = [np.dot(ir[:nobs - t], ir[t:nobs]) for t in range(10)]
return acovfexpl
def arma_acovf_historical(ar, ma, nobs=10):
if np.abs(np.sum(ar) - 1) > 0.9:
nobs_ir = max(1000, 2 * nobs)
else:
nobs_ir = max(100, 2 * nobs)
ir = arma_impulse_response(ar, ma, leads=nobs_ir)
while ir[-1] > 5 * 1e-5:
nobs_ir *= 10
ir = arma_impulse_response(ar, ma, leads=nobs_ir)
if nobs_ir > 50000 and nobs < 1001:
end = len(ir)
acovf = np.array([np.dot(ir[:end-nobs-t], ir[t:end-nobs])
for t in range(nobs)])
else:
acovf = np.correlate(ir, ir, 'full')[len(ir) - 1:]
return acovf[:nobs]
def arma_acovf_historical(ar, ma, nobs=10):
if np.abs(np.sum(ar) - 1) > 0.9:
nobs_ir = max(1000, 2 * nobs)
else:
nobs_ir = max(100, 2 * nobs)
ir = arma_impulse_response(ar, ma, leads=nobs_ir)
while ir[-1] > 5 * 1e-5:
nobs_ir *= 10
ir = arma_impulse_response(ar, ma, leads=nobs_ir)
if nobs_ir > 50000 and nobs < 1001:
end = len(ir)
acovf = np.array([np.dot(ir[:end-nobs-t], ir[t:end-nobs])
for t in range(nobs)])
else:
acovf = np.correlate(ir, ir, 'full')[len(ir) - 1:]
return acovf[:nobs]
def test_arma_impulse_response():
arrep = arma_impulse_response(armarep.ma, armarep.ar, leads=21)[1:]
marep = arma_impulse_response(armarep.ar, armarep.ma, leads=21)[1:]
assert_array_almost_equal(armarep.marep.ravel(), marep, 14)
# difference in sign convention to matlab for AR term
assert_array_almost_equal(-armarep.arrep.ravel(), arrep, 14)
def test_fi():
# test identity of ma and ar representation of fi lag polynomial
n = 100
mafromar = arma_impulse_response(lpol_fiar(0.4, n=n), [1], n)
assert_array_almost_equal(mafromar, lpol_fima(0.4, n=n), 13)
from statsmodels.tsa.arima_process import arma_generate_sample, arma_impulse_response
from statsmodels.tsa.arima_process import arma_acovf, arma_acf, ARIMA
#from movstat import acf, acovf
#from statsmodels.sandbox.tsa import acf, acovf, pacf
from statsmodels.tsa.stattools import acf, acovf, pacf
ar = [1., -0.6]
#ar = [1., 0.]
ma = [1., 0.4]
#ma = [1., 0.4, 0.6]
#ma = [1., 0.]
mod = ''#'ma2'
x = arma_generate_sample(ar, ma, 5000)
x_acf = acf(x)[:10]
x_ir = arma_impulse_response(ar, ma)
#print x_acf[:10]
#print x_ir[:10]
#irc2 = np.correlate(x_ir,x_ir,'full')[len(x_ir)-1:]
#print irc2[:10]
#print irc2[:10]/irc2[0]
#print irc2[:10-1] / irc2[1:10]
#print x_acf[:10-1] / x_acf[1:10]
# detrend helper from matplotlib.mlab
def detrend(x, key=None):
if key is None or key=='constant':
return detrend_mean(x)
elif key=='linear':
return detrend_linear(x)
def test_arma_impulse_response():
arrep = arma_impulse_response(armarep.ma, armarep.ar, leads=21)[1:]
marep = arma_impulse_response(armarep.ar, armarep.ma, leads=21)[1:]
assert_array_almost_equal(armarep.marep.ravel(), marep, 14)
# difference in sign convention to matlab for AR term
assert_array_almost_equal(-armarep.arrep.ravel(), arrep, 14)
def test_fi():
# test identity of ma and ar representation of fi lag polynomial
n = 100
mafromar = arma_impulse_response(lpol_fiar(0.4, n=n), [1], n)
assert_array_almost_equal(mafromar, lpol_fima(0.4, n=n), 13)
-0.00231864])
>>> # verified for points [[5,10,20,25]] at 4 decimals with Bhardwaj, Swanson, Journal of Eonometrics 2006
'''
print(lpol_fiar(0.4, n=20))
print(lpol_fima(-0.4, n=20))
print(np.sum((lpol_fima(-0.4, n=n)[1:] + riinv[1:])**2)) #different signs
print(np.sum((lpol_fiar(0.4, n=n)[1:] - riinv[1:])**2)) #corrected signs
#test is now in statsmodels.tsa.tests.test_arima_process
from statsmodels.tsa.tests.test_arima_process import test_fi
test_fi()
ar_true = [1, -0.4]
ma_true = [1, 0.5]
ar_desired = arma_impulse_response(ma_true, ar_true)
ar_app, ma_app, res = ar2arma(ar_desired,
2,
1,
n=100,
mse='ar',
start=[0.1])
print(ar_app, ma_app)
ar_app, ma_app, res = ar2arma(ar_desired,
2,
2,
n=100,
mse='ar',
start=[-0.1, 0.1])
print(ar_app, ma_app)
ar_app, ma_app, res = ar2arma(ar_desired, 2, 3, n=100,
from statsmodels.tsa.arima_process import arma_generate_sample, arma_impulse_response
from statsmodels.tsa.arima_process import arma_acovf, arma_acf, ARIMA
#from movstat import acf, acovf
#from statsmodels.sandbox.tsa import acf, acovf, pacf
from statsmodels.tsa.stattools import acf, acovf, pacf
ar = [1., -0.6]
#ar = [1., 0.]
ma = [1., 0.4]
#ma = [1., 0.4, 0.6]
#ma = [1., 0.]
mod = '' #'ma2'
x = arma_generate_sample(ar, ma, 5000)
x_acf = acf(x)[:10]
x_ir = arma_impulse_response(ar, ma)
#print x_acf[:10]
#print x_ir[:10]
#irc2 = np.correlate(x_ir,x_ir,'full')[len(x_ir)-1:]
#print irc2[:10]
#print irc2[:10]/irc2[0]
#print irc2[:10-1] / irc2[1:10]
#print x_acf[:10-1] / x_acf[1:10]
# detrend helper from matplotlib.mlab
def detrend(x, key=None):
if key is None or key == 'constant':
return detrend_mean(x)
elif key == 'linear':
plot_pacf(xt, lags=50, ax=ax_pacf)
plt.tight_layout()
return None
# Number of samples
n = 600
# Generate AR(1) dataset
ar = np.r_[1, 0.6]
ma = np.r_[1, 0.3]
ar1ma1_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ar1ma1_data)
# Impluse response curve
plt.plot(arima_process.arma_impulse_response(ar, ma, nobs=20))
plt.ylabel("Impact")
plt.xlabel("Lag")
# Build AR(1) model
ar1ma1 = smtsa.ARMA(ar1ma1_data.tolist(), order=(1, 1)).fit(maxlag=30,
method="mle",
trend="nc")
ar1ma1.summary()
# Optimize ARMA parameters
aicVal = []
for ari in range(1, 3):
for maj in range(1, 3):
arma_obj = smtsa.ARMA(ar1ma1_data.tolist(),
order=(ari, maj)).fit(maxlag=30,
plot_pacf(xt, lags=50, ax=ax_pacf)
plt.tight_layout()
return None
# Number of samples
n = 600
# Generate AR(1) dataset
ar = np.r_[1, 0.6]
ma = np.r_[1, 0.3]
ar1ma1_data = smtsa.arma_generate_sample(ar=ar, ma=ma, nsample=n)
plotds(ar1ma1_data )
# Impluse response curve
plt.plot(arima_process.arma_impulse_response(ar, ma, nobs=20))
plt.ylabel("Impact")
plt.xlabel("Lag")
# Build AR(1) model
ar1ma1 = smtsa.ARMA(ar1ma1_data.tolist(), order=(1, 1)).fit(
maxlag=30, method='mle', trend='nc')
ar1ma1.summary()
# Optimize ARMA parameters
aicVal=[]
for ari in range(1, 3):
for maj in range(1,3):
arma_obj = smtsa.ARMA(ar1ma1_data.tolist(), order=(ari, maj)).fit(maxlag=30, method='mle', trend='nc')
>>> # verified for points [[5,10,20,25]] at 4 decimals with Bhardwaj, Swanson, Journal of Eonometrics 2006
'''
print(lpol_fiar(0.4, n=20))
print(lpol_fima(-0.4, n=20))
print(np.sum((lpol_fima(-0.4, n=n)[1:] + riinv[1:])**2)) #different signs
print(np.sum((lpol_fiar(0.4, n=n)[1:] - riinv[1:])**2)) #corrected signs
#test is now in statsmodels.tsa.tests.test_arima_process
from statsmodels.tsa.tests.test_arima_process import test_fi
test_fi()
ar_true = [1, -0.4]
ma_true = [1, 0.5]
ar_desired = arma_impulse_response(ma_true, ar_true)
ar_app, ma_app, res = ar2arma(ar_desired, 2,1, n=100, mse='ar', start=[0.1])
print(ar_app, ma_app)
ar_app, ma_app, res = ar2arma(ar_desired, 2,2, n=100, mse='ar', start=[-0.1, 0.1])
print(ar_app, ma_app)
ar_app, ma_app, res = ar2arma(ar_desired, 2,3, n=100, mse='ar')#, start = [-0.1, 0.1])
print(ar_app, ma_app)
slow = 1
if slow:
ar_desired = lpol_fiar(0.4, n=100)
ar_app, ma_app, res = ar2arma(ar_desired, 3, 1, n=100, mse='ar')#, start = [-0.1, 0.1])
print(ar_app, ma_app)
ar_app, ma_app, res = ar2arma(ar_desired, 10, 10, n=100, mse='ar')#, start = [-0.1, 0.1])
print(ar_app, ma_app)
import statsmodels.tsa.arima_process as sm
import numpy as np
import matplotlib.pyplot as plt
AR = np.array([1, -0.9])
MA = np.array([1, 1.2])
arma_process = sm.arma_impulse_response(AR, MA, leads=20)
x = [1 * i for i in range(len(arma_process))]
print(x)
print(arma_process)
plt.scatter(x, arma_process)
plt.plot(x, arma_process)
plt.xlabel("Future Periods (h)")
plt.ylabel("Implus Responses")
plt.show()