U md@sTdZddlZddlmZddlmZdddZdd 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). N)stats) array_like?cCspt|d}|dk r&|dkr&td||dkr:td||dkrR||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. xNrzCThreshold distance must be positive if specified. Got epsilon of %fz?Threshold distance must be positive. Got distance multiplier %f)Zddof)r ValueErrorZstdnpabs)repsilondistancer M/home/sam/Atlas/atlas_env/lib/python3.8/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 : ndarray 2d array of distance threshold indicators embedding_dim : int 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)ndimrshapecorrelation_sumlenrZmeanZ triu_indices) indicators embedding_dimZindicators_jointZcorrsumnobsr r r rDs (rcCsJtd|f}t|d\|d<}td|D]}t|d\|d|f<}q*|S)a3 Calculate all correlation sums for embedding dimensions 1:max_dim Parameters ---------- indicators : 2d array matrix of distance threshold indicators max_dim : int maximum embedding dimension Returns ------- corrsums : ndarray Correlation sums r)rrrr)rzerosrrange)rmax_dimZcorrsumsir r r correlation_sumshs rc Cst|}t|d\}}|ddd|d|||d|d}td|df}td|dD]}d}td|D] } |||| |d| 7}qd||d||dd|d||d||d|d|d|df<qp||fS)a Calculate the variance of a BDS effect Parameters ---------- indicators : ndarray 2d array of distance threshold indicators max_dim : int maximum embedding dimension Returns ------- variances : float Variance of BDS effect rrr)rrsumrrr) rrr corrsum_1dim_k variancesrtmpjr r r _vars,r&rc CsVt|ddd}t|}|dks&||kr2td|t|||}t||}t||\}}t|} td|df} td|df} t d|dD]} | d} || }t || d| dfd\}}|d| df}||| }| d| df}t|||| d| df<dt j t| d| df}|| d| df<qt| t| fS)a BDS Test Statistic for Independence of a Time Series Parameters ---------- x : ndarray Observations of time series for which bds statistics is calculated. max_dim : int The maximum embedding dimension. epsilon : {float, None}, optional The threshold distance to use in calculating the correlation sum. distance : float, optional Specifies the distance multiplier to use when computing the test statistic if epsilon is omitted. 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)}) rr)rrzFMaximum embedding dimension must be in the range [2,len(x)-1]. Got %d.Nr)rrrrrr&rsqrtrrrrZnormZsfr Zsqueeze)rrr r Z nobs_fullrZ corrsum_mdimsr#r"ZstddevsZ bds_statsZpvaluesrZninitialrr r!Z corrsum_mdimZeffectsdZpvaluer r r bdss.&    "r))Nr)rNr) __doc__numpyrZscipyrZstatsmodels.tools.validationrrrrr&r)r r r r s   *$$