Calendar Corrected Chaotic Forecast of Financial Time Series

ABSTRACT Using daily returns from the NASDAQ Composite and TSE 300 Composite indices from 1984 to 2003, we specify a method that corrects the chaotic forecasting of financial time series taking into account the day-of-the-week, the turn-of-the-month and the holiday effects. When calendar effects are present in the series, the forecasting ability of the model leads to profitable opportunities compared to a buy-and-hold strategy. JEL Classification: C22, C53, G14 Keywords: Calendar effects; Forecasting; Least median of squares; Trading rules; Chaos (ProQuest Information and Learning: . denotes formulae omitted.) I. INTRODUCTION Empirical studies on financial time series have revealed the presence of calendar effects in the behavior of stock returns. Calendar studies questioned whether irregularities exist in the rates of return during the calendar year. Knowing this, would better allow investors to predict returns on stocks. According to the Efficient Market Hypothesis (EMH) such seasonal patterns should not persist since their existence implies the possibility of obtaining abnormal returns applying market-timing strategies. The day-of-the week effect, first documented by Osborne (1962); the weekend effect (significantly lower returns over the period between Friday's close and Monday's close), first documented by French (1980); the January effect (relatively higher returns in January), first reported by Wachtel (1942); the trading month effect studied by Ariel (1987); and the holiday effect documented by Lakonishok and Smidt (1988), are among the most important calendar effects. These calendar effects have been studied extensively in international level (e.g. Dubois and Louvet (1995), Hiraki and Maberly (1995), Aggarwal and Schatzberg (1997), Mookerjee and Yu (1999), Mills et al. (2000)) and the general conclusion is that there are particular periods of time where the investors' behavior changes significantly, affecting the distribution of returns. Given the existence of the aforementioned market anomalies, that provide evidence of market inefficiencies, the fundamental question is how this information can be utilized by forecasting models, leading to better portfolio performance. Jensen (1978) highlights the importance of trading profitability when assessing market efficiency: "if a trading rule is not strong enough to outperform a buy and hold strategy on a risk-adjusted basis then it is not economically significant", while Roll (2000) argues that "if calendar time anomalies represent evidence of market inefficiencies, then they ought to represent an exploitable opportunity". Extending previous work of Lisi and Medio (1997), Cao and Soofi (1999), among others, who applied non-linear techniques in financial applications providing better results compared to the random walk forecasts, this study utilizes a nonlinear chaotic forecasting method on the NASDAQ and Toronto Stock Exchange Composite indices, taking into account specific stylized irregularities of stock returns, reported in empirical finance literature, such as the calendar effects. The methodology applied in the present study overcomes the limitations of previous empirical work, in which either the calendar effects were not taken into account or the predictive ability of the forecasting models was not tested extensively. The rest of the study is organized as follows: Section 2 describes the data set. Section 3 introduces the algorithm that takes into account the day-of-the-week, the turn of the month and the holiday effect, while Section 4 presents the results of the proposed method. Finally, Section 5 concludes proposing directions for future research. II. THE DATA SETS AND PRELIMINARY DIAGNOSTICS The dataset used is comprised of the NASDAQ Composite and the Toronto Stock Exchange 300 Composite (TSE 300), both indices belonging to mature markets having a high trading volume. …