LjungBox¶

class hyppo.time_series.LjungBox(max_lag=0)¶

Ljung-Box for Cross Correlation (CorrX) test statistic and p-value.

Parameters: max_lag (int, default: 0) -- The maximum number of lags in the past to check dependence between x and the shifted y. If None, then max_lag=np.ceil(np.log(n)). Also the M hyperparmeter below.

Notes

The statistic can be derived as follows 1:

Let $x$ and $y$ be $(n, 1)$ and $(n, 1)$ series respectively, which each contain $y$ observations of the series $(X_{t})$ and $(Y_{t})$ . Similarly, let $x [j : n]$ be the $(n - j, p)$ last $n - j$ observations of $x$ . Let $y [0 : (n - j)]$ be the $(n - j, p)$ first $n - j$ observations of $y$ . Let $M$ be the maximum lag hyperparameter. The cross distance correlation is,

{Ljung - Box}_{n} (x, y) = n (n + 2) \sum_{j = 1}^{M} \frac{ρ^{2} (x [j : n], y [0 : (n - j)])}{n - j}

where $rho$ is the Pearson correlation coefficient. The p-value returned is calculated either via chi-squared distribution or using a permutation test.

References

1: Ronak Mehta, Jaewon Chung, Cencheng Shen, Ting Xu, and Joshua T. Vogelstein. Independence Testing for Multivariate Time Series. arXiv:1908.06486 [cs, stat], May 2020. arXiv:1908.06486.

Methods Summary

`LjungBox.statistic`(x, y)	Helper function that calculates the Ljung-Box cross correlation test statistic.
`LjungBox.test`(x, y[, reps, workers, auto, ...])	Calulates the time-series test test statistic and p-value.

LjungBox.statistic(x, y)¶

Helper function that calculates the Ljung-Box cross correlation test statistic.

Parameters

x,y (ndarray of float) -- Input data matrices. x and y must have the same number of samples. That is, the shapes must be (n, 1) and (n, 1) where n is the number of samples.

Returns

stat (float) -- The computed Ljung-Box statistic.
opt_lag (int) -- The computed optimal lag.

LjungBox.test(x, y, reps=1000, workers=1, auto=True, random_state=None)¶

Calulates the time-series test test statistic and p-value.

Parameters

x,y (ndarray of float) -- Input data matrices. x and y must have the same number of samples. That is, the shapes must be (n, p) and (n, q) where n is the number of samples and p and q are the number of dimensions. Alternatively, x and y can be distance matrices, where the shapes must both be (n, n).
reps (int, default: 1000) -- The number of replications used to estimate the null distribution when using the permutation test used to calculate the p-value.
workers (int, default: 1) -- The number of cores to parallelize the p-value computation over. Supply -1 to use all cores available to the Process.
is_distsim (bool, default: False) -- Whether or not x and y are input matrices.

Returns

stat (float) -- The computed time-series independence test statistic.
pvalue (float) -- The computed time-series independence p-value.
null_dist (list) -- The time-series independence p-value.

DcorrX

DiscrimOneSample