TimeSeriesSRC.gpac¶

TimeSeriesSRC.gpac(acf, nrows, ncols)¶

Compute the Generalized Partial Autocorrelation (GPAC) table.

Each cell (j, m) of the GPAC is the ratio of two determinants built from the ACF, following the Woodward & Gray (1981) construction. The table simultaneously identifies the MA order (row index + 1) and AR order (column index + 1) of an ARMA process: cells in an MA(q) column pattern or AR(p) row pattern help select model orders.

Parameters:

acf (array-like, shape (1, 2*L+1) or (2*L+1,) or (2*L,)) – Autocorrelation sequence. If two-sided (zero lag at center), the positive-lag half is extracted automatically. If one-sided (zero lag first), it is used directly.
nrows (int) – Number of GPAC rows (numerator orders 1 .. nrows).
ncols (int) – Number of GPAC columns (denominator orders 1 .. ncols).

Returns:

gpac_array – GPAC table. Row j corresponds to MA order j+1; column m corresponds to AR order m+1.

Return type:

ndarray, shape (nrows, ncols)

Notes

If nrows + ncols exceeds the half-length of the ACF, ncols is silently truncated and a UserWarning is issued.

Examples

>>> import numpy as np
>>> from scipy.signal import lfilter
>>> from TimeSeriesSRC.basefunctions.xcorr import func_xcorr
>>> from TimeSeriesSRC.basefunctions.gpac import func_gpac
>>> e = np.random.default_rng(0).standard_normal(500)
>>> y = lfilter([1], [1, -0.8], e)
>>> acf = func_xcorr(y, y, 25, 'biased')
>>> G = func_gpac(acf, nrows=5, ncols=5)
>>> G.shape
(5, 5)