I've got a multivariate time series $\mathbf{X}_t$, where $t$ is time and there are $p>1$ columns of $\mathbf{X}_t$. There is autocorrelation in the data. I'm interested in various functions of $\mathbf{X}_t$, and in quantifying their uncertainty.

For example, one of those functions is the distance of a given point $x$ from the mean of $\mathbf{X}_t$. This involves calculating the mean and covariance matrix of $\mathbf{X}_t$ so that I can calculate a mahalanobis distance. Since $\mathbf{X}_t$ is a time series, I'd like to use a stationary block bootstrap.

But how do I select a block length when I've got more than one variable? The algorithm of Politis & White (implemented in b.star in np in R) takes a vector of data. Or, when applied to a matrix of data, returns a variable-wise optimal block length.

The OP in this thread implies that the appropriate thing to do is to take the optimal (average) block length to be the maximum of the variable-wise optimal block lengths. Is this correct? Is it efficient?

Or, are there other approaches that don't even involve blocking?


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