Applied Quantitative Methods for Trading and Investment

John Wiley & Sons

Chapter One

CHRISTIAN L. DUNIS AND MARK WILLIAMS

ABSTRACT

This chapter examines and analyses the use of regression models in trading and investment with an application to foreign exchange (FX) forecasting and trading models. It is not intended as a general survey of all potential applications of regression methods to the field of quantitative trading and investment, as this would be well beyond the scope of a single chapter. For instance, time-varying parameter models are not covered here as they are the focus of another chapter in this book and Neural Network Regression (NNR) models are also covered in yet another chapter.

In this chapter, NNR models are benchmarked against some other traditional regression-based and alternative forecasting techniques to ascertain their potential added value as a forecasting and quantitative trading tool.

In addition to evaluating the various models using traditional forecasting accuracy measures, such as root-mean-squared errors, they are also assessed using financial criteria, such as risk-adjusted measures of return.

Having constructed a synthetic EUR/USD series for the period up to 4 January 1999, the models were developed using the same in-sample data,leaving the remainder for out-of-sample forecasting, October 1994 to May 2000, and May 2000 to July 2001, respectively. The out-of-sample period results were tested in terms of forecasting accuracy, and in terms of trading performance via a simulated trading strategy. Transaction costs are also taken into account.

It is concluded that regression models, and in particular NNR models do have the ability to forecast EUR/USD returns for the period investigated, and add value as a forecasting and quantitative trading tool.

1.1 INTRODUCTION

Since the breakdown of the Bretton Woods system of fixed exchange rates in 1971-1973 and the implementation of the floating exchange rate system, researchers have been motivated to explain the movements of exchange rates. The global FX market is massive with an estimated current daily trading volume of USD 1.5 trillion, the largest part concerning spot deals, and is considered deep and very liquid. By currency pairs, the EUR/USD is the most actively traded.

The primary factors affecting exchange rates include economic indicators, such as growth, interest rates and inflation, and political factors. Psychological factors also play a part given the large amount of speculative dealing in the market. In addition, the movement of several large FX dealers in the same direction can move the market. The interaction of these factors is complex, making FX prediction generally difficult.

There is justifiable scepticism in the ability to make money by predicting price changes in any given market. This scepticism reflects the efficient market hypothesis according to which markets fully integrate all of the available information, and prices fully adjust immediately once new information becomes available. In essence, the markets are fully efficient, making prediction useless. However, in actual markets the reaction to new information is not necessarily so immediate. It is the existence of market inefficiencies that allows forecasting. However, the FX spot market is generally considered the most efficient, again making prediction difficult.

Forecasting exchange rates is vital for fund managers, borrowers, corporate treasurers, and specialised traders. However, the difficulties involved are demonstrated by the fact that only three out of every 10 spot foreign exchange dealers make a profit in any given year (Carney and Cunningham, 1996).

It is often difficult to identify a forecasting model because the underlying laws may not be clearly understood. In addition, FX time series may display signs of nonlinearity which traditional linear forecasting techniques are ill equipped to handle, often producing unsatisfactory results. Researchers confronted with problems of this nature increasingly resort to techniques that are heuristic and nonlinear. Such techniques include the use of NNR models.

The prediction of FX time series is one of the most challenging problems in forecasting. Our main motivation in this chapter is to determine whether regression models and, among these, NNR models can extract any more from the data than traditional techniques. Over the past few years, NNR models have provided an attractive alternative tool for researchers and analysts, claiming improved performance over traditional techniques. However, they have received less attention within financial areas than in other fields.

Typically, NNR models are optimised using a mathematical criterion, and subsequently analysed using similar measures. However, statistical measures are often inappropriate for financial applications. Evaluation using financial measures may be more appropriate, such as risk-adjusted measures of return. In essence, trading driven by a model with a small forecast error may not be as profitable as a model selected using financial criteria.

The motivation for this chapter is to determine the added value, or otherwise, of NNR models by benchmarking their results against traditional regression-based and other forecasting techniques. Accordingly, financial trading models are developed for the EUR/USD exchange rate, using daily data from 17 October 1994 to 18 May 2000 for in-sample estimation, leaving the period from 19 May 2000 to 3 July 2001 for out-of-sample forecasting. The trading models are evaluated in terms of forecasting accuracy and in terms of trading performance via a simulated trading strategy.

Our results clearly show that NNR models do indeed add value to the forecasting process.

The chapter is organised as follows. Section 1.2 presents a brief review of some of the research in FX markets. Section 1.3 describes the data used, addressing issues such as stationarity. Section 1.4 presents the benchmark models selected and our methodology. Section 1.5 briefly discusses NNR model theory and methodology, raising some issues surrounding the technique. Section 1.6 describes the out-of-sample forecasting accuracy and trading simulation results. Finally, Section 1.7 provides some concluding remarks.

1.2 LITERATURE REVIEW

It is outside the scope of this chapter to provide an exhaustive survey of all FX applications. However, we present a brief review of some of the material concerning financial applications of NNR models that began to emerge in the late 1980s.

Bellgard and Goldschmidt (1999) examined the forecasting accuracy and trading performance of several traditional techniques, including random walk, exponential smoothing, and ARMA models with Recurrent Neural Network (RNN) models. The research was based on the Australian dollar to US dollar (AUD/USD) exchange rate using half hourly data during 1996. They conclude that statistical forecasting accuracy measures do not have a direct bearing on profitability, and FX time series exhibit nonlinear patterns that are better exploited by neural network models.

Tyree and Long (1995) disagree, finding the random walk model more effective than the NNR models examined. They argue that although price changes are not strictly random, in their case the US dollar to Deutsche Mark (USD/DEM) daily price changes from 1990 to 1994, from a forecasting perspective what little structure is actually present may well be too negligible to be of any use. They acknowledge that the random walk is unlikely to be the optimal forecasting technique. However, they do not assess the performance of the models financially.

The USD/DEM daily price changes were also the focus for Refenes and Zaidi (1993). However they use the period 1984 to 1992, and take a different approach. They developed a hybrid system for managing exchange rate strategies. The idea was to use a neural network model to predict which of a portfolio of strategies is likely to perform best in the current context. The evaluation was based upon returns, and concludes that the hybrid system is superior to the traditional techniques of moving averages and mean-reverting processes.

El-Shazly and El-Shazly (1997) examined the one-month forecasting performance of an NNR model compared with the forward rate of the British pound (GBP), German Mark (DEM), and Japanese yen (JPY) against a common currency, although they do not state which, using weekly data from 1988 to 1994. Evaluation was based on forecasting accuracy and in terms of correctly forecasting the direction of the exchange rate. Essentially, they conclude that neural networks outperformed the forward rate both in terms of accuracy and correctness.

Similar FX rates are the focus for Gençay (1999). He examined the predictability of daily spot exchange rates using four models applied to five currencies, namely the French franc (FRF), DEM, JPY, Swiss franc (CHF), and GBP against a common currency from 1973 to 1992. The models include random walk, GARCH(1,1), NNR models and nearest neighbours. The models are evaluated in terms of forecasting accuracy and correctness of sign. Essentially, he concludes that non-parametric models dominate parametric ones. Of the non-parametric models, nearest neighbours dominate NNR models.

Yao et al. (1996) also analysed the predictability of the GBP, DEM, JPY, CHF, and AUD against the USD, from 1984 to 1995, but using weekly data. However, they take an ARMA model as a benchmark. Correctness of sign and trading performance were used to evaluate the models. They conclude that NNR models produce a higher correctness of sign, and consequently produce higher returns, than ARMA models. In addition, they state that without the use of extensive market data or knowledge, useful predictions can be made and significant paper profit can be achieved.

Yao et al. (1997) examine the ability to forecast the daily USD/CHF exchange rate using data from 1983 to 1995. To evaluate the performance of the NNR model, "buy and hold" and "trend following" strategies were used as benchmarks. Again, the performance was evaluated through correctness of sign and via a trading simulation. Essentially, compared with the two benchmarks, the NNR model performed better and produced greater paper profit.

Carney and Cunningham (1996) used four data sets over the period 1979 to 1995 to examine the single-step and multi-step prediction of the weekly GBP/USD, daily GBP/USD, weekly DEM/SEK (Swedish krona) and daily GBP/DEM exchange rates. The neural network models were benchmarked by a naïve forecast and the evaluation was based on forecasting accuracy. The results were mixed, but concluded that neural network models are useful techniques that can make sense of complex data that defies traditional analysis.

A number of the successful forecasting claims using NNR models have been published. Unfortunately, some of the work suffers from inadequate documentation regarding methodology, for example El-Shazly and El-Shazly (1997), and Gençay (1999). This makes it difficult to both replicate previous work and obtain an accurate assessment of just how well NNR modelling techniques perform in comparison to other forecasting techniques, whether regression-based or not.

Notwithstanding, it seems pertinent to evaluate the use of NNR models as an alternative to traditional forecasting techniques, with the intention to ascertain their potential added value to this specific application, namely forecasting the EUR/USD exchange rate.

1.3 THE EXCHANGE RATE AND RELATED FINANCIAL DATA

The FX market is perhaps the only market that is open 24 hours a day, seven days a week. The market opens in Australasia, followed by the Far East, the Middle East and Europe, and finally America. Upon the close of America, Australasia returns to the market and begins the next 24-hour cycle. The implication for forecasting applications is that in certain circumstances, because of time-zone differences, researchers should be mindful when considering which data and which subsequent time lags to include.

In any time series analysis it is critical that the data used is clean and error free since the learning of patterns is totally data-dependent. Also significant in the study of FX time series forecasting is the rate at which data from the market is sampled. The sampling frequency depends on the objectives of the researcher and the availability of data. For example, intraday time series can be extremely noisy and "a typical off-floor trader ... would most likely use daily data if designing a neural network as a component of an overall trading system" (Kaastra and Boyd, 1996: 220). For these reasons the time series used in this chapter are all daily closing data obtained from a historical database provided by Datastream.

The investigation is based on the London daily closing prices for the EUR/USD exchange rate. In the absence of an indisputable theory of exchange rate determination, we assumed that the EUR/USD exchange rate could be explained by that rate's recent evolution, volatility spillovers from other financial markets, and macro-economic and monetary policy expectations. With this in mind it seemed reasonable to include, as potential inputs, other leading traded exchange rates, the evolution of important stock and commodity prices, and, as a measure of macro-economic and monetary policy expectations, the evolution of the yield curve. The data retained is presented in Table 1.1 along with the relevant Datastream mnemonics, and can be reviewed in Sheet 1 of the DataAppendix.xls Excel spreadsheet.

All the series span the period from 17 October 1994 to 3 July 2001, totalling 1749 trading days. The data is divided into two periods: the first period runs from 17 October 1994 to 18 May 2000 (1459 observations) used for model estimation and is classified in-sample, while the second period from 19 May 2000 to 3 July 2001 (290 observations) is reserved for out-of-sample forecasting and evaluation. The division amounts to approximately 17% being retained for out-of-sample purposes.

Over the review period there has been an overall appreciation of the USD against the euro, as presented in Figure 1.1. The summary statistics of the EUR/USD for the examined period are presented in Figure 1.2, highlighting a slight skewness and low kurtosis. The Jarque-Bera statistic confirms that the EUR/USD series is non-normal at the 99% confidence interval. Therefore, the indication is that the series requires some type of transformation. The use of data in levels in the FX market has many problems, "FX price movements are generally non-stationary and quite random in nature, and therefore not very suitable for learning purposes ...

Continues...

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