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
 x1d array
observations of time series for which bds statistics is calculated
 max_diminteger
maximum embedding dimension
 epsilonscalar, optional
the threshold distance to use in calculating the correlation sum
 distancescalar, optional
if epsilon is omitted, specifies the distance multiplier to use when computing it
 Returns
 bds_statfloat
The BDS statistic
 pvaluefloat
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)})