Time Series Filters Applied to Improve Box-Jenkins Forecasting Approach

Abstract

Data obtained from observations collected sequentially over time are extremely common in business, agriculture, manufacturing, biological science, meteorology and virtually endless. Box-Jenkins methodology have been severally used to obtain forecasts through the process of identification, estimation and diagnostics checks. This study employed the use of time series filters to improve or obtain more quality forecasts by the modification of the Box-Jenkins forecasting approach. This study used the Nigerian Naira versus the US Dollar exchange rates data (4th January, 2010 to 17th September, 2019) to demonstrate the tool of time series filters to improve or obtain more quality forecasts. The study identified and reviewed two band-pass filters (Baxter-King Filter and Christiano-Fitzgerald Filter) designed for use in a wide range of economic applications. The classical forecasting technique of Box and Jenkins approach based on ARIMA model was also used to forecast the exchange rates. The results show that the use of Baxter-King filter ARIMA performed better than the Christiano-Fitzgerald filter and the classical Box-Jenkins forecasting ARIMA models. The forecast results indicate that the Nigerian economy within the sampled period did not conform to the theory behind ARIMA models for forecasting future exchange rates.