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105

gated financial instruments. When the measurement interval exceeds a threshold value called the stabilization interval, the Epps effect gives way to a rather stable behavior of the correlation. There is some preliminary evidence of an inverse relationship between the stabilization interval and the mean tick frequency of the instruments involved. If financial markets are composed of heterogeneous agents as suggested in Section 7.4, the stabilization interval can be interpreted as a threshold between groups of agents. For extremely short-term traders focusing on time horizons below the stabilization interval, correlations between instruments may be less of an issue than for other agents.

In applications such as asset allocation or risk assessment, the return measurement intervals should preferably be chosen longer than the stabilization interval. However, there is no general "best" time interval for measuring correlation. It is important to choose the most relevant interval size for a specific application.



TRADING MODELS

i i.i introduction

Recently, the skepticism among academics to the possibility of developing profitable trading models has decreased with the publication of many papers that document profitable trading strategies in financial markets, even when including transaction costs.

In the earlier literature, simple technical indicators for the securities market have been tested by Brock et al. (1992). Their study indicates that patterns uncovered by technical rules cannot be explained by simple linear processes or by changes in the behavior of volatility.1 LeBaron (1992a), LeBaron (1997) and I .cvich and Thomas (1993b) follow the methodology of Brock et al. (1992) and use bootstrap simulations to demonstrate the statistical significance of the technical

In Gengay (1998b), the DJIA data set of Brock et al. (1992) is studied with simple moving average indicators within the nonparametric conditional mean models. The results indicate that nonparametric models with buy-sell signals of the moving average models provide more accurate sign and mean squared prediction errors (MSPE) relative to random walk and GARCH models. Gencay (1999) shows that past buy-sell signals of simple moving average rules provide statistically significant sign predictions for modeling the conditional mean of the returns for the foreign exchange rates. The results in Gencay (1999) also indicate that past buy-sell signals of the simple moving average rules are more powerful for modeling the conditional mean dynamics in the nonparametric models.



trading rules against well-known parametric null models of exchange rates. Sullivan et al. (1999) examine the trading rule performance by extending the Brock et al. (1992) data for the period of 1987-1996. They show that the trading rule performance remains superior for the time period that Brock et al. (1992) studied; however, these gains disappear in the last 10 years of the Dow Jones Industrial Average (DJIA) series. Lo etal. (2000) have proposed an approach to evaluate the efficacy of technical analysis based on technical pattern recognition using nonpara-metric kernel regression. They apply their method to a large number of U.S. stocks and they report that several technical indicators provide incremental information of practical value. Overall, the scope of the most recent literature supports the technical analysis, but it is generally limited to simple univariate technical rules. One particular exception is the study by Dacorogna et al. (1995), which examines real-time trading models of foreign exchanges under heterogeneous trading strategies. They conclude that it is the identification of the heterogeneous market microstructure in a trading model which leads to an excess return after adjusting for market risk.

Trading models are investment tools that provide explicit buy and sell trading recommendations. A clear distinction should be made between a price change forecast (presented in Chapter 9) and an actual trading recommendation. A trading recommendation naturally includes a type of price change forecast, but must also account for the specific risk profile of the dealer or user of the respective trading model. Another distinction is that a trading model must take into account its past trading history. This decision might be biased by the position it is currently holding and the price paid for entering in this position, whereas a price forecast is not submitted to such asymmetries. A trading model thus goes beyond predicting a return. It must decide if a certain action is to be taken. This decision is subject to the specific risk profile, the trading history, and institutional constraints such as opening hours or business holidays.

The purpose of this chapter is not to provide ready-to-use trading strategies, but to give a description of the main ingredients needed in order for any realtime trading model to be usable for actual trading on financial markets. Any reasonable trading strategy is composed of a set of tools that provides trading recommendations within a capital management system. In this book we shall not discuss the capital management part, but we wish to show that with a reasoned approach and high-quality data, it is possible to design practical and profitable trading models. Indeed, we have developed our own trading models and this presentation builds on this experience. Our models anticipate price movements in the foreign exchange (FX) market sufficiently well to be profitable for many years yet with acceptable risk behavior, and, they have been used by many banks.

Market investors mainly use trading models as decision tools, but in this chapter we will also illustrate that profitable trading models with robust performance measures can be employed as a statistical tool to study the market structure and to test the adequacy of price-generation processes.



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