Modeling macroeconomic series with regime-switching models characterized by a high-dimensional state space

The Markov-switching multifractal process, and recent extensions such as the factorial hidden Markov volatility model, correspond to tightly parametrized hidden Markov models characterized by a high-dimensional state space. Because the central component in these models is a Markov chain restricted to have positive support, the applicability of such models has been so far limited to the modeling of positive processes such as volatilities, inter-trade durations and trading volumes. By adapting the factorial hidden Markov volatility model, we develop a new regime-switching process for capturing time variation in the conditional mean of a time series with support on the whole real line. We show its promising performance to fit 21 widely used macroeconomic data sets.