Neural network linear forecasts for stock returns Angelos Kanas, страница 2

The remainder of this article is organized as follows. In Section 2 we describe the data used. In Section 3 we outline the neural network and linear models used to obtain out-of-sample forecasts. In Section 4 we discuss the empirical results from the directional accuracy and forecast encompassing tests. Section 5 provides a summary and concludes.

2. DATA AND PRELIMINARY STATISTICS

This study uses monthly data for aggregate stock returns, trading volume and dividends for two countries, namely the UK and the US. The stock index for the UK is the FT All Share index (FT), and the Dow Jones Industrial Average (DJ) for the US. As in Campbell et al. (1993), trading volume is the number of shares traded on the London Stock Exchange (LSE), and on the New York Stock Exchange (NYSE). The dividend series for each country is the dividend index constructed by Datastream. All series are expressed in natural logarithms. The monthly stock returns are continuous rates of return, computed as 100 times the first difference of the natural logarithm of the monthly stock price in successive months. Similarly, the percentage change in trading volume and the percentage change in dividends are computed as 100 times the first difference of the natural logarithms of the trading volume and dividend index series in successive months. The period under examination extends from January 1980 to June 1999, with a total of 234 observations for each series. The period from January 1980 to December 1994 is treated as the ‘trading’ in-simple period for the ANN and the estimation of the linear model. The subsequent period from January 1995 to June 1999 is the ‘testing’ out-of-sample period.

Descriptive statistics for stock returns, percentage changes in trading volume and dividends for the training period are reported in Table 1. As shown in this table, the sample mean of monthly stock returns is positive and statistically different from zero. The variances range from 0.003 (FT returns) to 0.11 (% change in trading volume on LSE). The measures for skewness and kurtosis indicate that the distributions of all the series are different from the standard normal. This Table also reports the augmented Dickey–Fuller (ADF) statistics for nonstationarity for all the series, as well as the BDS statistic for nonlinearities in the univariate stock return series for the DJ and the FT indices. The ADF test results suggest that all series are stationary, and the BDS test indicates that there is no nonlinear structure in the univariate series of FT and DJ returns.

Table 1. Preliminary statistics: period: January 1980–December 1994