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
Returns:  bds_stat (float) – The BDS statistic
 pvalue (float) – The pvalues 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 m1 initial values, which are required to calculate the mhistories: x_t^m = (x_t, x_{t1}, … x_{t(m1)})