Bayesian Model Averaging under Regime Switching with Application to Cyclical Macro Variable Forecasting

• Published date: 01 April 2016
• Author: Jianmin Shi
• DOI: http://doi.org/10.1002/for.2375
• Date: 01 April 2016

Bayesian Model Averaging under Regime Switching with

Application to Cyclical Macro Variable Forecasting

JIANMIN SHI

1,2

*

1

Haitong Securities Co. Ltd, Shanghai, China

2

School of Economics and Management, Wuhan University, Wuhan, China

ABSTRACT

Model uncertainty and recurrent or cyclical structural changes in macroeconomic time series dynamics are substantial

challenges to macroeconomic forecasting. This paper discusses a macro variable forecasting methodology that com-

bines model uncertainty and regime switching simultaneously. The proposed predictive regression specification per-

mits both regime switching of the regression parameters and uncertainty about the inclusion of forecasting variables

by employing Bayesian model averaging. In an empirical exercise involving quarterly US inflation, we observed that

our Bayesian model averaging with regime switching leads to substantial improvements in forecast performance, par-

ticularly in the medium horizon (two to four quarters). Copyright © 2015 John Wiley & Sons, Ltd.

key words model uncertainty; Bayesian model averaging; regime switching; inflation forecasting; mac-

roeconomic forecasting

INTRODUCTION

Macro variable (e.g. gross domestic product, GDP; consumer price index, CPI) forecasting involves a very wide

range of interactive and uncertain influencing forces or factors, and it is challenging to identify real, useful predictors.

Furthermore, macro variables themselves and their relationship with potentially relevant factors are not stable but

change over time. The former problem is usually known in the literature as model uncertainty. Model uncertainty as-

serts that, among the enormous number of competing models with different variables or structures, it is difficult to

determine which is the true or best model; therefore, analysis or forecasting using a single model is dangerous. To

address the challenge of model uncertainty, Bayesian model averaging (BMA), which was pioneered by Raftery

et al. (1997) and aims to address model uncertainty in multivariate linear regression, is frequently used in macroeco-

nomic forecasting (see, among others, Koop and Potter, 2003, 2004; Kapetanios et al., 2008; Wright, 2008, 2009).

Another important issue that arises in macroeconomic forecasting is instability in either the dynamics of the macro

variables themselves or the relationship between the macro variables and predictor variables. In addition to occasional

breaks, recurrent or cyclical structural changes are common phenomena in macroeconomic time series, such as in the

different stages of business cycles. The regime switching (RS) model, originally proposed by Hamilton (1989, 1994),

is a popular approach that attempts to overcome the limitations of traditional stationary time series models inprocess-

ing such structural changes. By introducing a latent Markov state variable following certain transition probability, the

RS model is more flexible in the specification of structural changes of model parameters such as mean and variance.

The RS model has been developed and widely applied in many macroeconomic and financial areas (see the survey of

Hamilton (1990, 2008)).

The effects of model uncertainty and recurrent structural breaks on macro variable prediction have only been con-

sidered in isolation and have not been incorporated jointly into predictive regression models for macroeconomic var-

iables. Two similar but essentially different studies are Ravazzolo et al. (2008) and Belmonte and Koop (2013).

Ravazzolo et al. (2008) jointly discuss the effects of structural changes and model uncertainty in stock returns predic-

tion, but their focus is on occasional structural breaks assuming a beta statistical distribution rather than recurrent

Markov RS, which is more suitable for structural changes in macroeconomic time series. Belmonte and Koop

(2013) investigate both Markov switching and model averaging, but they use Markov RS as a weighting mechanism

for variable selection and state space model averaging

1

rather than the Bayesian averaging of a Markov RS model.

The latter is the subject of our paper, and thus the idea and the methods described are very different from those of

Belmonte and Koop (2013).

To summarize, the aim of this paper is to discuss model (predictor) uncertainty in RS models that characterize

macroeconomic variable time series. The predictive regression specification that we suggest permits cyclical or recur-

rent structural changes of regression parameters as well as uncertainty in the inclusion of forecasting variables in the

*Correspondence to: Jianmin Shi, Haitong Securities Co. Ltd, Rm. 1301, 689 Guangdong Road, 200001 Shanghai, China.

E-mail: shijm@htsec.com

1

Somewhat in the same spirit of Elliott and Timmermann (2005).

Journal of Forecasting,J. Forecast. 35, 250–262 (2016)

Published online 3 November 2015 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/for.2375

Copyright © 2015 John Wiley & Sons, Ltd.