Structured Hidden Markov Models

The lion’s share of hidden Markov models (HMMs) /Markov regime switching models considered in economic research incorporates a comparably small number of states. The popularity of models with mostly two or three states principally results from their good interpretability: often regime changes can be linked to abrupt external events. A further reason lies in the number of parameters of the transition probability matrix (TPM) having a growth rate which is quadratic in the number of states. Thus, the estimation procedures quickly become unstable and strongly dependent on the choice of the initial values due to overparametrization. From the intuitive point of view it is at least discussible whether, e.g., macroeconomic or political changes are not anticipated. If this is the case, HMMs with comparably smooth transition between many states constitute an attractive alternative. We present structured hidden Markov model (SHMMs). The SHMM approach reduces the number of parameters significantly by providing the TPM with a distinct architecture. We compare the performance of SHMMs with common HMMs in the context of return series. Moreover, we present an implementation of the estimation procedures via the freely available software package R