M/PhLdZddlZddlmZddlmZd dZdZdZ d Z d d Z 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?ct|d}||dkrtd|z|dkrtd|z|||dz}tj|dddf|z |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)ddof)r ValueErrorstdnpabs)repsilondistances T/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/_bds.pydistance_indicatorsrs0 1cAw!||.07899 91}}79ABCC C QUUU]]* 6!AAAtG*q. ! !G ++c|jdkstd|jd|jdkstd|dkr|}n3t||dz \}}|ddddf|ddddfz}t |}t j|t j|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)ndimr shapecorrelation_sumlenr mean triu_indices) indicators embedding_dimindicators_jointcorrsumnobss rrrDs( ?a  6777  A *"21"5 5 5FGGG%-j-!:KLL%abb!""f-j"crc.BB  Dg&rtQ'?'?@AAG $ $$rctjd|f}t|d\|d<}td|D]}t|d\|d|f<}|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)r zerosrrange)rmax_dimcorrsumsis rcorrelation_sumsr'hsm"xG %%H!0Q!?!?HTNJ 1g  DD%4Z%C%C"A Orc&t|}t|d\}}|ddzd|zz d|zz||dz z|dz zz }tjd|dz f}t d|dzD]h}d}t d|D]} |||| z z|d| zzzz }d||zd|zz|dz dz|d|zzzz|dz|z|d|zdz zzz z|d|dz f<i||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)rrsumr r"r#) rr$r corrsum_1dim_k variancesrtmpjs r_varr2s z??D%j!44OL! ..  Q  # # % %*..*:*:(: : 4 D1H%2 4A!Wq[)**Iq'A+..NN q-(( D DA A )*\AE-BC CCC() }  G a! # q=7H(I J KA  "lQ5F5J&K L M)N !]1_$%% a<rrc \t|dd}t|}|dks||krtd|zt|||}t ||}t ||\}}t j|} t jd|dz f} t jd|dz f} td|dzD]} | dz } || z }t|| d| dfd\}}|d| dz f}||| zz }| d| dz f}t j||z|z | d| dz f<dtj t j| d| dz fz}|| d| dz f<t j| t j| 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)rrr rr'r2r sqrtr"r#rrnormsfr squeeze)rr$rr nobs_fullr corrsum_mdimsr/r.stddevs bds_statspvaluesrninitialr r,r- corrsum_mdimeffectsdpvalues rbdsrBsL 1c"""AAI{{g**24;<== =%Q::J%Z99M G,,LIqgi  G!Wq[)**Ih7Q;'((Gq'!),,// !A%8#**XYY 5I*JANN a$Q (9%9: }!<= Q )) *+-'$--&*@2*E !]Q&&'5:== !]Q5F2F(G!H!HIII(.=1$$%% :i "*W"5"5 55r)Nr)rNr) __doc__numpyr scipyrstatsmodels.tools.validationrrrr'r2rBrrrHs&333333',',',',T!%!%!%H4!!!HM6M6M6M6M6M6r