statsmodels.tsa.stattools.ccf#

statsmodels.tsa.stattools.ccf(x, y, adjusted=True, fft=True, *, nlags=None, alpha=None, result_object=None)[source]#

The cross-correlation function

Parameters:

x, yarray_like: The time series data to use in the calculation.
adjustedbool, optional: If True, then denominators for cross-covariance are the number of overlapping observations at each lag k, min(m, n-k), otherwise n.
fftbool, optional: If True, use FFT convolution. This method should be preferred for long time series.
nlagsint, optional: Number of lags to return cross-correlations for. If not provided, the number of lags equals len(x).
alphafloat, optional: If a number is given, the confidence intervals for the given level are returned. For instance if alpha=.05, 95 % confidence intervals are returned where the standard deviation is computed according to 1/sqrt(len(x)).
result_objectbool, optional: Flag controlling whether a CcfResult is returned. When alpha is not None a CcfResult is always returned; it holds the same two values as the legacy tuple it replaces. When alpha is None a bare array is returned unless result_object=True, which additionally yields a CcfResult with confint set to None.

Returns:

CcfResult or ndarray

When alpha is not None (or result_object=True), a result object with fields:

ccfndarray: The cross-correlation function of x and y: the element at index k is the correlation between {x[k], x[k+1], …, x[n]} and {y[0], y[1], …, y[m-k]}, where n and m are the lengths of x and y, respectively.
confintndarray or None: Confidence intervals for the CCF at lags 0, 1, …, nlags-1 using the level given by alpha and the standard deviation calculated as 1/sqrt(len(x)) [1]. Shape (nlags, 2). None when alpha is None.

When alpha is None a bare ndarray of cross-correlations is returned instead.