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...
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