Neural network linear forecasts for stock returns Angelos Kanas

INTERNATIONAL JOURNAL OF FINANCE AND ECONOMICS

Int. J. Fin. Econ. 6: 245–254 (2001)

DOI: 10.1002/ijfe.156

NEURAL NETWORK LINEAR FORECASTS FOR STOCK RETURNS

ANGELOS KANAS*

Department of Economics, Uniersity of Crete, Rethymnon, Crete, Greece

ABSTRACT

We examine the out-of-sample performance of monthly returns forecasts for the Dow Jones and the FT, using a linear and an artificial neural network (ANN) model. The comparison of out-of-sample forecasts is done on the basis of directional accuracy, using the Pesaran and Timmermann (1992. A simple nonparametric test of predictive performance, Journal of Business and Economic Statistics 10: 461–465) test, and forecast encompassing, using the Clements and Hendry (1998. Forecasting Economic Time Series. Cambridge University Press: Cambridge, UK) approach. While both models perform badly in terms of predicting the directional change of the two indices, the ANN forecasts can explain the forecast errors of the linear model while the linear model cannot explain the forecast errors of the ANN for both indices. Thus, the ANN forecasts are preferable to linear forecasts, indicating that the inclusion of nonlinear terms in the relation between stock returns and fundamentals is important in out-of-sample forecasting. This conclusion is consistent with the view that the underlying relation between stock returns and fundamentals is nonlinear. Copyright © 2001 John Wiley & Sons, Ltd.

KEY WORDS:artificial neural networks; directional accuracy; dividends; forecast encompassing; nonlinearity; stock returns; trading volume

JEL CODE:G12

1. INTRODUCTION

Recent theoretical approaches to modeling the behavior of stock prices introduce nonlinearity in the relation between stock prices and fundamental variables, namely dividends, and trading volume. With regard to the stock price–dividend relation, Froot and Obstfeld (1991) introduced the intrinsic bubbles specification in which the bubbles are driven by the dividends. An important property of an intrinsic bubble is that for a given level of dividends the bubble will remain constant over time. Stable and highly persistent dividends lead to stable and highly persistent departures from the linear PV model, thereby entailing nonlinearity in the stock price–dividend relation. In addition, intrinsic bubbles can cause stock prices to overreact to changes in dividends. Similarly, the fads model proposed by Summers (1986) also leads to nonlinearity between stock prices and dividends. If there are fads in the stock market, one may observe long temporary price swings, which can be modeled as a slowly decaying stationary component in prices. The decay over time in the transitory component will entail mean reversion in stock prices. van Norden and Schaller (1994) show how this fads model entails regime switching and thus, nonlinearity in the stock price–dividend relation.

With regard to the stock price–trading volume relation, Brock (1993) developed a theoretical noise trading model which establishes a nonlinear relation between these variables. Similarly, Campbell et al. (1993) developed a model that has implications for the autocorrelation properties of stock returns as a nonlinear function of trading volume. In this model, risk-averse market makers accommodate buying or selling pressure from ‘noninformational’ traders. Trading volume occurs when random shifts in the stock demand of noninformational traders are accommodated by risk-averse market makers. The model shows that there is an abnormally large increase in trading volume followed by stock return reversals for such traders.

* Correspondence to: Department of Economics, University of Crete, 74100 Rethymnon, Crete, Greece. E-mail: a-kanas@

econ.soc.uoc.gr

Copyright © 2001 John Wiley & Sons, Ltd.

In this article we compare the forecasting performance of a linear and an artificial neural network (ANN) model of monthly aggregate stock returns. Our aim is to examine whether forecasts from the ANN model are preferable to forecasts from the linear model in terms of directional accuracy as well as forecast encompassing. Granger and Newbold (1986) indicated that a more stringent requirement than accuracy would be that the competing forecasts embody no useful information absent in the preferred forecasts. Clements and Hendry (1993) refer to this situation as forecast encompassing. In this article, we examine whether a ANN model encompasses a competitor linear model, in the sense of being able to explain the forecast errors made by the linear model.

On the basis of directional accuracy, we examine whether one model is better at predicting the direction of change of stock returns using the Pesaran and Timmermann (1992) testing procedure. On the basis of the forecast encompassing criterion, we examine whether the forecast errors of one model can be explained by the forecast of the other model, following the testing procedure in Clements and Hendry (1998). It should be noted that although the ANN model is expected to have a superior in-sample performance, since it may nest the linear model, there is no guarantee that it will dominate the linear model out-of-sample (Donaldson and Kamstra, 1996). Evidence of superiority of ANN forecasts might imply that nonlinearities in the relation between stock returns, trading volume and dividends do matter in forecasting. This would be consistent with the previous work suggesting that the relation between stock returns and these variables is nonlinear, thereby explaining the failure of linear present value models in describing stock market fluctuations.