'''Collection of alternative implementations for time series analysis
'''
'''
>>> signal.fftconvolve(x,x[::-1])[len(x)-1:len(x)+10]/x.shape[0]
array([ 2.12286549e+00, 1.27450889e+00, 7.86898619e-02,
-5.80017553e-01, -5.74814915e-01, -2.28006995e-01,
9.39554926e-02, 2.00610244e-01, 1.32239575e-01,
1.24504352e-03, -8.81846018e-02])
>>> sm.tsa.stattools.acovf(X, fft=True)[:order+1]
array([ 2.12286549e+00, 1.27450889e+00, 7.86898619e-02,
-5.80017553e-01, -5.74814915e-01, -2.28006995e-01,
9.39554926e-02, 2.00610244e-01, 1.32239575e-01,
1.24504352e-03, -8.81846018e-02])
>>> import nitime.utils as ut
>>> ut.autocov(s)[:order+1]
array([ 2.12286549e+00, 1.27450889e+00, 7.86898619e-02,
-5.80017553e-01, -5.74814915e-01, -2.28006995e-01,
9.39554926e-02, 2.00610244e-01, 1.32239575e-01,
1.24504352e-03, -8.81846018e-02])
'''
[docs]def acovf_fft(x, demean=True):
'''autocovariance function with call to fftconvolve, biased
Parameters
----------
x : array_like
timeseries, signal
demean : boolean
If true, then demean time series
Returns
-------
acovf : array
autocovariance for data, same length as x
might work for nd in parallel with time along axis 0
'''
from scipy import signal
x = np.asarray(x)
if demean:
x = x - x.mean()
signal.fftconvolve(x,x[::-1])[len(x)-1:len(x)+10]/x.shape[0]