Confidence intervals for hidden Markov model parameters

Three methods for computing confidence intervals (CIs) of hidden Markov model parameters are compared in the context of 'long' time series. T > 100, namely likelihood profiling, bootstrapping and CIs based on a finite-differences approximation to the Hessian. First it is shown that with 'long' time series computing the exact Hessian is not feasible. In simulation studies quadratic and cubic interpolation polynomials for the likelihood profiles are compared. Likelihood profiling and bootstrapping produce similar CIs, whereas the CIs from the finite-differences approximation of the Hessian are mostly too small.