Joint Distribution of Correlated Variables with Markov Switching

I am modeling a portfolio of correlated assets whose lack of liquidity can be reasonably described by a Markov-switching model. That is, not only is movement size among assets correlated, but so is whether there is any movement at all. For example: Asset B generally moves only when Asset A moves, and when they do move, their moves are correlated. Because moves in the two assets are vastly differently distributed, I have opted to incorporate the correlation through a t-copula with 3 degrees of freedom (I prefer to err on the side of caution and prefer to have too-heavy tails than too-thin ones), but I am still at a loss for how to model the switching component.

My question is this: is there a mechanism I can incorporate to incorporate the coincidental timing of regime switches between the assets, to better reflect the dynamics of the underlying data?

A few notes:

• Assets consists of daily electricity futures price changes
• My copula is based on Pearson correlation
• Frequency of changes increases as asset maturity approaches
• Data are stationary (based on ADF Test with alpha = 0.05)
• Implementation is in Python with Pandas, NumPy, SciPy and StatsModels

Thank you for your kind assistance!

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