Uncertainty estimation for stochastic process parameters

When a simple Markov or semi-Markov model is fitted to a large set of data over several points in time, confidence intervals based on the asymptotic distribution of the maximum likelihood estimates are generally too narrow. Accordingly, the estimated precision of forecasts is too optimistic. These problems arise not only because of inhomogeneities in the sample, but also because of time inhomogeneities in the parameter values themselves. In this paper, some approaches to finding more realistic interval estimates will be surveyed.