!gJdZddlZddlmZddlmZd dZdZdZ dZ d d Z y) 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_likect|d}||dkrtd|z|dkrtd|z|||jdz}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 Q/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/tsa/_bds.pydistance_indicatorsrs0 1cAw!|.0789 91}79ABC C QUUU]* 66!AtG*q. !G ++cb|jdk(s td|jd|jdk(s td|dk(r|}n)t||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 677   A *"2"21"5 5FGG%-j-!:KL%ab!"f-j"crc.BB  Dgg&rtQ'?@AG $ $$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&hsc"xxG %H!0Q!?HTNJ 1g D%4Z%C"A D Orct|}t|d\}}|jddzjd|jzz d|zz||dz z|dz zz }tjd|dz f}t d|dzD]f}d}t d|D]} |||| z z|d| zzzz }d||zd|zz|dz dz|d|zzzz|dz|z|d|zdz zzz z|d|dz f<h||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_varr1sh z?D%j!4OL! .. Q  # # %*..*:(: : 4 D1H%2 4A!Wq[)*Iq'A+.N q-( DA A )*\AE-BC CC D() }  G a! # q=7H(I J KA  "lQ5F5J&K L M)N !]1_$% N a<rc t|dd}t|}|dks||k\rtd|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<dtjjt 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&r1r sqrtr!r"rrnormsfr squeeze)rr#r r nobs_fullr corrsum_mdimsr.r-stddevs bds_statspvaluesrninitialrr+r, corrsum_mdimeffectsdpvalues rbdsrAsL 1c"AAI{g*24;<= =%Q:J%Z9M G,LIqggi G!Wq[)*Ihh7Q;'(Gq'!),/ !A%8#**XY 5I*JAN a$Q (9%9: }!<= Q )) *+-''$-&*@2*E !]Q&&'5::== !]Q5F2F(G!HII(.=1$$%%/( ::i "**W"5 55r)N?)rNrB) __doc__numpyr scipyrstatsmodels.tools.validationrrrr&r1rArrrHs2&3',T!%H4!HM6r