# Calculating covariance matrix with different time periods

Instead of using a covariance matrix that was calculated by using the entire sample to simulate results, I am interested in possibly using a covariance matrix that was calculated by using a selected part of the sample. I am wondering if what I am doing makes theoretical sense and trying to find any relevant academic works (suggestions to papers or books will be helpful).

For example, let's say I have VAR model with S&P stock index returns and U.S. inflation rates. Although the covariance found by using the data in the past ten years might be small, during the times of crisis, it rose from time to time. So, when I try to generate a scenario when S&P drops significantly, I might attempt to use a covariance that is calculated by using the data from crisis period.

Any thought on this approach?

What you are suggesting is essentially a Mixture model of sorts. Here the `hidden' variable is the market state at the moment. To match up exactly with a textbook, assume the portfolio has mean 0 and variance described by the market state i.e. $X_{i} = N(0,\Sigma_{i})$. What you are saying is can I have
$Y = \sum w_{i}X_{i}$
where $w_{i}$ is the indicator of the state you are in. This is the standard Gaussian mixture model with hidden variables. Look up standard EM procedures to tackle such problems