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I am trying to forecast an index option's implied volatility using a sliding window regression and I'm a little confused on how I can go about cross validating with respect to the training and test set size. What I have so far is I cross validate the training window size by fixing the test set to be 1. I then do my sliding regression across time as such: enter image description here

Now this generates my predictions over all the points after my 1st training window and I calculate the $R^{2}$ across this set of predictions and get an optimal training window size from this. I then fix my training window to be this size and do the same cross validation procedure but this time varying my test set size, from 1 to 100s.

Intuitively, it makes sense that my $R^{2}$ is going to generally be monotonically decreasing as I expand the test set size since I'm not incorporating new, relevant info quick enough. But I am wondering what are the cons of choosing a test set size of just 1?

I'm doing OLS so computational intensity of retraining the model at every step is negligible and I don't see how this would be overfitting the model.

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Maybe I'm not understanding correctly but your test set size is all your data points (minus the initial training set) right? The size 1 is the forecasting horizon, how many data points forward you forecast for a given training dataset. There's no issue setting that to 1 if it makes sense for your application.

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  • $\begingroup$ Yes, this is correct. I was just wondering if there's any direct issue with my forecasting horizon being 1 apart from cost of retraining at every step, but I think it makes sense for my purposes $\endgroup$ Oct 13, 2023 at 16:48

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