Multivariate Stochastic Volatility model

Questions
1

Hi All,
For last few days I have been trying to implement a multivariate Stochastic Volatility model similar to the example - https://docs.pymc.io/notebooks/stochastic_volatility.html. But I am having trouble in creating a time varying covariance Matrix. I can see that there are already few posts on this topic where @junpenglao & @twiecki have giving some suggestions. I am very new to the Bayesian world so any sample code will be very helpful.

While at it, let me also share how I ended up with trying to generate Multivariate Stochastic Volatility model. I welcome any suggestion/comment on the idea.

I have a multi variate non stationary time series (for example some macro economic indicators and some stock prices). An RL (deep reinforcement learning) agent is trained to make decision of buying and selling the stocks based on the macro economic indicator data. The problem with the agent is as expected, it is over fitting to the data. It is happening since from an RL point of view this whole time series is just one data point. To solve the over fitting problem, I was thinking of generating more multivariate time series data by sampling from the posterior distribution. Does this idea make sense ?

2

So your aim is to write a generative model to generate data? If you are not doing inference, it might be easier to write it in numpy/scipy.

Otherwise, you can try Gaussian process, it is not the same formulation as a MV stochastic volatility model, but it “learns” the time series and can generate time series once you fit it.

3

Can a Gaussian process capture the change in covariance over time ?

4

Yes :slight_smile: