# statsmodels.tsa.stattools.bds¶

statsmodels.tsa.stattools.bds(x, max_dim=2, epsilon=None, distance=1.5)[source]

Calculate the BDS test statistic for independence of a time series

Parameters: x (1d array) – observations of time series for which bds statistics is calculated max_dim (integer) – maximum embedding dimension epsilon (scalar, optional) – the threshold distance to use in calculating the correlation sum distance (scalar, optional) – if epsilon is omitted, specifies the distance multiplier to use when computing it bds_stat (float) – The BDS statistic pvalue (float) – The p-values associated with the BDS statistic

Notes

The null hypothesis of the test statistic is for an independent and identically distributed (i.i.d.) time series, and an unspecified alternative hypothesis.

This test is often used as a residual diagnostic.

The calculation involves matrices of size (nobs, nobs), so this test will not work with very long datasets.

Implementation conditions on the first m-1 initial values, which are required to calculate the m-histories: x_t^m = (x_t, x_{t-1}, … x_{t-(m-1)})