Adaptive learning from model space

• Author: Jan Prüser
• DOI: http://doi.org/10.1002/for.2549
• Published date: 01 January 2019
• Date: 01 January 2019

Received: 3 April 2018 Revised: 12 July 2018 Accepted: 3 August 2018

DOI: 10.1002/for.2549

RESEARCH ARTICLE

Adaptive learning from model space

Jan Prüser1,2

1Faculty of Economics and Business

Administration, University of

Duisburg-Essen, Essen, Germany

2Ruhr Graduate School in Economics,

RWI—Leibniz Institute for Economic

Research, Essen, Germany

Correspondence

Jan Prüser, RuhrGraduate School in

Economics, RWI—Leibniz Institute for

Economic Research, Hohenzollernstrasse

1-3, D-45128 Essen, Germany.

Email: jan.prueser@rgs-econ.de

Abstract

Dynamic model averaging (DMA) is used extensively for the purpose of eco-

nomic forecasting. This study extends the framework of DMA by introducing

adaptive learning from model space. In the conventional DMA framework all

models are estimated independently and hence the information of the other

models is left unexploited. In order to exploit the information in the estima-

tion of the individual time-varying parameter models, this paper proposes not

only to average over the forecasts but, in addition, also to dynamically average

over the time-varying parameters. This is done by approximating the mixture of

individual posteriors with a single posterior, which is then used in the upcom-

ing period as the prior for each of the individual models. The relevance of

this extension is illustrated in three empirical examples involving forecasting

US inflation, US consumption expenditures, and forecasting of five major US

exchange rate returns. In all applications adaptive learning from model space

delivers improvements in out-of-sample forecasting performance.

KEYWORDS

fat data, forecasting, model change, variable selection

1INTRODUCTION

Forecasting in economics is challenging for three major

reasons. First, the existence of many potential predictors

can result in a huge number of potential models. While

regressions with many predictors may overfit, small mod-

els may miss important predictors. This leads to the need

for model selection strategies. Second, a useful forecasting

model may change over time. For instance, some variables

may predict well in recessions, where as others may pre-

dict well in expansions, or the set of relevant predictors

may change between certain events such as the Great Mod-

eration. This further complicates the statistical problem

as a researcher needs to select one model in each period.

Third, in the case of parameter change the marginal effect

of predictors may change over time. However, modeling

such change will increase the risk of overfitting the data,

resulting in poor out-of-sample predictions. Recently, a

growing literature has addressed these points by using

dynamic model averaging (DMA), proposed by Raftery,

Kárný, and Ettler (2010). Koop and Korobilis (2012) intro-

duced DMA to the economic literature by forecasting

inflation. They found a favorable forecasting performance

of DMA over simple benchmark regressions and more

sophisticated approaches. Studies that use DMA to fore-

cast a variety of different economic time series include:

Buncic and Moretto (2015), Drachal (2016), and Naser

(2016), forecasting commodities; Bruyn, Gupta, and Eyden

(2015), Beckmann and Schüssler (2016), and Byrne, Koro-

bilis, and Ribeiro (2018), forecasting exchange rates; Liu,

Ma, and Wang (2015), forecasting stock returns; Gupta,

Hammoudeh, Kim, and Simo-Kengne (2014), forecasting

foreign exchange reserves; Bork and Moller (2015), Risse

and Kern (2016), and Wei and Cao (2017), forecasting

house price growth; Aye, Gupta, Hammoudeh, and Joong

(2015) and Baur, Beckmann, and Czudaj (2016) forecast-

ing gold prices; Koop and Korobilis (2011) and Filippo

(2015), forecasting inflation; and Wang, Ma, Wei, and

Journal of Forecasting. 2019;38:29–38. wileyonlinelibrary.com/journal/for © 2018 John Wiley & Sons, Ltd. 29