is anyone here familiar with loss functions like MSE? I have basically 1000 simulated return matrices (T x N where T=700 and N = 5 stocks). Now I have to calculate the one step ahead volatility forecasts on the simulated returns using different models for eg multivariate EWMA,DCC GARCH and input these forecasts into the loss function to select a superior model. I have two questions regarding how to proceed from here:
1) should I calculate the one step ahead volatility forecasts based on the last period's return only? Because both the models mentioned above predict a different covariance forecast for each time period based on the previous time period's forecast.
2) When it comes to choosing a volatility proxy to input in the loss function, the paper I am following mentions that they have used the outer product of error terms (Et' * Et). Now my understanding of loss functions is fairly limited but as far as I know I have to compare the forecasts with the real volatility denoted by the proxy so I am assuming I should take the outer product of error terms on the real return data (as opposed to the simulated returns) but since I have only simulated returns for 700 periods while the actual return data I have is for 1000 periods, should I take the time into consideration when taking the outer product because each time period has a different covariance matrix (1000 periods vs 700 periods)?
Thanks in advance!