Suppose I divide a time series into 10 sequential time windows, where each window contains 1000 data points.
I want to do test 5 different garch models using cross validation.
So for each model, I will fit it on 9 out of 10 time windows, and test it on data in the left-out window. This will be done for 10 different "left out" windows.
However, for each optimised garch model, the latent volatility variable will be a problem when I step over the "gap" created by the left-out window. The only time this won't be a problem is when the left-out window is either the first or last window. In the 8 other cases, I will have to take a guess at the initial volatility to use, using something such as the sample variance, or rolling volatility.
So 8 of the tests will have two starting points. And 2 of the models will have 1 starting point. And I will need to guess the volatility at each starting point.
So my question is, with all the guessing of these starting points... What is the recommended best practice? And how valid will be cross validation results be?