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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.

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  • $\begingroup$ 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. $\endgroup$
    – noob2
    Jun 21 at 18:12
  • $\begingroup$ @noob2 I guess that's a bit more robust than a naïve percent change between the two in a window. Thanks for the suggestion $\endgroup$ Jun 21 at 20:00
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If it is traditional pairs trading in a quantitative ways, as in two unit-root non stationary time series where the return is best described as uncorrelated innovations, you can frequently find that a linear combination of the two is unit-root stationary and, thus, mean reverting. (if that is the case will depend on the underlyings though - e.g. 1980s Royal Dutch discount relative to shell).

This uses frameworks called Cointegration and Error Correction Models.

There is for example "Analysis of Financial Time Series" by Ruey S. Tsay (mainly basic ideas), "Pairs Trading - Quantitative Methods and Analysis" by Vidyamurthy and "Statistical Arbitrage: Algorithmic Trading Insights and Techniques" by Pole

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