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Box & Jenkins Method

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I. Introduction

Many market participants, namely, international investors, banks, non-bank financial institutions, portfolio managers, are interested in coming up with a model, which accurately predicts exchange rates. Managers of multinational corporations are interested in accuracy of such foreign exchange prediction models as it directly impacts their activities relating to exposure management, hedging, arbitraging, investing and financing decisions. Policymakers frequently monitor exchange rates to better understand their impact on trade positions, and consequently, domestic employment, business and revenue prospects. Nowadays, more attention is being focused on foreign exchange rate prediction models since the foreign exchange market is considered to be the world's biggest financial market, with an average daily trading of $ 1.2 trillion.

The failure of standard economic models to display any out-of-sample forecasting ability over horizons of up to one year "continues to exert a pessimistic effect on the field of empirical exchange rate modeling in particular and international finance in general" (Frankel and Rose, 1994). 1 As a result of this lack of success, many economists have turned to alternative approaches to modeling exchange rates over shorter horizons. One important line of research considers the effect that technical analysts or noise traders may have on the market. Technical analysts ignore fundamental variables (such as money supplies, income levels or interest rates) and instead use statistical, graphical or, in some cases, astrological techniques to predict exchange rates. Many economists argue that dealing by noise traders may be sufficient to drive a wedge between the market price and the `true' fundamental price. The market price only returns to the fundamental price in the long run when the random effects of the supposedly irrational noise traders wash out. It is argued, therefore, that economic models may only display long run forecasting ability.

Forecasts of exchange rates have traditionally relied on both structural and time series models. Some studies such as Mussa (1979), Meese and Rogoff (1983), Huang (1984) and Chiang (1986) have concluded that exchange rates follow a random walk process, and that out-of-sample forecasts of exchange rates underperform the forecasts derived using the random walk model. Such poor performance of traditional exchange rate models has been documented in numerous studies [Diebold and Nassan (1990), Prescott and Stengos (1988), White (1988), Meese and Rose (1989) and Haache and Townsend (1981)]. Reasons for dismal performance of exchange rate forecasting models include volatility of time-varying premiums, volatility of long run exchange rates, poor measurement of inflationary expectations and misspecification of money demand functions (Meese and Rogoff (1983)).

Forecast performance of exchange rate prediction models have been extensively studied. Goodman (1979) rated 23 commercial exchange rate forecasting services and found that technically oriented services were more accurate than economically oriented services, but Levich (1980) discovered that econometrically based services outperformed technically based services in the short run. Many studies have been successful in developing forecast models, which do better than the random walk model. Hogan (1986) found that forecast models do better than random walk models in forecasting the Australian/U. S. dollar exchange rate. Similar results were obtained by Shinasi and Swamy (1986).

Even professionals in the currency markets, who are able to incorporate fundamental determinants, technical analysis and other factors into their forecasts, seem unable to out-perform a naive prediction of no change. The best prediction of the in three months' time still appears to be today's rate. Finally, it should be noted that this conclusion is based on forecasts over a three-month horizon. Considerable evidence exists that simply using fundamental factors can help predict the exchange rate over long horizons (i.e. in excess of twelve months), while there have been no studies to date of ultra-short horizon forecasts. This latter area of one day, one hour or even one minute forecast horizons should be investigated if we are to gain a better insight into the operation of the foreign exchange rate market.

II. Popular Exchange Rate Forecasting Models

Structural and time-series models have been typically used to forecast exchange rates. The Structural approach to exchange rate modeling was developed in several studies such as those by Bilson (1978, 1979), Frenkel (1976), Dornbusch (1976), Frankel (1979, 1981) and Hooper and Morton (1982). These structural models could not outperform the random walk models at horizons up to one year.

Time series models of exchange rate determination were also developed to get better forecasts. It is better for the fact that the method is stochastic. Among the approaches used in forecasting exchange rates were the Vector Auto-regression (Canarella and Pollard (1988)), univariate and multivariate autoregressive models (Meyer and Startz (1982)) and the popular random walk model (Finn (1986); Hakkio (1986) and Frattiani et al. (1987)). All of these are based on Box & Jenkins model of Time series analysis.

Exponential smoothing models are adaptable to adjustments to include trend and/or seasonality (Jarrett (1987)). Further, they provide self-correcting forecasts with built-in adjustments that regulate forecast values by changing them after "learning" from direction of past errors. It has been found that these models perform quite well, in the aggregate, when compared with time series models.

Forecasting foreign exchange rates is a vital task for fund managers, lenders and corporate treasurers as well as specialized traders. This task is very difficult as shown by the fact that only three out of every ten spot foreign exchange dealers will make a trading profit in a given year. Given the complexity of the task and the large potential for profit if successful, many have shown an interest in applying Neural networks to forecasting exchange rates. Institutions such as Chemical Bank, Citibank, Morgan Stanley, Dresdner Bank, ABN-AMRO, Societe Generale and Daimler-Benz have either published the results of their research in this area or attended conferences devoted to it.

There are two types of forecasting that are of value in currency trading. Multi-step prediction aims to determine general trends in a currency exchange rate for a given time-period such as the next twenty trading days. To produce this prediction, the forecasts of the network are fed back as inputs to give a prediction



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