The analysis and surveillance of exchange rate movement has been a significant topic within macroeconomics. However, accurately predicting exchange rate levels has been a challenge for both academics and market professionals since the Bretton Woods system collapse. While numerous exchange rate forecasting models have been proposed, results from empirical studies have not been fully satisfying. This paper aims to compare the forecast performance of various competing models for exchange rate prediction, with an overview and classification provided in Section 2 and evaluation criteria discussed in Section 3.

The report presents the forecasting results in Section 4, while Section 5 provides a conclusion and explains the varying results seen in different studies regarding this issue. Additionally, the document includes an overview and classifications of mod

...els in Section 2a.

According to the Purchasing Power Parity (PPP) Model, changes in the price levels of two economies result in movements in their exchange rate. The PPP model uses the goods-market arbitrage mechanism to equalize prices between the two economies, as described by Madura in 2006. Mathematically, the exchange rate determination under this model is represented as lnet = lnpt – lnpt*, where et is the nominal exchange rate, and pt and pt* are domestic and foreign prices respectively. This model follows the same restrictive error-correction form used by Cheung et al.

(2004) is formulated as an equation: lnet+h – lnet = ? o + ? 1 (lnet - ? o – ? 1lnp~t) + ? t, where p~t is the relative domestic price level to the foreign price level, ? is a zero mean error term, and h is the forecast horizon. This setup permits the exchange rate to vary

as a correction of its last-period deviation from a long-run equilibrium b. Additionally, the Uncover Interest Rate Parity (UIP) Model describes how the exchange rate changes based on expected returns when holding assets in two different currencies. The UIP does not consider transaction costs or liquidity constraints and provides an arbitrage mechanism that drives the exchange rate towards a value that equalizes the returns on domestic and foreign assets (Madura, 2006).

The arbitrage relationship indicates that if the Uncovered Interest Parity (UIP) holds true, then Et(lnet+h – lnet) = it – it* where Et(lnet+h – lnet) is the expected exchange rate return from time t to time t+h. Moreover, it and it* represent the interest rate for the domestic and foreign currencies respectively (Cheung et al. 2004). In addition, the restrictive error-correction form tests the UIP model, which is lnet+h – lnet = ? o + ? 1 (lnet - ? o – ? 1lni~t) + ? t where i~t is the domestic long-term interest rate relative to the foreign country. The Structural Models, as chosen by Meess and Rogoff (1983), consist of three models that represent this category.

The three models available are the Frenkel-Bilson model, which allows for flexible pricing; the Dornbusch-Frankel model, which has sticky prices; and the Hooper-Morton model, which is a sticky-asset model. All three models share a similar quasi-reduced form specification, with the equation lnet = ao + a1(lnmt – lnm*t) + a2(lnyt - lny*t) + a3(lnis - lni*s) + a4(ln? e-ln? e*) + a5TB + a6TB* + u. In this equation, mt represents the domestic money supply, yt is domestic output, is is the short-term interest rate, and ? e

represents the expected long-run inflation. TB and TB* denote cumulated U.S. and foreign trade balances, while u is a disturbance term. The exchange rate displays first-degree homogeneity in relative money supplies (i).

Regardless of the model, the parameter a1 equals 1. The Frenkel-Bilson model enforces a4 = a5 = a6 = 0 to uphold purchasing power parity. On the other hand, the Dornbusch-Frankel model accounts for slow domestic price adjustment and deviations from PPP by setting a5 = a6 = 0. The Hooper-Morton model, which allows for long-run changes in the real exchange rate, places no such restrictions on the coefficients.

d. Meess and Rogoff (1983) used an unconstrained vector autoregression (VAR) as a representation of a multivariate time series model. The VAR model regresses the contemporaneous value of each variable against lagged values of itself and all other variables. The equation includes: lnet = ai1st-1 + ai2st-2 + … ainst-n + B’i1Xt-1 + B’i2Xt-2 + … B’inXt-n + uit, where Xt-1 is the vector of explanatory variables lagged j periods.

e. The Productivity Model assigns a central role to productivity differentials in explaining fluctuations in real and nominal exchange rates.

The text describes different models for determining the real exchange rate. One model drops the purchasing power parity assumption and considers the relative price of nontradables, which is a function of productivity differentials, as a factor. Another model, the Composite Model, includes various variables such as the relative price of nontradables, the real interest rate, the government debt to GDP ratio, the terms of trade and the net foreign asset. The Monetary Fundamental Model determines the fundamental value of the exchange rate through the relation

between the nominal exchange rate and monetary factors such as the relative money supplies and output levels.

The error-correction model for the basic exchange rate equation at forecast horizon k is represented by Lnet+k – Lnet = ? k + ? kzt + vt, where zt = ft – lnet. The value of ? k being equal to zero indicates an unpredictable exchange rate, while a positive ? k indicates the usefulness of the monetary model in describing long-run movements in the exchange rate. Meese and Rogoff (1983) and Cheung et al (2005) utilized a simple random walk model as a benchmark for evaluating the performance of different models.

Heaton (2008) specifies the driftless random walk model for an exchange rate in level as et+h = et + ? t. In 2005, Cheung et al re-evaluated exchange rate prediction by comparing the performance of five models: IRP, productivity-based, a composite specification, PPP, and the sticky-price monetary mode against the random walk. The models were estimated in error correction and first-difference specification, and their performance was evaluated at 1, 4, and 20 quarters forecast horizons by using the ratio between the mean squared error (MSE) of the models and a driftless random walk. A value smaller (larger) than one indicates a better performance of the models (random walk). The Diebold-Mariano statistic was used as a test for the null hypothesis of no difference in accuracy.

- The direction of change statistic measures the accuracy of predicting the direction of change and is calculated by dividing the number of correct predictions by the total number of predictions. A value above 50% indicates better forecasting, while a value below 50% implies

worse forecasting. The consistency criterion assesses the time series aspects of forecasting in terms of the long-term relative variation between forecasts and actual outcomes.

Meese and Rogoff (1983) conducted research to compare the out of sample accuracy of various exchange rate models with the random walk model. They used ordinary least squares, generalized least squares, and Fair's (1970) instrumental variable techniques to estimate each model. Mean error (ME), mean absolute error (MAE), and root mean squared error (RMSE) were used to measure out of sample accuracy. By analyzing these errors, the researchers were able to determine whether a model consistently over- or underpredicts.

The forecasting performance of standard exchange rate models based on macroeconomic fundamentals for the ?, German mark, CAD$, and Swiss franc versus the US$ was examined by Faust et al (2003) in real time. Different data vintages, real time data on the lagged economic fundamentals, and forecasts of future values of fundamentals were employed to compare the forecasting performance of the models on an international real-time data set. The monetary fundamental model used in Mark's (1995) paper was employed by Abhyankar et al (2005) to investigate whether the economic value of exchange rate forecasts from a fundamental model has greater value than random walk forecasts over various horizons. The study measured the economical or utility-based value to an investor who relies on this model to allocate her wealth between two assets that are identical in all respects except for the denominated currency. The study focused on two aspects: firstly, how exchange rate predictability affects optimal portfolio choice for investors with different horizons up to ten years and secondly, whether there is any additional economic

value to a utility-maximizing investor who uses exchange rate forecasts from a monetary-fundamental model compared to an investor who uses forecasts from a naive random walk model.

According to table 1 of Meese and Rogoff's 1983 study, none of the empirical models achieved a significantly lower RSME than the random walk model at any horizon. This means that even though the structural models were based on realized values of explanatory variables, they did not outperform the random walk model. The same result was found for univariate time series models.

Neither of the models were better than the random walk model for dollar/mark rate at any timeframe. Nevertheless, the models in table 2 had lower ME compared to their corresponding MAE (which had the same rankings as RMSE), implying that the models did not consistently under- or over-predict. The random walk model was not as dominant in ME as in RMSE and MAE. Cheung et al (2005) obtained comparable outcomes. The structural models did not obtain favorable MSE results overall.

Table 1 showed that, in most cases, it was not possible to distinguish between the forecasting performance of a structural model and a random walk model. However, Table 2 results indicated that the structural model was better at predicting the direction of change criterion than the random walk model. The highest prediction for correctly predicting the direction of change was PPP, followed by sticky price, composite, productivity, and IRP models. Interestingly, correct direction of change predictions were currency specific and clustered at the long forecast horizon.

According to Table 3 ; 4, the consistency criterion was met by just 9% of dollar-based exchange rate forecast series and 12% of yen-based.

Abhyankar et al's study in Figure 1 and Table 2 reported the implications for optimal portfolio weights when predicting the exchange rate versus it being a random walk. Predictability plays a crucial role in an investor's choices for all countries and various coefficient values of risk aversion. The predictability of monetary fundamentals has more economic value than a random walk model, leading to different optimal weights between foreign and non-predictable assets.

Moreover, if an individual has a low level of risk aversion, the predictability's economic value is not significantly influenced by the investment horizon's length. Mainly, at horizons spanning over a year, monetary fundamentals tend to predict future nominal exchange rates better than a naive random walk. The study conducted by Faust et al (2003) Figs 6-9 found that the mere data revisions effect on exchange rate predictability is reported. The revisions alone lead to a significant increase in the P-values connected to the test of long-horizon forecasting power and have a modest but crucial influence on the assessed relative RMSE. While their magnitude changes, their direction of effects remains alike across horizons and countries. Furthermore, as the data revision increases, the associated P-values are influenced similarly as relative RMSE increases, and ? k falls.

Regarding both real-time and revised-data forecasts, the monetary model's relative RMSE typically exceeds 1 and grows as the horizon lengthens, indicating the model's breakdown during that time period. Despite this, the relative RMSE is lower for all countries and horizons in the real-time test compared to the revised-data experiment. As a result, the monetary model's out-of-sample predictive ability is stronger when utilising real-time data rather than ex-post revised fundamental data. The Meese

and Rogoff (1983) study demonstrated the random-walk model's superior performance in out-of-sample exchange rate forecasting.

The results of various studies suggest that the random walk performs at least as well as univariate time series, unconstrained VAR, and structural models in terms of predictability. Faust et al (2003) found less evidence of predictability, supporting this conclusion. However, in Abhyankar et al's (2005) experiments, predictability significantly influenced the choice of domestic and foreign assets for all currencies and levels of risk aversion. In contrast, the monetary model typically produced weaker predictions than the random walk. These results suggest that utilizing fundamentals to forecast exchange rates can lead to significant gains.

Despite Cheung et al's (2005) results indicating that no specific model combinations were particularly successful, some models performed better than others at certain horizons and for certain exchange rates, but not for others or across all criteria. This has resulted in conflicting conclusions about the efficacy of models for exchange rate forecasting. The shortcomings may be tied to difficulties in selecting suitable fundamental data.

Meese and Rogoff (1983) utilized realized values of the fundamentals during the forecast period to make their predictions. Despite the advantage gained by providing the model with genuine future data for prediction, the models underperformed compared to a random-walk model. Meese and Rogoff attributed this failure to the instability of the global economy in 1980s, oil price shocks, changes in macroeconomic policy regimes, the inability of the models to incorporate other real disturbances accurately, as well as misspecification of money demand functions. Faust et al. (2003), on the other hand, based their analysis on original releases rather than fully-revised data and used real-time forecasts instead of

actual future fundamentals.

The research conducted by Abhyankar et al (2005) investigated whether there is any economic value for investors in exchange rate predictability, rather than relying on statistical measures such as RMSE, MAE or MSE to determine forecast accuracy. Meanwhile, Cheung et al's (2005) differing results could be linked to limitations in their study, including the fact that it only assessed linear models and did not incorporate the potential benefits of systems-based estimation (Mark and Sul, 2001) or panel regression techniques using long-run relationships (MacDonald and Marsh, 1997). Additionally, Cheung et al's study was solely focused on evaluating forecasting performance.

According to Clements and Henry (2001), the results do not always reflect the capacity of models to clarify exchange rate behaviour. The reference citation is Abhyankar, A., Sarno, L., Valente, G. (2005) in the Journal of International Economics, volume 66, pages 325-348, which provides evidence on the economic value of predictability regarding exchange rates and fundamentals.

The citation "Cheung, Y. , Chinn, M. , Pascual, A. 2005, ‘Empirical exchange rate models of the nineties: are any fit to survive? ’, Journal of International Money and Finance, 24, p. 1150-1175" is enclosed in a

tag.The Econometric Journal published Clements and Hendry's work in 2001 titled "Forecasting with difference and trend stationary models" in volume 4, pages S1 to S19.

The article 'The estimation of simultaneous equations models with lagged endogenous variables and first order serially correlated errors' by Fair, Ray C. in 1970 was published in Econometrica 38 and is accompanied by works from Faust, J., Rogers, J., and Wright, J.

Heaton (2008) published a fifth edition of A Practical Guide to Economic Forecasting, while

in 2003 he also wrote 'Exchange rate forecasting: the errors we've really made' for the Journal of International Economics (pp. 35-60).

p. MacDonald and I. Marsh wrote an article titled "On fundamentals and exchange rates: a Casselian perspective" in 1997.

The review titled "Review of Economics and Statistics" with a reference number of 79 and a page range of 655-664, as well as the book "International Financial Management" written by J. Madura in its 9th edition and published by South-Western Publishing in New York in 2006, along with the article authored by N. C. Mark in 1995 titled "Exchange rates and fundamentals: evidence on long-horizon predictability" in the American Economic Review with a page range of 201-218 are discussed.The citation for the article titled "Nominal exchange rates and monetary fundamentals: evidence from a small post Bretton Woods panel" by Mark, N. and Sul, D. is recorded as:

Journal of International Economics 53, 29e52.

Meese and Rogoff's (1983) article, "Empirical exchange rate models of the seventies: do they fit out of sample?" published in the Journal of International Economics, examines the adequacy of exchange rate models based on empirical evidence.

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