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Cointegration and Error Correction for Time-Series Divergence

Article Quant Q&A · Author: Little Code
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Summary

The document asks how to quantify rolling divergence or convergence between financial series, using asset prices and a relative strength index as an example. Its answer redirects the problem toward pairs trading when the series are nonstationary and their returns can be treated as uncorrelated innovations.

The proposed framework is cointegration: a linear combination of two nonstationary series may be stationary and mean reverting. An error correction model can then describe how deviations from that long-run relationship evolve. This offers a statistical basis for convergence analysis, unlike measuring distance from a fixed target. The answer does not give an estimation procedure, rolling-window choices, tests, or empirical results, and it cautions that whether cointegration exists depends on the assets being studied.

Key ideas

  • Cointegration can identify a stationary, mean-reverting combination of nonstationary series.
  • Error correction models describe adjustment toward a long-run relationship.
  • The suitability of this framework depends on the selected assets.
  • The document does not specify tests or procedures for a rolling analysis.

Tags

Pairs tradingMean reversionStatistics
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# Quantative way to evaluate divergence and convergence between time series


# 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.

## Answer by AKdemy (score 2, accepted)

https://quant.stackexchange.com/a/65669

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.