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 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
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])
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])
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 scikits.statsmodels.api as sm
print sm.regression.yule_walker(x, 10)
import matplotlib.pyplot as plt
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 scikits.statsmodels.api as sm
print sm.regression.yule_walker(x, 10)
import matplotlib.pyplot as plt
#ax = plt.axes()
plt.plot(x)
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 scikits.statsmodels.tsa.stattools import acovf, acf
aav = acovf(x[:,0])
print aav[0] == np.var(x[:,0])
aac = acf(x[:,0])
