Maximum spacing estimation for hidden Markov models

This article generalizes the maximum spacing (MSP) method to dependent observations by considering hidden Markov models. The MSP method for estimating the model parameters is applied in two steps: at first the parameters of the marginal distribution of observations are estimated, in the second step the transition probabilities of the underlying Markov chain are estimated using the obtained marginal parameter estimates. We prove that the proposed MSP estimation procedure gives consistent estimators. The possibility of using the proposed estimation procedure in the context of model validation is investigated in simulation examples. It is demonstrated that when the observations are dependent, then taking into account the dependence structure by considering two-dimensional spacings provides additional information about a suitable number of mixture components in the model. The proposed estimation method is also applied in a real data example.