B Z@sTdZddlmZddlZddlmZdddZdd Zd d Z d d Z dddZ dS)a  BDS test for IID time series References ---------- Broock, W. A., J. A. Scheinkman, W. D. Dechert, and B. LeBaron. 1996. "A Test for Independence Based on the Correlation Dimension." Econometric Reviews 15 (3): 197-235. Kanzler, Ludwig. 1999. "Very Fast and Correctly Sized Estimation of the BDS Statistic". SSRN Scholarly Paper ID 151669. Rochester, NY: Social Science Research Network. LeBaron, Blake. 1997. "A Fast Algorithm for the BDS Statistic." Studies in Nonlinear Dynamics & Econometrics 2 (2) (January 1). )divisionN)stats?cCsxt|}t|}|dk r.|dkr.td||dkrBtd||dkrZ||jdd}t|dddf||kS)a Calculate all pairwise threshold distance indicators for a time series Parameters ---------- x : 1d array observations of time series for which heaviside distance indicators are calculated epsilon : scalar, optional the threshold distance to use in calculating the heaviside indicators distance : scalar, optional if epsilon is omitted, specifies the distance multiplier to use when computing it Returns ------- indicators : 2d array matrix of distance threshold indicators Notes ----- Since this can be a very large matrix, use np.int8 to save some space. NrzCThreshold distance must be positive if specified. Got epsilon of %fz?Threshold distance must be positive. Got distance multiplier %f)Zddof)npasarraylen ValueErrorZstdabs)xepsilondistancenobsr3lib/python3.7/site-packages/statsmodels/tsa/_bds.pydistance_indicatorss rcCs|jdkstd|jd|jdks.td|dkr<|}n:t||d\}}|ddddf|ddddf}t|}t|t|d}||fS)a Calculate a correlation sum Useful as an estimator of a correlation integral Parameters ---------- indicators : 2d array matrix of distance threshold indicators embedding_dim : integer embedding dimension Returns ------- corrsum : float Correlation sum indicators_joint matrix of joint-distance-threshold indicators zIndicators must be a matrixrrz+Indicator matrix must be symmetric (square)N)ndimr shapecorrelation_sumrrZmeanZ triu_indices) indicators embedding_dimZindicators_jointZcorrsumrrrrrEs (rcCsNtd|f}t|d\|d<}x(td|D]}t|d\|d|f<}q,W|S)a9 Calculate all correlation sums for embedding dimensions 1:max_dim Parameters ---------- indicators : 2d array matrix of distance threshold indicators max_dim : integer maximum embedding dimension Returns ------- corrsums : 1d array Correlation sums r)rrrr)rzerosrrange)rmax_dimZcorrsumsirrrcorrelation_sumsjs rc Cs t|}t|d\}}|ddd|d|||d|d}td|df}xtd|dD]}d}x.td|D] } |||| |d| 7}qWd||d||dd|d||d||d|d|d|df<qrW||fS)a" Calculate the variance of a BDS effect Parameters ---------- indicators : 2d array matrix of distance threshold indicators max_dim : integer maximum embedding dimension Returns ------- variances : float Variance of BDS effect rrr)rrsumrrr) rrr corrsum_1dim_k variancesrZtmpjrrr_vars &0r&rc CsVt|}t|}|dks"||kr.td|t|||}t||}t||\}}t|} td|df} td|df} xt d|dD]} | d} || }t || d| dfd\}}|d| df}||| }| d| df}t|||| d| df<dt j t| d| df}|| d| df<qWt| t| fS)a 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 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)}) rzFMaximum embedding dimension must be in the range [2,len(x)-1]. Got %d.rNr)rrrr rrr&ZsqrtrrrrZnormZsfr Zsqueeze)r rr r Z nobs_fullrZ corrsum_mdimsr$r#ZstddevsZ bds_statsZpvaluesrZninitialrr!r"Z corrsum_mdimZeffectZsdZpvaluerrrbdss,'     "r')Nr)rNr) __doc__Z __future__rZnumpyrZscipyrrrrr&r'rrrrs   ,%%