A New Approach of Kernel Bandwidth Applications for Time-series Using the Example of the Prediction of the Euro's Exchange Rate

Abstract

In recent years the application of kernel smoothing methods in nonparametric regression framework to financial time-series analysis has become widespread. Kernel smoothing methods have not been applied, however, to a wide range of problems arising in time-series simulations and forecasting. Forgetting factors can be both fixed and variable. Gijbels et al (1999) propose an understanding of fixed forgetting factors via kernel smoothing. However the variable forgetting approach is not mentioned. This paper describes the variable forgetting factor and the fixed forgetting factor, and establishes the linkage for the first time between the variable forgetting factor approach and kernel smoothing. The forgetting factor method uses a sample of data and estimates the value of the forgetting factor from the sample. This method fits better than a parametric approach, which uses some assumed parameters. Since the forgetting factor method is equivalent to a kernel estimation - which is a non-parametric method - it is likely to give more accurate estimates and better forecasting performance in financial time-series than a parametric one. The major area of interest in this application is whether kernel estimation, using Cho's approach [see Cho et al (1991) and Brailsford et al (2002)] for kernel bandwidth selection, can improve the Euro's forecasting performance within the framework of subset AR modelling. The forecasting performance is compared with the performance of AR modelling without the use of the forgetting factor. If improved forecasting performance is achieved, this can increase the potential use of kernel smoothing methods in time-series forecasting. The findings show that the kernel bandwidth so determined can improve the forecasting performance.