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)})