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To determine the optimal number of states in a HMM is indeed an intricate one. Please have a look at the following paper: The Number of Regimes Across Asset Returns: Identification and Economic Value by M. Gatumel and F. Ielpo (2011) From the abstract: A shared belief in the financial industry is that markets are driven by two types of regimes. Bull ...


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In the paper you cited in the question, the equation (1) is not the equation of state in kalman filter model, but an $AR(3)$ estimated via OLS as shown in Stock & Watson (2002). What the authors estimated in the paper using the Kalman filter is the latent variables $f_t,_h$ and the relative lags through which they estimated both the equation (1) and ...


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It is not about estimating those equations via PC. There are various methods to estimate the latent factor fth, one of which is principal components. They have asked us to use that. Series(z) in those equations is observed data so we use the estimated fth and observed z to perform the OLS as suggested AR(3) or ARMA(1,0,3) would make the residual series ...


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I don't understand how technical indicators are at all relevant to the question. State probabilities can be generated directly from the returns if the model is known. There is no need to guess at heuristic trading rules based on technical indicators. Let $r_t$ be the return at time $t$. Your model is $E\{r_t | s_t=i\} \sim N(\mu_i,\sigma^2_i), i=0,1$ ...



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