Forecasting with Specification‐Switching VARs

• Author: Youngjin Hwang
• Published date: 01 August 2017
• DOI: http://doi.org/10.1002/for.2455
• Date: 01 August 2017

Journal of Forecasting,J. Forecast. 36, 581–596 (2017)

Published online 28 November 2016 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/for.2455

Forecasting with Specification-Switching VARs

Youngjin Hwang

Department of Economics, Hanyang University, Ansan, Korea

ABSTRACT

The specification choices of vector autoregressions (VARs) in forecasting are often not straightforward, as they are

complicated by various factors. Todeal with model uncertainty and better utilize multiple VARs, this paper adopts the

dynamic model averaging/selection (DMA/DMS) algorithm, in which forecasting models are updated and switch over

time in a Bayesian manner. In an empirical application to a pool of Bayesian VAR (BVAR) models whose specifica-

tions include level and difference, along with differing lag lengths, we demonstrate that specification-switching VARs

are flexible and powerful forecast tools that yield good performance. In particular, they beat the overallbest BVAR in

most cases and are comparable to or better than the individual best models (for each combination of variable, forecast

horizon, and evaluation metrics) for medium- and long-horizon forecasts. Wealso examine several extensions in which

forecast model pools consist of additional individual models in partial differences as well as all level/differencemod-

els, and/or time variations in VAR innovations are allowed, and discuss the potential advantages and disadvantages of

such specification choices. Copyright © 2016 John Wiley & Sons, Ltd.

KEY WORDS forecasting; dynamic model averaging; dynamic model selection; VAR; Bayesian estimation

INTRODUCTION

Vector autoregressions (VARs) have a long and successful tradition in forecasting and are among the most popular

toolkits in empirical macroeconomics. In forecasting using VARs, forecasters are faced with a host of questions about

model specification, such as the selection of variables for inclusion in the system, the transformation of data, and

the determination of lag length. Although there are several pre-tests and criteria regarding these issues and related

economic theories are sometimes helpful, unified guidelines are arguably non-existent, and those that are available

are often complicated at best; they are neither clear nor operational.

Rather than exploring this direction further and choosing a single best forecasting model, this paper develops an

eclectic forecast method in which forecasts are generated from a pool of multiple standard Bayesian VAR (BVAR)

models, addressing model uncertainty in a dynamic way. Specifically, our method allows the specific VAR(s) used

for forecasting to switch over time in a data-based manner; we implement this VAR switching using an algorithm

developed by Raftery et al. (2010) and extended by Koop and Korobilis(2012, 2013), which is referred to as dynamic

model averaging/selection (DMA/DMS). The basic idea of DMA/DMS is that the best forecast model is updated at

each time point in a Bayesian fashion through a prediction-updating algorithm similar to Kalman filtering, and the

algorithm allocates more weight to models that have forecasted well in the past.

In considering a pool of VAR models for DMA/DMS, one important decision is which VAR models to include.

While there are a range of issues in (Bayesian) VAR specification (addressed above), we focus on two key issues:

(log) level versus difference (in data transformation) and lag length. This is mainly motivated by the observation that

differences in forecasting performance are likely to be more significant with level/difference and differing lags than

with other issues. In fact, the recent literature shows that even when some ingredients in the VAR specification and

forecasting procedure (such as prior tightness and VAR system dimensions) are optimally selected or are allowed

to vary over time, there turns out to be little variation in them, or only modest differences are found in the overall

forecast outcomes (Koop and Korobilis, 2013; Carriero et al., 2015).

Compared to standard forecasting methods using a single or fixed VAR model, forecasting with specification-

switching VARs provides several practical benefits and important implications. First, it enables us to better utilize

multiple VARs, each of which might be useful at some point. It is unlikely that a single or fixed VAR will beat the

other competitors all the time, and one that is poor on average may forecast well on some occasions. For example, a

VAR may predict well in expansions but not in recessions. When the economy undergoes a turbulent period, another

VAR model may work well. In fact, many studies show that forecasting models change over time (e.g., Pesaran and

Timmermann, 2005; Stock and Watson, 2008). Rather than rely on a single or fixed forecast model, specification-

switching VARs, in which multiple VARs are allowed to compete and each of their information is efficiently weighted,

may provide improved forecasting.

Correspondence to: YoungjinHwang, Department of Economics, Hanyang University, Ansan, Korea. E-mail: youngjinh@hanyang.ac.kr

Copyright © 2016 John Wiley & Sons, Ltd

582 Y. Hwang

Second, with multiple VAR models available and the best among them a priori not fixed, allowing for switches

between different VARs may better accommodate various types of structural changes and is likely to be more robust

and immune to model misspecification. As structural breaks are often attributed to one of the primary sources in

forecasting failures, allowing for specification switching is a potentially useful addition in this regard.

We adopt the idea of specification switching in an empirical application to small-scale BVARs involving quarterly

Korean macroeconomic data, with a focus on forecasting output and inflation. In evaluating the forecast performance,

we use root mean square error (RMSE) and predictive likelihood. Our main findings are as follows. First, there is

substantial switching in the selection by specification-switching VARs over time, which is closely linked to business

cycles. While BVARs in difference with lag length of two (BVARD(2)) perform well on average, during recession

periods either BVAR in level (at short horizons) or BVAR in differencewith longer lags (at long horizons) are selected,

each better reflecting the changing dynamics of variables over business cycles. These results are largely due to the

difference in persistence implied by each model’s specification.

Second, we show that specification-switching BVARs significantly improve forecast performances. In particular,

we find that they forecast better than several alternatives, including the overall best BVAR model and the individual

best models in many cases, in particular over longer horizons.

We also consider several alternative specifications in which forecast model pools consist of additional individual

models in partial differences as well as all level/difference models, and/or time variations in VAR innovations are

allowed. It is shown that considering a richer model pool by including these additional models seems to do more harm

than good because these additional models (some of which are competitive but not particularly useful) may hinder

the selection of appropriate models and distort the model averaging scheme. On the other hand, with time-varying

volatilities, forecasts improve substantially,and especially in terms of density forecasting, although their performance

is to some extent dependent upon the characteristics of the data.

This paper is closely related to several lines of research in the recent forecasting literature. Over the last several

decades, interest in forecasting using multiple models such as model averaging/combination has grown noticeably

(see Timmermann, 2006, for a survey). While weights are constant over time in the traditional model averaging

scheme, model averaging in DMA is flexible, allowing weights to vary and be updated coherently in a data-based

manner. Examples of DMA/DMS in the forecasting literature include predictor selection in linear regression (Koop

and Korobilis, 2012; Bork and Moller, 2015), as well as prior and/or dimension selection in BVARs (Koop, 2014;

Koop and Korobilis, 2013), all of which demonstrate that DMA/DMS can be a useful addition to forecasting methods.

One notable and interesting study in this regard is Amisano and Geweke (2013), who examine the forecasts of several

potentially misspecified macroeconometric models, including VARs in level and in differences (as well as dynamic

stochastic general equilibrium (DSGE) and factor models). Despite some similarities, their study differs from this one

in that the VARs remain fixed with predetermined lag lengths in their forecast pool and they consider only the short-

run (one-quarter-ahead) forecast. Moreover, the model selection/combination scheme is solely based on predictive

likelihood, while it is extended in a Bayesian fashion in this paper.

Another strand of recent research has studied the effects of various specification choices on the forecast perfor-

mance of VAR models (Koop and Korobilis, 2013; Carriero et al., 2015, 2016; Giannone et al., 2015). While these

studies all share similar motivations with this paper, most are conducted in a limited context or with a focus on differ-

ent aspects. For example, Carriero et al. (2015) examine an extensive set of issues in BVAR specification including

level/difference, lag length, and prior shrinkage. However, they investigate all the cases with fixed models, in which

model specifications do not vary over time. In this regard, Koop and Korobilis (2013) is most closely related to this

paper. They extend time-varying parameterVARs using a DMA/DMS framework in which VAR dimension and prior

tightness can switch over time.

The rest of this paper is organized as follows. The next section provides a theoretical discussion on VAR specifica-

tion in terms of level versus difference and lag length. The third section describes the model specification and forecast

methodology, and the fourth section presents the main forecast results. The fifth section concludes.

THEORETICAL BACKGROUND OF VAR MODEL SPECIFICATION: IMPLICATIONS FOR FORECASTING

The specification choices for (Bayesian) VARs and other decisions associated with forecasting are generally not

straightforward. While there are numerous issues, it is often unclear and hard to tell a priori which approach would

be best.1This section provides some theoretical background on VAR specification with a focus on the issues of (log)

level versus difference and lag length determination in the context of forecasting.2

1It is beyond the scope of this paper to address these issues in detail. See Carriero et al. (2015) for an investigation of a range of issues associated

with the forecast performance of Bayesian VARs.

2The discussion in this section largely draws on Hamilton (1994), Lütkepohl (2005), and Enders (2010).

Copyright © 2016 John Wiley & Sons, Ltd J. Forecast. 36, 581–596 (2017)