# Quantative way to evaluate divergence and convergence between time series

Given, for example, two time series asset price and its associated relative strength index (RSI), what would be the quant way to evaluate convergence or divergence on a rolling-window basis? I'm guessing WindowRMSD (root mean square deviation) would not be appropriate and there are more suitable options out there?

Also something like CUSUM Control Charts would not be appropriate because it involves defining a "target" from which divergence is measured. This of course would not be suitable for financial time-series because the "target" would be constantly moving.

• I am not sure what you are looking for. In Pairs Trading they compare where the ratio of two stock prices is currently, to where the ratio has been on average over the last N (say 20) days. They express this difference in terms of how many standard deviations we are now from the mean, where the standard deviation and the mean are both taken over the last N days. You can easily do this calculation in Excel. HTH. Jun 21 at 18:12
• @noob2 I guess that's a bit more robust than a naïve percent change between the two in a window. Thanks for the suggestion Jun 21 at 20:00

This uses frameworks called Cointegration and Error Correction Models.