Jump Estimation of Hidden Markov Models with Time-Varying Transition Probabilities

Sammanfattning: The Hidden Markov model is applicable to a wide variety of fields. Applied to financial time series, its assumed underlying state sequence can reflect the time series' tendency to behave differently over different periods of time. In many situations, models could be improved by including exogenous data. However, that may in some cases be inappropriate in practice as the model could get too mathematically complex to learn or require too strong assumptions. The jump estimator for learning Hidden Markov models by clustering temporal features is very flexible in that regard. In this thesis we conduct a simulation study to show that, assuming time-varying transition probabilities depending on exogenous variables, the jump estimator's prediction accuracy of latent states can be significantly improved as its feature space is extended with the relevant exogenous data. To facilitate the simulation study, we use an EM-algorithm to estimate Hidden Markov models applied to the S&P 500 index with transition probabilities depending on exogenous variables. Four variables are considered in a forward selection scheme resulting in the CBOE Volatility Index being deemed the most important exogenous variable in this setting. For practical purposes, our results indicate in particular that when applying the jump estimator to the S&P 500, including features based on the volatility index improves its ability to segment the S&P 500 into periods with bullish and bearish market conditions.