# Decorrelating Two Time Series

Suppose that I have two time series $\{x_1, \ldots,x_t\}$ and $\{y_{1+k}, \ldots,y_t\}$ which have some level of correlation over an overlapping time period. What techniques can I use to decorrelate these two time series? Perhaps multivariate AR models or something of the like?

• What do you mean by "decorrelate", and what is your ultimate goal? By the way, multivariate AR is commonly known as vector AR, i.e. VAR (there is a tag for it here, too). – Richard Hardy Oct 13 '16 at 16:55
• Cross-correlation statistics between two time series are often (always) misleading . Take a look at empslocal.ex.ac.uk/people/staff/dbs202/cat/stats/corr.html for more .... – IrishStat Oct 13 '16 at 17:37
• By "decorrelate," I've assumed you really mean *whitening. * This Wiki article describes it this way, "A whitening transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix meaning that they are uncorrelated and all have variance 1. The transformation is called "whitening" because it changes the input vector into a white noise vector." en.wikipedia.org/wiki/Whitening_transformation Is this what you mean? – Mike Hunter Oct 13 '16 at 17:47

Depending on what you want to do, you can build an ARMA model or similar to take into account the correlation in the your predictions.

If you are simply trying to use the data for something else that assumes there is no correlation, you can try to either transform the data sets or, perhaps with more success, resample the data sets at a more coarse frequency such that the correlation disappears.

You can create a cross-correlation plot (similar to the one below) to check for correlation between two time series. Any insignificant correlation you can ignore, as well as most correlations at higher lags (depending on how much data you have; calculating the correlation with a few data points can create spurious significant results). Hope that helps!

What is the purpose of decorrelating?

Maybe you may want to simulate them without correlation, if that is the case, you should simply ignore the other while you study X or Y.

• This does not constitute and "answer" to the OPs question and, as such, should be treated as a comment. – Mike Hunter Oct 13 '16 at 17:43