Subset Autoregressive Filtering Using the Forgetting Factor for Financial Simulations
22 Pages Posted: 6 Dec 2002
Date Written: October 2002
Statistical filter researchers for time-series systems are often concerned that the coefficients of their established filters may not be constant over time, but vary when the filters are disturbed by changes arising from outside environmental factors. This concern has motivated researchers to develop sequential estimation algorithms that allow for the coefficients to evolve, such as a recursive estimation of an autoregressive (AR) filter [see Hannan and Deistler (1988)], and a recursive updating procedure for the training process of a multiplayer neural network [see Azimi-Sadjadi et al (1993)]. These studies utilise the fixed forgetting factor (henceforth called the forgetting factor) in the filtering and simulations of nonstationary time series. Conventional methods for determining the forgetting factor for AR filters are mostly based on arbitrary or personal choices. In this paper we use the bootstrap to select the forgetting factor for financial simulations. We also apply the forgetting factor to a time-update recursive algorithm for subset autoregressive filtering. In one illustration using real exchange rates, we demonstrate in Section 4.1 the effect of the forgetting factor in subset AR filtering on ex ante forecasting of nonstationary financial time series. In a second illustration the time-update recursions are applied in Section 4.2 to detect the direct cause-and-effect relationships between the movements of the Euro's exchange rate and the money supply.
JEL Classification: C50, F30, G10
Suggested Citation: Suggested Citation