Inference for Nonlinear State Space Models: A Comparison of Different Methods applied to Markov-Switching Multifractal Models

Nonlinear, non-Gaussian state space models have found wide applications in many areas. These usually do not allow for an analytical representation of their likelihood function and thus, sequential Monte Carlo or particle filter methods are mostly applied to estimate parameters. Finding the best-fitting parameters a model is non-trivial task since stochastic approximations lead non-smooth functions. Recently proposed iterative filtering algorithms developed this purpose compared with simpler on-line filters more traditional inference. A highly nonlinear class Markov-switching models, so called multifractal (MSM) used as illustrative example comparison different optimisation routines. Besides well-established univariate discrete-time MSM, multivariate continuous-time versions MSM considered. simulation experiments indicate that across variety specifications, classical Nelder-Mead simplex algorithm appears still efficient robust number online iterated filters. very close competitor one recently while other alternatives dominated by these two algorithms. An empirical application both discrete seven financial time series shows dominate GARCH FIGARCH terms in-sample goodness-of-fit. Out-of-sample forecast comparisons show majority cases clear dominance under mean absolute error criterion, less conclusive results squared criterion.