# naginterfaces.library.tsa.multi_​xcorr¶

naginterfaces.library.tsa.multi_xcorr(x, y, nl)[source]

multi_xcorr calculates cross-correlations between two time series.

For full information please refer to the NAG Library document for g13bc

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/g13/g13bcf.html

Parameters
xfloat, array-like, shape

The values of the series.

yfloat, array-like, shape

The values of the series.

nlint

, the maximum lag for calculating cross-correlations.

Returns
sfloat

The ratio of the standard deviation of the series to the standard deviation of the series, .

r0float

The cross-correlation between the and series at lag zero.

rfloat, ndarray, shape

contains the cross-correlations between the and series at lags , , for .

statfloat

The statistic for testing for absence of cross-correlation.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

One or both of the and series have zero variance.

Notes

Given two series and the function calculates the cross-correlations between and lagged values of :

where

and similarly for .

The ratio of standard deviations is also returned, and a portmanteau statistic is calculated:

Provided is large, much less than , and both are samples of series whose true autocorrelation functions are zero, then, under the null hypothesis that the true cross-correlations between the series are zero, has a -distribution with degrees of freedom. Values of in the upper tail of this distribution provide evidence against the null hypothesis.

References

Box, G E P and Jenkins, G M, 1976, Time Series Analysis: Forecasting and Control, (Revised Edition), Holden–Day