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I am trying to some time series regression, is there an optimal lookback window for regression?I am always also curious about in a pairs trading, how to determine the optimal lookback window to calibrate your spread?Not sure if these two are related. Any advice would be appreciated greatly.

There is no 'optimal', since the answer depends on many factors, not least of which include; asset class, execution speed, and trading costs. Nor, is it likely to be stable, since what might work in one regime might not work in another (eg high/low volatility).For marketing purposes, a sometimes used practice is to try lots of different window sizes and then present the one that gives the best performance, but without understanding what was driving that performance (eg say if it was due to some special circumstances specific to that time period, and those circumstances are not likely to persist). This is one reason why back-tested performance cannot always be trusted as an indicator of live trading performance.Good luck!

Thanks

QuoteOriginally posted by: yugmorf2There is no 'optimal', since the answer depends on many factors, not least of which include; asset class, execution speed, and trading costs. Nor, is it likely to be stable, since what might work in one regime might not work in another (eg high/low volatility).For marketing purposes, a sometimes used practice is to try lots of different window sizes and then present the one that gives the best performance, but without understanding what was driving that performance (eg say if it was due to some special circumstances specific to that time period, and those circumstances are not likely to persist). This is one reason why back-tested performance cannot always be trusted as an indicator of live trading performance.Good luck!All good comments. I will just add, that there is some theory, too, under the rubrik of 'optimal filtering'.An example of optimal filtering theory is Nelson & Foster. To the extent that you really understand what is driving your observations, there could be a rationale for a particular window size.

could go bayesian for that task and use all possible window sizes at once!

OLS Regression assumes that there is a constant (but noisy) relationship that you are attempting to discover.A rolling regression pre-supposes that the relationship changes over time. PRINCIPLE: Whenever you are trying to have it both ways, you are asking for trouble.Which is it (constant or changing)? Decide and select the right tool for the job.Bayesian Regression (Dynamic Linear Models) are your best bet.