url
24
Nov
2013

## Performance of CHEERs Based Equilibrium Exchange Rate of Pakistan: Data Analysis

5.11 Forecasting

As the PPP-UIP model is build now, following test will check to see whether this model can perform well when used for forecasting.
Using PPP-UIP model the forecasting Exchange Rate for next 20 time periods will be done and the comparison ability will be compared with the forecast of Random Walk Model. For this purpose last 20 observations are left out of estimation intentionally. Following two methods will be done to see if the estimated model can perform better than a random walk model in forecasting the exchange rate.

5.11.1 Root Mean Square Ratio

In this Root Mean Square is calculated for both models will be calculated as:
Where Sa = Actual Exchange Rate, mss= №sf= RMSBir/R&tSBggr S = Forecasted Exchange Rate, RMSE m = Root Mean Square of Estimated Model, and RMSE rw = Root Mean Square of Random Walk Model
The calculation showed that the RMSE m and RMSE rw came out to be 0.816 and 0.014 respectively hence the RATIO turns out to be 57, suggesting that the forecasts of the Random Walk Model are more bounded near to the Actual Exchange Rate as compared to the PPP-UIP Model estimate.
But this result might be misleading this case as the PPP-UIP model is already suggesting the presence of misalignment so while forecasting it will still continue the same way, where as the Random Walk is forecasting Exchange Rate in the base of past information available in the Exchange Rate which tends to be near to the actual observations. Hence evaluation of the forecasting ability requires some other method that considers the movement directions important as compared to the actual realization of the Exchange Rate.

5.11.2 Direction Ability Test

The previous method by construction was incapable of doing a better forecast that can match the actual Exchange Rate incidence, so a second best method is applied in the following that gives importance to the ability to forecast the direction of the future Exchange Rate.
In this evaluation method, a binary indicator will be created that will have magnitude 1 of the change in the Actual Exchange Rate and Estimated Exchange Rate have same signs otherwise it will have magnitude 0 suggesting that the model has failed to forecast even the direction of the future Exchange Rate.
This procedure will be applied to both of the PPP-UIP and Random Walk Model of the Exchange Rate and then the averages of that indicator will be compared to see which model has higher average, hence higher direction forecasting ability.

5.11 Forecasting As the PPP-UIP model is build now, following test will check to see whether this model can perform well when used for forecasting. Using PPP-UIP model the forecasting Exchange Rate for next 20 time periods will be done and the comparison ability will be compared with the forecast of Random Walk Model. For this purpose last 20 observations are left out of estimation intentionally. Following two methods will be done to see if the estimated model can perform better than a random walk model in forecasting the exchange rate. 5.11.1 Root Mean Square Ratio In this Root Mean Square is calculated for both models will be calculated as: Where Sa = Actual Exchange Rate, mss= №sf= RMSBir/R&tSBggr S