Improving Moving Average Trading Rules with Boosting and Statistical Learning Methods

Journal of Forecasting

J. Forecast. 27, 433–449 (2008)

Published online 10 May 2008 in Wiley InterScience

(www.interscience.wiley.com) DOI: 10.1002/for.1068

Improving Moving Average Trading Rules

with Boosting and Statistical Learning Methods

JULIÁN ANDRADA-FÉLIX AND

FERNANDO FERNÁNDEZ-RODRÍGUEZ*

Department of Quantitative Methods in Economics and

Management, University of Las Palmas de Gran Canaria, Spain

ABSTRACT

We present a system for combining the different types of predictions given by a wide category of mechanical trading rules through statistical learning methods (boosting, and several model averaging methods like Bayesian or simple averaging methods). Statistical learning methods supply better out-of-sample results than most of the single moving average rules in the NYSE Composite Index from January 1993 to December 2002. Moreover, using a fi lter to reduce trading frequency, the fi ltered boosting model produces a technical strategy which, although it is not able to overcome the returns of the buy-and-hold (B&H) strategy during rising periods, it does overcome the B&H during falling periods and is able to absorb a considerable part of falls in the market. Copyright © 2008 John Wiley & Sons, Ltd.

key words  technical analysis; boosting; statistical learning; model selection;

combining forecasts

INTRODUCTION

Technical analysis consists of the attempt to forecast prices of a fi nancial market by the study of past prices and other related summary statistics concerning security trading. In spite of the sceptical attitude of academics towards technical analysis, during the last 20 years technical analysis has been enjoying a renaissance in the academic world, and a considerable amount of theoretical and empirical work has been developed supporting the technical analysis. Thus theoretical models have been proposed by Hellwig (1982), Treynor and Ferguson (1985), Brown and Jennings (1989) and Blume et al. (1994). Also, many empirical papers provide evidence of the profi tability of technical trading rules, outstanding among others are Brock et al. (1992), Levich and Thomas (1993), Blume et al. (1994), Knez and Ready (1996), Gençay (1996), Neely et al. (1997) and Chang and Osler (1999).

* Correspondence to: Fernando Fernández-Rodríguez, Facultad de Ciencias Económicas y Empresariales, 35017 Las Palmas de Gran Canaria, Spain. E-mail: ffernandez@dmc.ulpgc.es

The purpose of our paper is to provide a system for combining the different types of predictions provided by a wide category of mechanical trading rules. Through statistical learning methods (such as boosting, and several model averaging methods like Bayesian or committee), new predictions will be constructed based on a given a set of technical predictions.

The remainder of this paper has been structured as follows. In the next section a brief review of technical trading rules used in this paper is presented. The third section focuses on describing the most popular statistical learning methods such as ‘Boosting’, and ‘Bayesian model averaging’. The fourth section presents the fi tness measures employed to evaluate and compare the technical trading rules created. The fi fth section shows the empirical results. The sixth section presents the main conclusions.

TECHNICAL TRADING RULES

In this paper we study the predictive power concerning the combination of information from one of the most popular trading rule families employed in technical analysis, the variable moving average rules (VMA henceforth). VMA rules involve comparison of a short-term moving average of prices to a long-term moving average. Therefore, buy (sell) signals are emitted when the short-term average exceeds (is less than) the long-term average by at least a pre-specifi ed percentage band. The introduction of a band around the moving average reduces the number of buy (sell) signals by eliminating the market ‘whiplash’ when the short- and long-period moving averages are close. This band, which is normally considered as 1%, reduces the number of buy and sell signals. No signal is generated when the short moving average is within the band. With a band of zero, the technical rule provided by the VMA classifi es all days into either buy days or sell days.

The length of the moving averages must be selected by the technician. The most popular rule used in technical analysis is 1–200, where the short period is 1 day and the long period is 200 days. Nevertheless, other much-used trading rules are 1–50, 1–150, 5–150, 1–200 and 2–200 (see Brock et al., 1992).

The sceptical attitude of the academic world concerning technical analysis is motivated by the effi cient market hypothesis, which holds that available public information, like past prices, should not help traders earn unusually high returns once a risk premium has been discounted. Thus Fama (1970, 1976) defi nes a market as being weak-form effi cient if current prices fully refl ect the information contained in past prices. Weak-form effi ciency implies that technical analysis of past stock prices has no value.