Minimum Mean Squared Error ARIMA Forecasts for India Rupee/Pound Sterling Exchange Rate

Abstract

The main purpose for constructing a time series model is to generate forecasting. A Forecast is a quantitative estimate about the likelihood of future events for which models are developed on the basis of past and current information. By extrapolating models beyond the period over which they were estimated, one can make Forecasts about future events. Moreover, Forecast provides guidelines for model building. A Forecast, which is found to be way off target when actual data become available, provides information which may lead to revision of the model which generated the Forecast. Three different techniques are used to generate Forecasts. These are (a) Econometric Forecasting, (b) Transfer Function Forecasts and (c) ARIMA Forecasting. Econometric forecasting and Transfer Function forecasting are beset with several practical limitations. As a result, ARIMA forecasting has become the modern day useful technique for forecasting. The present study is devoted to generating Forecasts for the Indian currency exchange rate vis-`a-vis Pound Sterling. More specifically we have (i) Identified and estimated the univariate ARIMA(p, d, q) process for Indian Rupee/Pound Sterling Exchange Rate over the period 1st March, 2023 through 5th April, 2024. The dataset is daily by nature. (ii) Used the ARIMA (p, d, q) structure for generating one-period ahead Forecasts for the corresponding exchange rate at levels. (iii) Examined the efficiency of such Forecasts. The exchange rate series has been found to be non-stationary at level and I(1) by nature. The series has been found to follow an ARIMA[(2, 4), 1, 0] structure. The Forecasts have Minimum Mean-Squared Errors. Thus these Forecasts were found to be efficient.