Adding Flexibility to Markov Switching Models

Very often time series are subject to abrupt changes in the level, which are generally represented by Markov Switching (MS) models, assuming that the level is constant within a certain state (regime). This is not a realistic framework because in the same regime the level could change with minor jumps with respect to a change of state; this is a typical situation in many economic time series such as the Gross Domestic Product (GDP) or the volatility of financial markets. We propose to make the state flexible, introducing a very general model which provides oscillations of the level of the time series within each state of the MS model; these movements are driven by a forcing variable. The new model allows for consideration of extreme jumps in a parsimonious way, without the adoption of a large number of regimes (in our examples the two-state MS models are used). Moreover, this model increases the interpretability and in particular the out-of-sample performance with respect to the most used alternative models. This approach can be applied in several fields, also using unobservable data. We show its advantages in three distinct applications, extending particular MS models, which involve macroeconomic variables, volatilities of financial markets and conditional correlations.