On improving the forecast accuracy of the hidden Markov model - Rooney, Thomas J A (Division of Actuarial Science, 2017)
The forecast accuracy of a hidden Markov model (HMM) may be low due first, to the measure of forecast accuracy being ignored in the parameterestimation method and, second, to overfitting caused by the large number of parameters that must be estimated. A general approach to forecasting is described which aims to resolve these two problems and so improve the forecast accuracy of the HMM. First, the application of extremum estimators to the HMM is proposed. Extremum estimators aim to improve the forecast accuracy of the HMM by minimising an estimate of the forecast error on the observed data. The forecast accuracy is measured by a score function and the use of some general classes of score functions is proposed. This approach contrasts with the standard use of a minus log-likelihood score function. Second, penalised estimation for the HMM is described. The aim of penalised estimation is to reduce overfitting and so increase the forecast accuracy of the HMM. Penalties on both the state-dependent distribution parameters and transition probability matrix are proposed. In addition, a number of cross-validation approaches for tuning the penalty function are investigated. Empirical assessment of the proposed approach on both simulated and real data demonstrated that, in terms of forecast accuracy, penalised HMMs fitted using extremum estimators generally outperformed unpenalised HMMs fitted using maximum likelihood.