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2

The basic approach is as follows: When you estimate the HMM you estimate three things: When you are in which state The drifts of your assets The covariance matrices of your assets You would then take 2. and 3. for each state (1.) and feed it into your favourite allocation optimizer to estimate your optimal portfolio for each state. Voila!

1

I don't think you'll find anything. Why don't you contact the authors? They must have some code to generate the HMM simulations in the paper, maybe they can share the code with you? Have you checked the Supplementary Materials? Some papers have it. If you're really determined, you can implement a HMM model yourself. You'll need to supply the Markov ...

0

When $X_1$ is unobserved, at iteration $k=1$ of EM, the posterior mean value (when $X_2=3$) is $5.18$ by using an inference algorithm, i.e. Junction tree/Kalman filter. Then the sufficient statistics for $X_1$ is: $s_1=\Sigma_{i=1}^nx_{i1}=9+4+5.18$ and $s_{11}=\Sigma_{i=1}^nx_{i1}^2=9^2+4^2+(5.18^2+\sigma_{11.2})$ where $\sigma_{11.2}$ is the posterior ...

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