I have a time series $x_t$ which may go through different phases of volatility. One example might be some stock that has high variance from 9 AM to 11 AM, low variance from 11 AM to 2 PM, and then high variance again afterwards. Is there a way to identify these different periods of variance?
I am thinking of taking a sliding window of length $L$, computing the variance in that window and running change point detection on that, but I think this requires me to know the distribution of the estimated variance. Another idea I had was to take the variance of the windows and try to fit a Markov chain to it, but I don't know beforehand how many states there should be.
Sorry, the motivating example is not just in finance. I would like to have a way to model "risk" in a time series, which might be risk associated with a financial asset. Another example is in wind energy production - energy produced from wind turbines is highly volatile and unpredictable, but it would be nice to have a learning algorithm that could identify what days of the month is variance of wind energy production high and when is it low