Guest Editors’ Introduction: Regime Switching and Threshold Models

This special issue of the Journal of Business & Economic Statistics on “Regime Switching and Threshold Models” is motivated by the mounting empirical evidence of important nonlinearities in regression models commonly used to model the dynamics in macroeconomic and financial time-series. Commonly cited examples include the very different behavior of second moments for many macroeconomic time series before and after the Great Moderation in the early eighties, the different behavior of U.S. interest rates during the Federal Reserve’s Monetarist Experiment from 1979 to 1982, and the behavior of a variety of risk indicators during the more recent global financial crisis. These are episodes that can be difficult to model in the context of standard linear regression models. The key difference between Markov switching models and threshold models is that the former assume that the underlying state process that gives rise to the nonlinear dynamics (regime switching) is latent, whereas threshold models commonly allow the nonlinear effect to be driven by observable variables but assume the number of thresholds and the threshold values to be unknown. However, it is often overlooked that the general formulation of the threshold model includes the Markov switching model (Tong and Lim 1980, p. 285 line 12); see also Tong (2011) for further discussion. Thus, these two classes of models share many common features. From an econometric perspective, both classes of models are affected by the presence of unidentified parameters under the null, which pose challenges to inference, including the number of thresholds (or regimes) and their location. Empirically, both types of models can, by design, allow for discrete, nonlinear effects. The articles brought together in this special issue highlight both similarities and differences for threshold and regime switching models, offering many novel insights along both methodological, computational, and empirical lines. Luc Bauwens, Jean-François Carpantier, and Arnaud Dufays, in their article “Autoregressive Moving Average Infinite Hidden Markov-Switching Models,” study a class of Markov switching models in which regime switches only affect some parameters, while other parameters can remain the same across regimes. Limiting regime switches to a subset of the parameters can lead to simpler models with fewer unknown parameters and better out-of-sample forecasting performance. In particular, the authors propose to decouple the regime switching dynamics for the mean and variance parameters. The methodology developed by Bauwens, Carpantier, and Dufays allows the number of regimes to be determined as part of the estimation process and so has no need to use extraneous criteria for selecting the number of regimes. Detailed empirical applications to quarterly U.S. GDP growth and monthly U.S. inflation show that the new class of “sticky infinite hidden Markov switching autoregressive moving average” models can lead to better forecasts than more conventional models. These findings are corroborated on a set of 18 additional macroeconomic variables. In their article “Forecasting Macroeconomic Variables Under Model Instability,” Pettenuzzo and Timmermann compare a range of methods in common use in macroeconomic forecasting for handling parameter instability. Specifically, the article focuses on comparing and contrasting approaches that assume small but frequent changes to the model parameters (time-varying parameter models) versus models that assume rare, but large (discrete) breaks to the model parameters. The article considers breaks in the parameters of both the first and second moments of the modeled process and studies their impact using predictive accuracy measures that focus on either the conditional mean or on the entire probability distribution of the outcome. In an empirical out-of-sample forecasting exercise for U.S. GDP growth and inflation, the authors find that models that allow for parameter instability generate more accurate density forecasts than constant-parameter models. Conversely, such models fail to produce better point forecasts. Overall, a model specification that allows for both time-varying parameters and stochastic volatility is found to perform best. Model combination methods also deliver gains in the performance of density forecasts, but fail to improve on the predictive accuracy of the time-varying parameter model with stochastic volatility. These results suggest that accounting for model instability can deliver better probability forecasts for key macroeconomic variables whereas gains in predictive accuracy for traditional point forecasts are harder to come by. Jesús Gonzalo and Jean-Yves Pitarakis, in their article “Inferring the Predictability Induced by a Persistent Regressor in a