Forecasting economic and financial time-series with non-linear models

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Abstract

In this paper we discuss the current state-of-the-art in estimating, evaluating, and selecting among non-linear forecasting models for economic and financial time series. We review theoretical and empirical issues, including predictive density, interval and point evaluation and model selection, loss functions, data-mining, and aggregation. In addition, we argue that although the evidence in favor of constructing forecasts using non-linear models is rather sparse, there is reason to be optimistic. However, much remains to be done. Finally, we outline a variety of topics for future research, and discuss a number of areas which have received considerable attention in the recent literature, but where many questions remain.

Introduction

Whilst non-linear models are often used for a variety of purposes, one of their prime uses is for forecasting, and it is in terms of their forecasting performance that they are most often judged. However, a casual review of the literature suggests that often the forecasting performance of such models is not particularly good. Some studies find in favor, but equally there are studies in which their added complexity relative to rival linear models does not result in the expected gains in terms of forecast accuracy. Just over a decade ago, in their review of non-linear time series models, De Gooijer and Kumar (1992) concluded that there was no clear evidence in favor of non-linear over linear models in terms of forecast performance, and we suspect that the situation has not changed very much since then. It seems that we have not come very far in the area of non-linear forecast model construction.

We argue that the relatively poor forecasting performance of non-linear models calls for substantive further research in this area, given that one might feel uncomfortable asserting that non-linearities are unimportant in describing economic and financial phenomena. The problem may simply be that our non-linear models are not mimicing reality any better than simpler linear approximations, and in the next section we discuss this and related reasons why a good forecast performance ‘across the board’ may constitute something of a ‘holy grail’ for non-linear models.

We discuss the current state-of-the-art in non-linear modeling and forecasting, with particular emphasis placed on outlining a number of open issues. The topics we focus on include joint and conditional predictive density evaluation, loss functions, estimation and specification, and data-mining, amongst others. As such, this paper complements the rest of the papers in this special issue of the International Journal of Forecasting.

The rest of the paper is organized as follows. In Section 2 we discuss why one might want to consider non-linear models, and a number of reasons why their forecasting ability relative to linear models may not be as good as expected. In Section 3 we discuss recent theoretical and methodological issues to do with forecasting with non-linear models, many of which go beyond the traditional preoccupation with point forecasts to consider the whole predictive density. Section 4 highlights a number of empirical issues, and how these are dealt with in the papers collected in this issue. Concluding remarks are gathered in Section 5.

Section snippets

Why consider non-linear models

Many of us believe that linear models ought to be a relatively poor way of capturing certain types of economic behavior, or economic performance, at certain times. The obvious example would be a linear (e.g. Box–Jenkins ARMA) model of output growth in a Western economy subject to the business cycle, where the properties of output growth in recessions are in some ways quite different from expansions (e.g. Hamilton, 1989, Sichel, 1994, but references are innumerable). Output growth

Theoretical and methodological issues

There are various theoretical issues involved in constructing non-linear models for forecasting. In this section we outline a number of these. An obvious starting point is which non-linear model to use, given the many possibilities that are available, even once we have determined the purpose to which it is to be put (here, forecasting). The different types of models often require different theoretical and empirical tools (see e.g. the recent surveys by Franses & van Dijk, 2000, van Dijk,

Empirical issues

In this section we discuss various practical issues. In contrast to linear models, the design of non-linear models for actual data and the estimation of parameters are less straightforward.

How should we select a model?4

Concluding remarks

In this paper we have summarized the state-of-the-art in forecast construction and evaluation for non-linear models, and in selection among alternative non-linear prediction models. We conclude that the day is still long off when simple, reliable and easy to use non-linear model specification, estimation and forecasting procedures will be readily available. Nevertheless, there are grounds for optimism. The papers in this issue suggest that careful application of existing techniques, and new

Acknowledgements

The authors wish to thank Valentina Corradi and Dick van Dijk for helpful conversations, and are grateful to Jan De Gooijer for reading and commenting on the manuscript. Swanson gratefully acknowledges financial support from Rutgers University in the form of a Research Council grant.

Michael P. Clements is a Reader in the Department of Economics at the University of Warwick. His research interests include time-series modeling and forecasting. He has published in a variety of international journals, has co-authored two books on forecasting, and co-edited (with David F. Hendry) of A Companion to Economic Forecasting 2002, Blackwells. He is also an editor of the International Journal of Forecasting.

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    Michael P. Clements is a Reader in the Department of Economics at the University of Warwick. His research interests include time-series modeling and forecasting. He has published in a variety of international journals, has co-authored two books on forecasting, and co-edited (with David F. Hendry) of A Companion to Economic Forecasting 2002, Blackwells. He is also an editor of the International Journal of Forecasting.

    Philip Hans Franses is Professor of Applied Econometrics and Professor of Marketing Research, both at the Erasmus University Rotterdam. He publishes on his research interests, which are applied econometrics, time series, forecasting, marketing research and empirical finance.

    Norman Swanson, a 1994 University of California, San Diego Ph.D. is currently Associate Professor at Rutgers University. His research interests include forecasting, financial- and macro-econometrics. He is currently an associate editor of the Journal of Business and Economic Statistics, the International Journal of Forecasting, and Studies in Non-linear Dynamics and Econometrics. He has recently been awarded a National Science Foundation research grant entitled the Award for Young Researchers, and is a member of various professional organizations, including the Econometric Society, the American Statistical Association, and the American Economic Association. Swanson has recent publications in Journal of Development Economics, Journal of Econometrics, Review of Economics and Statistics, Journal of Business and Economic Statistics, Journal of the American Statistical Association, Journal of Time Series Analysis, Journal of Empirical Finance and International Journal of Forecasting, among others. Further details about Swanson, including copies of all papers cited above, are available at his website: http://econweb.rutgers.edu/nswanson/.

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