Forecasting Nominal Exchange Rate of Indian Rupee vs. US Dollar

Forecasting Nominal Exchange Rate of Indian Rupee vs. US Dollar Ajay Kumar Panda* In this paper the Theory of Flexible Price and Sticky Price Monetary model are empirically analyzed by using the Vector Autoregression (VAR) model to forecast nominal exchange rate of Indian Rupee against US Dollar. The period considered for analysis is January 1990 to January 2005. The forecast performance of the two models has been evaluated through RMSE, MAE, and MAPE in case of in-sample and out-of-sample. The study concludes that Sticky Price Monetary model performs better than Flexible Price Monetary model for in-sample as well as out-of sample. It is also found that the model is able to predict in-sample exchange rate better than out-of-sample exchange rate. Introduction Forecasting exchange rate is extremely varied both in terms of its type and the reasons for which the forecasts are made. Forecasts are required for currencies that float against other currencies and also for currencies which are pegged within stated intervention bands. It also varies on the basis of forecast horizons as per the requirements of economic agents. Forecasts are required by traders for very short-run to medium-run horizons and by corporate planners for long-run horizon. Hence, it seems unlikely that a single forecasting approach would lead to similar results in these varied settings. To be successful, an exchange rate forecasting should be carried out in a framework, which takes into account three key economic factors, namely, the exchange rate system, forecast horizon, and exchange rate units. Exchange rate system refers to the institutional system; the system could be a pegged, a fully floating, or a managed floating system. Likewise, under exchange rate horizon, the time period has to be pre-fixed over which the forecast is to be done, namely, short-term, medium-term or long-term horizon. And thirdly, one has to move along one s objective of forecasting either nominal or real exchange rate (i.e., exchange rate units). In any forecasting exercise, there are two aspects, which are of particular importance, namely, the degree of predictability and the accuracy of forecast. The variables to be forecast vary greatly in their degree of predictability. Some variables can be predicted to a considerable degree of certainty, whereas some are very uncertain. The forecasting accuracy is also important. A high forecasting accuracy could facilitate gaining a high return from the investment and helps in avoiding unprofitable ventures. There will be however, some forecasting errors that is inevitable. A forecasting method with less error, greater accuracy, and a high correlation with actual value should be adopted and appreciated. Questions have, however, been raised about the predictability (and therefore the possibility of good forecasts) of exchange rates. * Research Scholar, Department of Economics, University of Hyderabad, Hyderabad, Andhra Pradesh, India. E-mail: ajayeco@yahoo.com 2007 The Icfai University Press. All Rights Reserved. 66 The Icfai Journal of Applied Finance, Vol. 13, No. 6, 2007

Now the question is: how to forecast? What are the variables that are having a deterministic power on exchange rate? There are many theoretical models that explain the behavioral relationships between exchange rate and macroeconomic variables. In particular, more importance was given to capital account balance by the end of the 1960s. This thinking reflected in two different classes of asset equilibrium models, namely, the monetary approach and the portfolio balance approach to the balance of payments. Within each class, there have been different variations based on different assumptions. These models had their empirical counter parts in the form of single equation reduced form models, which could be tested. This study aims at forecasting monthly exchange rate (i.e., Rupee vs. Dollar) for flexible price and sticky price monetary model by using the VAR methodology, and tests the comparative predictability of the two theoretical models by using RMSE, MAE, and MAPE. Monetary Model of Exchange Rate Determination The monetary model of exchange rate determination contends that exchange rate movements can be explained by changes in supply and demand for national money. The monetary model is based on the uncover interest parity condition, which states that the difference between domestic and foreign interest rates is equal to the expected rate of depreciation of the exchange rate, i.e., E s = r r*...(1) Based on these two basic assumptions, several models are put forward to explain exchange rate behavior. These models differ among themselves in the further assumptions that they make. Three of the most important versions of the monetary model are: the flexible price monetary model, the sticky price monetary model, and the real interest rate differential model. A common characteristic of each of these models is that the supply and demand for money is the main determinant of the exchange rate. This study discusses only the flexible price monetary model and the sticky price monetary model. The Flexible Price Monetary Model This model was developed by Frenkel (1976), Mussa (1976), and Bilson (1978) which explicitly introduced relative money stocks into the picture as determinants of the relative prices, which in turn determines the exchange rate. It begins by assuming that there is a conventional money demand function, written as: m p = y r...(2) where, m = log of domestic money shocks, p = log of domestic price level, y = log of domestic real income, and r = the domestic interest rate. The equation (2) implies that the demand to hold real money balance is positively related to real income due to increased transaction demand and inversely related to the domestic interest rate. Forecasting Nominal Exchange Rate of Indian Rupee vs. US Dollar 67

A similar relationship holds good for the foreign money demand function, as m* p* = * y* *r*...(3) where, m*= log of foreign nominal money stocks, p* = log of foreign price level, y* = log of foreign real income, and r* = foreign interest rate. It is assumed that Purchasing Power Parity (PPP) holds continuously which is written as: Es = p p*...(4) Equations (2) and (3) may be rewritten as: p = m y + r...(5) and p* = m* *y* + *r*...(6) where the parameters and * are the income elasticities of the demand for real money balances while and * are the interest rate semi-elasticities. Now, by substituting (5) and (6) in equation (4) we will get: Ex = (m y + r) (m* *y* + *r*)...(7) When two money demand functions are assumed to be identical, Ex = (m m*) (y y*) + (r r*)...(8) Equation (8) is a reduced form exchange rate equation, which states that Ex is determined by m, y, and r independently, and these are the determinants of exchange rate for flexible price monetary model. It can be noted here that an essential assumption of this model is that all prices including exchange rates are perfectly flexible in both the short- and the long-run. Sticky-Price Monetary Model The flexible price monetary model assumes that PPP holds continuously, and exchange rates are flexible in both the directions. In fact, it is price change that induced exchange rate changes through PPP. So, the model cannot explain prolonged departures from PPP. But empirical observations have shown that the PPP does not hold in the short-run. Dornbusch (1976) proposed a model that explains these departures from PPP. This model is termed as the sticky price monetary model. The basic idea underlying the model is that prices in the goods market and wages in the labor market are determined in sticky price market and they only tend to change slowly over time in response to economic shocks. Prices and wages are especially resistant to downward pressure. However, the exchange rate is determined in flexible price market and it can immediately appreciate or depreciate in response to new shocks. In such cases, exchange rate is unable to match with corresponding price movement, and so, there can be a persistent and prolonged departure from PPP. As a result, the exchange rate jumps its long-run equilibrium value in the shortrun, which Dornbusch noted as exchange rate overshooting. The sticky price monetary model introduced by Frankel (1979) was based on a specification form as: 68 The Icfai Journal of Applied Finance, Vol. 13, No. 6, 2007

Ex = (m m*) (y y*) (r r*) + (Ee Ee*)...(9) where, Ee and Ee* denote expectations held about the long-run rates of inflation in the two countries. Review of Literature Meese and Rogoff (1983a) studied the exchange rate models of the 1970s and tested the forecasting accuracy of popular exchange rate models. Three models were tested, including the flexible price monetary model, real interest rate differential model, and the sticky price and portfolio balance model. These models were estimated by using ordinary least square, generalized least square, and Fair s instrumental variable techniques. They concluded that Random Walk model performed better than univariate time series, vector autoregression, and the structural models in forecasting the three bilateral exchange rates, namely, Dollar/Mark, Dollar/Pound, and Dollar/Yen. One of the earlier studies to use more sophisticated time series methods was Backus (1986), who used VAR to check the causality between exchange rate, relative price levels and trade balances. The result of impulse response function in the VAR model was also taken into account. Kamaiah et al. (1989) have developed a VAR model for the Deutschemark (DM)-US Dollar bilateral exchange rate, which is different from the Meese-Rogoff model that the VAR system in their model contains a deterministic component. The model uses real GDP as a component exogenous to the VAR system. Paul and Ashtekar (1990) employed a time series method, making use of information from structural model literatures through VAR, for the purpose of forecasting exchange rate. The exchange rates studied were Dollar-Sterling, Mark-Dollar, Yen-Dollar, Swiss Franc-Dollar, and Rupee-Dollar exchange rates. Kulkarni and Chakraborty (1990) found that Indian Rupee has steadily depreciated in the last two decades vis-à-vis Dollar. One explanation for this phenomenon is the relative differences in the inflation rates of India and the US. The study was intended to test the argument of the PPP theory with respect to the fluctuation of the Indian Rupee vis-à-vis US Dollar. MacDonald and Taylor (1993) examined the monetary model of exchange rate from a number of complementary perspectives such as from the point of validity of the model in its forward looking and rational expectation formulation. The purposes of the study are: (a) to show that the static monetary approach to the exchange rate has some validity when considered as a long-run equilibrium condition, (b) to see how monetary models reject the assumption of speculative bubbles hypothesis, (c) to see if the full set of rational expectation restrictions imposed by the forward-looking monetary model are rejected, and finally (d) to demonstrate that the monetary model can be used to generate a dynamic error-correction exchange rate equation that has robust in-sample and out-of-sample properties including beating a random walk in post-sample forecasting. Forecasting Nominal Exchange Rate of Indian Rupee vs. US Dollar 69

Johnston and Yan Sun (1997) studied the role of long-run monetary and cyclical factors in determining the exchange rate movements. Their empirical analysis was applied to a dataset that includes Canada, Germany, Japan, the United Kingdom, and the United States. Diebold and Kilian (1995) studied the usefulness of unit root tests as diagnostic tool for forecasting the models. The difference stationary and trend stationary models of economic time series often imply very different predictions. Therefore, a pre-decision of which model to take is very important for a researcher from the point of view of which model to apply for forecast. Generally, the forecasters follow three basic procedures (1) difference the data, (2) never difference the data, and (3) use a unit root pre-test. Here, authors purposefully want to explore systematically the extent to which pre-testing for unit roots affect forecast accuracy for a variety of degrees of persistence, forecast horizons, and sample size. They focused on the univariate trending autoregressive, AR (1) case with high persistence. Apart from these, many extensive studies have taken place such as Diebold and Mariano (1995), Meese and Rogoff (1983b), and Lin and Chen (1998) on different aspects of exchange rate modeling of monetary models. Time Series Modeling The flexible price and sticky price monetary presented the causal inter-relationships and dynamic interactions between the exchange rate and macroeconomic variables in an economy. The study employed the time series mode, that is, VAR model to forecast exchange rate using the macroeconomic variables of the respective models and finally compared the predictive accuracy of these two models with the help of Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). A time series where mean, variance and covariance are time invariant is said to be (covariance or weakly) stationary. The data, which do not possesses this property, is called non-stationary, for example, a random walk process. A non-stationary process is also called a unit root process. Most of the macroeconomic time series data in general and financial variables in particular are sensitive to shocks and known to be non-stationary. Since econometric models using non-stationary data are likely to violate the desirable statistical properties of the estimators and or give misleading inferences, it has become necessary to test the stationarity of the series before attempting any econometric exercise. For the test of stationarity, the study uses Dicky-Fuller, Augmented Dicky-Fuller and Phillips-Perron tests. The next important task is selection of lag length. In principle, it is possible to have different lag lengths for different variables both within and across equations. If there are good reasons to do this, one can specify and estimate such a model called the near VAR. The Seemingly Unrelated Regression Estimation (SURE) method can be used to get efficient VAR estimates. On the other hand, if all the variables in the VAR model have the same lag length, then the model will be symmetric and can be estimated using Ordinary Least Square (OLS) method. The OLS estimators then will be consistent and asymptotically efficient. Further, in a VAR model, fewer lags are preferred because higher lag length for any variable implies more parameters to be estimated and less degree of 70 The Icfai Journal of Applied Finance, Vol. 13, No. 6, 2007

freedom. Thus, it would be convenient to use the optimal and the same lag length for all equations. There are various alternative criteria that can be used for selecting the optimal lag length. The present study used Akaike s Final Prediction Error (FPE), Akaike Information Criterion (AIC), Schwarz Criterion (SC), Likelihood Ratio (LR) criterion and Hannan-Quinn information criterion (HQ). The next task is orderings of the variables which is very crucial in VAR modeling. This is in a way related to the problem of identification in simultaneous system, which the VAR model imitates. In structural VAR, it is essential to have parametric restrictions (often zero values restrictions) to identify all the coefficients. This will result in recursive systems sometimes. Alternatively, Choleski decomposition, which restricts the variance-covariance matrix of residuals of the standard VAR, can be used to get identification. Yet another way is to order the variables in the standard VAR, keeping the economic theory and model structure in mind. This study has taken the orderings from the model itself. Vector Autoregression (VAR) In single equation time series framework, it is possible to study the effect of a shock of a time dependent and an exogenous variable using intervention and transfer function analysis respectively. Sometimes, the relationship between variables in a dynamic system cannot be represented in a single equation time series model. Further, when one is not confident that a variable is truly exogenous, a natural extension of transfer function analysis is to treat each variable symmetrically. This can be explained with the help of a simple example. Following Enders (1995), let the time path of consumption expenditure (c t ) be affected linearly by the current and past realizations of income (y t ) and vice versa. This implies the following simple bivariate system between these variables: c t b 10 b y t + 11 c t 1 + y t 2 + ct...(10) y t b 20 b c t + c t 1 + 22 y t 1 + yt...(11) It is assumed that both c t and y t are stationary and the error terms, ct and yt satisfy the OLS assumptions (white noise properties). The above two equations (10) and (11) constitute a first order Vector Autoregression (VAR) because the longest lag length is unity. Such a system is also known as a structural or primitive VAR. This simple two variable first-order VAR is useful and can be generalized to a multivariate higher-order system. Here, the structure of the model incorporates feedback effects since (c t ) and (y t ) are allowed to affect each other. Hence, ct has an indirect contemporaneous effect on y t and yt has an indirect contemporaneous effect on c t due to the feedback inherent in the system. The reduced form of the above system can be written as: c t a 10 + a 11 c t 1 + a y t 1 + e ct...() y t a 20 + a c t 1 + a 22 y t 1 + e yt...(13) where, a 10 b10 bb 1 b b 20 a 11 11 b 1 b b a b 1 b b 22 Forecasting Nominal Exchange Rate of Indian Rupee vs. US Dollar 71

a 20 b20 bb 1 b b 10 a b 1 b b 11 a 22 22 b 1 b b e ct ct b 1 b b yt and e yt yt b ct 1 b b In contrast to the system in equations (10) and (11), the reduced form model in equations () and (13) is called the standard VAR or simply the VAR model. Since ct and yt are white-noise processes, it follows that e ct and e yt have zero mean, constant variance and are individually serially uncorrelated. Clearly, there is the well-known identification problem in the sense that the coefficients of the structural VAR (ten in number, including the two variances of ct and yt ) cannot be obtained from the coefficients of the standard VAR (only nine in number, including the two variances and one covariance of e ct and e yt ) without imposing identifying restrictions on the parameters of the structural VAR and error variance-covariance terms. To identify both the structural equations, at least two zero restrictions are needed on the parameters of the structural VAR. If one is not interested in the structural model, one may specify and estimate only the standard VAR. This option may be alright for say impulse response, variance decomposition, and forecasting purposes, as in the study. But, one cannot retrieve the structural model. Sometimes, it may be necessary to include more than just one lag of the variables in the model. With p lags included, a more general reduced form will be of the following form: c t 1 + 1 c t 1 +...+ p c t p + 1 y t 1 +...+ p y t p + ct...(14) y t 2 + r 1 c t 1 +...+ r p c t p + 1 y t 1 +...+ p y t p + yt...(15) Writing the above equations (14) and (15) in vector and matrix notation, we get: Y t = V+A 1 Y t 1 + +A p Y t p + U t...(16) where, ct Yt yt 1 V 2 A i i ri i i U t ct yt The process in equation (11) looks like an autoregressive process, but the variables in the equations, Y t, V, A 1, Y t 1, U t are all in a vector form. So this is known as Vector Autoregressive (VAR) model of order p and this is a bivariate system. Similarly, a system of m variables can also be written as: 72 The Icfai Journal of Applied Finance, Vol. 13, No. 6, 2007

Y t = V+A 1 Y t 1 +A 2 Y t 2 +. +A p Y t p +U t where, Y t = (Y 1t, Y 2t, Y mt ) T V = (V 1, V 2, V 3,V m ) T U = ( 1t, 2t,, mt ) T A i 11,i m1,i...... 1m,i mm,i U t has the same stochastic properties as the reduced form error in the system of dynamic equation. Forecast Performance Measures There are many alternative criteria to evaluate forecasting performance. The following criteria have been used in this study: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). To understand the above criteria, let Xˆ ˆ ˆ, X,..., X denote the predicted values 1 2 N of X 1, X2,..., X N for a sample of size N. The criteria are listed below: RMSE: The root mean square error between actual and predicted values is computed as: RMSE 1 N N t 1 ( X t Xˆ t ) 2 This measures the dispersion of the forecast errors. MAE: The mean absolute error between actual and predicted values is: 1 MAE N N t 1 X t Xˆ t MAPE: The mean absolute percentage error between actual and predicted values is calculated as: 1 MAPE N N t 1 X Xˆ t X t t *100 Forecasting Nominal Exchange Rate of Indian Rupee vs. US Dollar 73

Variable Description For this study five macroeconomic variables have been taken from the model of flexible price monetary model and sticky price monetary model. The variables are broad money (M 3 ) seasonally adjusted and in billions of rupees, Index of Industrial Production (IIP) as a proxy for monthly GDP, and rate of interest (R). The study has taken commercial lending rate, exchange rate (Ex) and expected rate of inflation (Ee). These are for domestic variables. For foreign variables (for US) the study has used star notation (*) to distinguish it from domestic components. These variables are M 3*, IIP*, R* and Ee*. Exchange rate is multiplied with M 3 * to convert Dollar to Rupee. The expected rate of inflation is estimated from inflation rate using three period moving average rates and inflation rate is generated from WPI. All these components are in monthly variables. M 3 and M 3 * are converted to log 10 for the purpose of making the variable smooth. The differences between domestic and foreign variables are taken for analysis as per the theoretical models. Except all these macroeconomic variables, the study has used a dummy variable which is placed as a constant in the model to counter an immediate increase in exchange rate. The dummy is set as zero upto 1993:01 and then one. The total data period ranges from January 1990 to January 2005. For in-sample and out-of-sample forecasting, total data period is divided into two parts, i.e., 1990:01 to 1999:11 and 1999: to 2005:01 respectively. Results and Discussion Unit Root Properties of the Variables In order to test unit root, the study has used Dickey-Fuller, Augmented Dickey-Fuller and Phillips-Perron Test. Unit root results are shown in Tables 1(a) and 1(b) with level and Variable Table 1(a): The Estimated -Statistic Values from Unit Root Tests at Level Intercept Alone Intercept + Trend DF ADF PP DF ADF PP M 3 1.04 1.36 (6) 1. (4) 1.41 1.72 (6) 1.48 (4) R 0.99 2.37 (8) 1.35 (4) 1.55 3.27 (8) 1.86 (4) Ex 2.53 2.64 (7) 2.47 (1) 0.43 0.87 (4) 0.63 (4) IIP 2.4 0.74 (4) 1.64 (4) 5.53* 3.63 (3)** 5.47 (4)* Ee 2.57 2.66 (3) 2.11 (1) 0.13 2.71 (8) 1.14 (4) Table 1(b): The Estimated -Statistic Values from Unit Root Tests at 1 st Difference Variable Intercept Alone Intercept + Trend DF ADF PP DF ADF PP M 3 14.49* 9.39 (1)* 14.45 (4)* 14.56* 9.48 (1)* 14.51 (4)* R 11.48* 7.32 (1)* 11.84 (4)* 11.47* 7.33 (1)* 11.84 (4)* Ex.01* 8.56 (1)*.06 (4)*.38* 8.97 (1)*.37 (4)* IIP.11* 11.94 (1)*.78 (4)*.*.02 (1)*.88 (4)* Ee 5.91* 7.98 (1)* 6.47 (2)* 6.11* 8.28 (2)* 6.66 (2)* Note: The critical values for unit root test are: 3.47 and 2.88 (without trend) and 4.04, 3.45 (with trend) respectively for 1% and 5% level. * and ** implies stationarity at 1% and 5% level. 74 The Icfai Journal of Applied Finance, Vol. 13, No. 6, 2007

1 st difference respectively. From the tables, it is evident that variables like m 3, r, Ex and Ee are non-stationary at level but stationary at 1 st difference. But IIP is seen to be trend stationary at level. Hence, it is necessary to de-trend IIP and the de-trended series will be the suitable variable. The variables on 1 st difference are stationary at 1% level, whereas for IIP, Dickey-Fuller and Phillips-Perron prove stationary at 1% level and ADF at 5% level. Choice of Lag Length and Ordering of Variables Out of LR, FPE, AIC, SC, and HQ criteria LR, FPE and AIC suggest four lags, whereas SC and HQ suggest two lags for variables. Hence, the study selected the lag length suggested by three out of five lag length selection criteria. Then comes ordering of the variables for which the orderings according to the theoretical model, keeping in view the policy and target variables, are taken into account. Exchange Rate Forecasts using VAR Model The VAR model was applied on both flexible price monetary model and sticky price monetary model in order to forecast exchange rate both for in-sample and out-of-sample forecasting. Figures 1(a) and 1(b) represent in-sample and out-of-sample forecast of flexible price monetary model and Figures 2(a) and 2(b) represents in-sample and out-of-sample forecast of sticky price monetary model, respectively. The relative performances of both the models are presented in Table 2. Figure 1(a): In-sample Exchange Rate Forecasting for Flexiable Price Monetary Model using VAR Exchange Rate 50 45 40 35 30 25 20 15 10 5 0 1990M1 1990M8 1991M3 1991M10 1992M5 1992M 1993M7 1994M2 1994M9 1995M4 Month Ex Ex-Forecasted 1995M11 1996M6 1997M1 1997M8 1998M3 1998M10 1999M5 Ex Ex-Forecasted Forecasting Nominal Exchange Rate of Indian Rupee vs. US Dollar 75

Figure 1(b): Out-of-Sample Exchange Rate Forecasting for Flexible Price Monetary Model Using VAR Exchange Rate 50 49 48 47 46 45 44 43 42 41 40 1990M 2000M3 2000M6 2000M9 2000M 2001M3 2001M6 2001M9 2001M 2002M3 2002M6 2002M9 2002M 2003M3 Month Ex Ex-Forecasted 2003M6 2003M9 2003M 2004M3 2004M6 2004M9 2004M Figure 2(a): In-sample Exchange Rate Forecasting for Sticky Price Monetary Model Using VAR Exchange Rate 50 45 40 35 30 25 20 15 10 5 0 1990M1 1990M7 1991M1 1991M7 1992M1 1992M7 1993M1 1993M7 1994M1 1994M7 1995M1 1995M7 1996M1 Month Ex Ex-Forecasted 1996M7 1997M1 1997M7 1998M1 1998M7 1999M1 1999M7 Ex Ex-Forecasted 76 The Icfai Journal of Applied Finance, Vol. 13, No. 6, 2007

Figure 2(b): Out-of-Sample Exchange Rate Forecasting for Sticky Price Monetary Model using VAR 50 48 Exchange Rate 46 44 42 40 38 1999M 2000M3 2000M6 2000M9 2000M 2001M3 2001M6 2001M9 2001M 2002M3 2002M6 2002M9 2002M Month Ex Ex-Forecasted 2003M3 2003M6 2003M9 2003M 2004M3 2004M6 2004M9 2004M Forecast Performance Measures From the Figures of the forecasted exchange rate with actual exchange rate, it can be noted that both the theoretical models are forecasting the exchange rate better for in-sample forecast than out-of-sample forecast. But, the out-of-sample forecasted exchange rate of sticky price monetary model passes comparatively closer with actual exchange rate than flexible price monetary model. The Figures, however, are not sufficient to conclude which out of the two models provide a better forecast. Hence, three performance measure criteria such as RMSE, MAE and MAPE. The results are provided in Table 2. It is clear from Table 2 that the RMSE, MAE and MAPE values are less in sticky price monetary model than flexible price monetary model both in case of in-sample and out-of-sample forecasting. Hence, it is concluded that sticky price monetary model is comparatively providing better forecasts than flexible price monetary model. Another way of analyzing this is that the presence of the new variable i.e., expected rate of inflation in the monetary model is able to increase its predictive ability. Methodologically, VAR is predicting Table 2: Estimated In-sample and Out-of-sample Performance Measures of Flexible Price and Sticky Price Monetary Model in Forecasting Monthly Exchange Rate using VAR Model Flexible Price Monetary Model Sticky Price Monetary Model In-Sample Out-of-Sample In-Sample Out-of-Sample RMSE 1.944 2.791 1.651 2.407 MAE 1.7 2.385 1.431 2.196 MAPE 5.676 5.045 4.899 4.728 Forecasting Nominal Exchange Rate of Indian Rupee vs. US Dollar 77

in-sample better than out-of-sample. The predictive ability of the VAR model may increase with a structural VAR if proper restrictions are imposed on the variables for the construction of a structural VAR. Conclusion In this paper, a reduced form of the VAR model is used to forecast nominal exchange rate for in-sample and out-of-sample data period. The model is applied over flexible price and sticky price monetary models. The performance measure criteria such as RMSE, MAE, and MAPE concludes that sticky price monetary model is comparatively provides better forecasts over flexible price monetary model both in case of in-sample as well as out-of-sample forecasting. This proves the importance of expected rate of inflation of the sticky price monetary model, which is able to capture the exchange rate movements efficiently than the flexible price monetary model, and increases its predictive ability. Methodologically, it can be concluded that the standard VAR model predicts in-sample better than out-of-sample. The predictive ability of VAR model may increase with a structural VAR if proper restrictions are imposed on the variables and the identification of the model is properly diagnosed. References Reference # 01J-2007-06-04-01 1. Backus D (1986), The Canadian-US Exchange Rate: Evidence from a Vector Autoregression, Review of Economics and Statistics, Vol. 68, pp. 628-637. 2. Bilson J (1978), The Monetary Approach to the Exchange Rate: Some Empirical Evidence, IMF Staff Papers, Vol. 25, pp. 48-75. 3. Diebold F and Mariano R S (1995), Comparing Predictive Accuracy, Journal of Business and Economic Statistics, Vol. 13, pp. 253-263. 4. Diebold F X and Kilian L (2000), Unit-Root Tests are Useful for Selecting Forecasting Models, Journal of Business and Economics Statistics, Vol. 18, pp. 265-273. 5. Dornbusch R (1976), The Theory of Flexible Exchange Rate Regimes and Macroeconomic Policy, Scandinavian Journal of Economics, Vol. 84, pp. 255-275. 6. Enders W (1995), Applied Econometric Time Series, John Wiley & Sons, Inc., New York. 7. Frenkel J A (1976), A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence, Scandinavian Journal of Economics, Vol. 78, pp. 169-191. 8. Frankel J A(1979), On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Rate Differentials, American Economic Review, Vol. 69, pp. 610-622. 9. Johnston R B and Yan Sun (1997), Some Evidence on Exchange Rate Determination in Major Industrial Countries, IMF Working Paper (Monetary and Exchange Affairs Department), August, WP/97/98. 10. Kamaiah B, Nandkumar P and Pradhan H K (1989), Modeling of DM-Dollar Exchange Rate: A VAR Approach, Prajnan, Vol. 18, pp. 277-288. 78 The Icfai Journal of Applied Finance, Vol. 13, No. 6, 2007

11. Kulkarni K G and Chakraborty D (1990), An Empirical Evidence of Purchasing Power Parity Theory: A Case of Indian Rupee and the US Dollar, Margin, Vol. 22, pp. 52-56.. Lin W T and Chen Y H (1998), Forecasting Foreign Exchange Rates with an Intrinsically Nonlinear Dynamic Speed of Adjustment Model, Applied Economics, Vol. 30, pp. 295-3. 13. MacDonald R and Taylor M P (1993), The Monetary Approach to the Exchange Rate: Rational Expectations, Long-run Equilibrium and Forecasting, IMF Staff Papers, Vol. 40, pp. 89-107. 14. Meese R A and Rogoff K (1983a), Empirical Exchange Rate Models of the 1970s: Do they Fit Out of Sample?, Journal of International Economics, Vol. 14, pp. 3-24. 15. Meese R A and Rogoff K (1983b), The Out-of-Sample Failure of Exchange Rate Models: Sampling Error or Misspecification, in Frenkel J A (Ed.), Exchange Rates and International Economics, Chicago: University of Chicago Press. 16. Mussa M L (1976), The Exchange Rate, the BOPs and Monetary and Fiscal Policy under a Regime of Controlled Floating, Scandinavian Journal of Economics, Vol. 78, pp. 229-248. 17. Paul M T and Ashtekar M (1990), Foreign Exchange Forecasting: Some VAR Results, Journal of Foreign Exchange and International Finance, Vol. 4, pp. 69-77. Forecasting Nominal Exchange Rate of Indian Rupee vs. US Dollar 79