Estimating Regime-Switching Correlation and Covariance Matrices

Summary

The document outlines a proposed workflow for estimating multivariate covariance under changing market regimes. It begins by fitting a GARCH(1,1) model to each series, removing estimated volatility, and fitting a hidden Markov model to classify observations into high, medium, and low regimes. One proposed approach pools observations assigned to each regime to estimate a separate correlation matrix, while the questioner worries that fitting GARCH to the full sample may impose overly stable relationships.

The questions focus on whether regime-specific matrices should remain constant, how to fit dynamic correlation models, whether to use all observations from a regime or only data since its latest transition, and how dependence should carry across regime changes. No answers, empirical evidence, or selected model are provided. The document therefore frames modeling choices rather than prescribing a solution; it leaves issues such as parameter stability, limited observations per regime, and model fit unresolved.

Key ideas

• The proposed workflow combines GARCH volatility estimates with hidden Markov regime classification.
• Pooling observations by regime can produce a separate correlation matrix for each state.
• Dynamic correlation estimation raises a choice between pooling all state observations and using only the latest regime segment.
• The document asks how dependence should evolve across time and regime transitions but provides no answers.

Tags

# modeling regime switching for Correlation matrix


# modeling regime switching for Correlation matrix












I am trying to estimate covariance in multiple time series. However, I want to do this using a regime-switching framework. So, I start with fitting a GARCH(1,1) model and then de-volatalize the series. Using this series I try to fit an HMM. Suppose I have only 3 regimes ie: high, medium and low. Now I can assume that correlation is constant across a regime in which case I can use all sample data from a particular regime and fit 3 separate correlation matrices to multiple time series. Also, entire data series was used to fit the GARCH model which implies both correlation and convariance remain constant across a regime for the entire period in consideration. I have a few questions

- Is it a problem to have a constant correlation and convariance matrix for a particular regime for the entire time series?

- In the above procedure if I want the correlation in a time period for a regime to not be constant, then I will can fit a dynamic correlation model. What regime data should be used to fit the dynamic model? Should it be all data for the regime or just data for this regime since the last switch? What if the dynamic model fails to fit?

- How does correlation one time period affect the correlation in another regime in the next period?

- How does correlation one time period affect the correlation in the same regime in the next period, ie after a switch?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.