Forecast Combination for Euro Area Inflation: A Cure in Times of Crisis?

• Published date: 01 August 2017
• Author: Frauke Skudelny,Kirstin Hubrich
• Date: 01 August 2017
• DOI: http://doi.org/10.1002/for.2451

Forecast Combination for Euro Area Inflation: A Cure in Times of

Crisis?

KIRSTIN HUBRICH

1

*AND FRAUKE SKUDELNY

2

1

Federal Reserve Board, Washington, DC, USA

2

European Central Bank, Frankfurt, Germany

ABSTRACT

The period of extraordinary volatility in euro area headline inflation starting in 2007 raised the question whether

forecast combination methods can be used to hedge against bad forecast performance of single models during such

periods and provide more robust forecasts. We investigate this issue for forecasts from a range of short-term

forecasting models. Our analysis shows that there is considerable variation of the relative performance of the different

models over time. To take that into account we suggest employing performance-based forecast combination

methods—in particular, one with more weight on the recent forecast performance. We compare such an approach

with equal forecast combination that has been found to outperform more sophisticated forecast combination methods

in the past, and investigate whether it can improve forecast accuracy over the single best model. The time-varying

weights assign weights to the economic interpretations of the forecast stemming from different models. We also

include a number of benchmark models in our analysis. The combination methods are evaluated for HICP headline

inflation and HICP excluding food and energy. We investigate how forecast accuracy of the combination methods

differs between pre-crisis times, the period after the global financial crisis and the full evaluation period, including

the global financial crisis with its extraordinary volatility in inflation. Overall, we find that forecast combination

helps hedge against bad forecast performance and that performance-based weighting outperforms simple averaging.

Copyright © 2017 John Wiley & Sons, Ltd.

key words forecasting; euro area inflation; forecast combinations; forecast evaluation

INTRODUCTION

The period of high volatility in euro area headline inflation starting from around 2007 made it extremely difficult to

forecast inflation, even in the short term. Chart 1 shows the evolution of forecasts for annual inflation in 2009 from

different institutions and private forecasters. This was a year where it was particularly difficult to forecast inflation,

since the volatility of headline inflation was particularly high. The first forecasts represented in the chart were made

in January 2008 and were subsequently revised over time at different time intervals (mostly monthly or quarterly).

The last forecast for annual inflation in 2009 was published in October 2009. While the outcome of annual inflation

in 2009 was 0.3% (the solid square represents end 2009), it took until mid 2009 for forecasts of different institutions

and private forecasters to come close to this number. Also, the different forecasts appear quite diverse. This raises the

question whether forecast combination methods can be used to hedge against bad forecast performance of single

models during such periods and provide more robust forecasts.

The increasing number of different models used for short-term inflation forecasting pose a challenge on how to

extract and summarise the most important information from the different forecasts in real time. We investigate

whether forecast combination methods can help summarise the forecasts from many different models in a meaningful

and accurate point forecast. Our analysis shows that there is considerable variation in the relative performance of the

different models over time, and this variation can be utilised in a performance-based forecast combina tion method—

in particular, one with more weight on the recent forecast performance. Forecast combination with time-varying

weights might also be viewed as an approximation of underlying nonlinearities. For example, in an environment

of relatively stable inflation, a simple autoregressive model might work very well, whereas in episodes of more

volatile inflation a multivariate model allowing for feedback effects or a model including conditioning information

may improve forecast accuracy for inflation.

We investigate how a forecast combination approach with time-varying performance-based combination weights

compares with equal weights forecast combination, which has been found to outperform more sophisticated forecast

combination methods in the past, and whether it can improve forecast accuracy over the single best model. We employ

a range of single-equation and vector autoregressive models built to forecast HICP components and HICP headline

inflation and also include a number of benchmark models in our analysis. The combination methods are evaluated

for the Harmonized Index of Consumer Prices (HICP) headline inflation and inflation in HICP excluding food and en-

ergy in terms of forecast accuracy to investigate the source of good forecast performance and forecast failures in more

*Correspondence to: Kirstin Hubrich, Division of Research and Statistics, Federal Reserve Board, Constitution Ave NW and 20th St NW,

Washington, DC 20551, USA. E-mail: kirstin.hubrich@frb.gov

Journal of Forecasting,J. Forecast. 36, 515–540 (2017)

Published online 24 January 2017 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/for.2451

Copyright © 2017 John Wiley & Sons, Ltd.

detail. We investigate to what extent the forecast accuracy of the combination methods differs between normal times

before the global financial crisis and the post-crisis period, as well as over the full sample, including the global financial

crisis with its extraordinary volatility in inflation.

In addition, we provide further evidence on the comparison of a direct forecast of all inflation items in comparison

with forecasting the disaggregate components of inflation and aggregating those forecasts and new insights into the

role of combinations in that context. This evidence is presented in the Appendix.

The paper is organised as follows. The next section presentssome theoretical and empirical considerations to motivate

forecast combination and discusses the forecast combination methods employed in this paper. The third section presents

the data and the models used for forecasting inflation as well as the methods of evaluation. The fourth section presents

the results of the forecast evaluation for the individual models and for the forecast combination methods. The time-

varying performance-based forecast combination weights are discussed. Finally, concluding remarks are presented.

FORECAST COMBINATION

Motivation for forecast combination

The literature on forecast combination has recommended combining forecasts in the following situations to get more

accurate forecasts:

•Models are misspecified in some dimension: forecast combination is more robust against misspecification bias.

•Information sets underlying the forecasts are sufficiently different and combining information sets might not

provide the best forecast.

•Forecasts from different models will be differently affected by structural breaks.

Combining has often been argued to be a useful hedging strategy against structural breaks. Clements and Hendry

(2004) argue that this might be the case in the presence of an (unknown) break after the estimation period, in

particular when a shift occurs in the intercept of a single variable, or a shift of two correlated predictor variables

occurs in the opposite direction. Stock and Watson (2004) show empirically that combined forecasts tend to

outperform individual forecasts and that simple averages are best in terms of point forecast accuracy. Also, Aiolfi

and Timmermann (2006) have shown that an equal-weight combination is best in many situations.

In this study, our motivation to use a forecast combination approach is threefold: first, to investigate wheth er

forecast combination can be a useful hedging strategy against bad forecast performance of single models in the

presence of high inflation volatility and potential structural shifts during the recent global financial crisis; second,

to take into account potential nonlinearities and time variation in the performance of single models and investigate

whether that improves forecast accuracy over equal-weight combination schemes; and third, to improve over single

forecasts, even though that is not always possible and depends on the particular situation. The performance-based

combination weights can potentially also be used in real time to inform the forecaster how well the different models

have performed recently relative to each other. They also allow evaluating the relative importance of the underlying

economic interpretations of the forecast from the different models.

A combination issue separate from the one just discussed (which focuses on the combination of forecasts of the

same variable of interest) is whether combining forecasts of different disaggregate variables to forecast the aggregate

(‘indirect forecast’of the aggregate) is preferable to combining disaggregate information in a model for the aggregate

and use this for forecasting (‘direct forecast’of the aggregate). We present some new results on forecasting the ag-

gregate versus aggregating component forecasts in the context of the models employed in this study in Appendix IV.

Chart 1. Forecasts for annual inflation in 2009. The chart shows annual inflationforecasts (y-axis) forecast at different points in time

(x-axis) by a number of institutions (see legend). The published rangesare shown for the Eurosystem Macroeconomic Projections.

[Colour figure can be viewed at wileyonlinelibrary.com]

516 K. Hubrich and F. Skudelny

Copyright © 2017 John Wiley & Sons, Ltd. J. Forecast. 36, 515–540 (2017)