Monash University

How Reliable Is the Band-Pass Filter?

Email address: Ashton.deSilva@BusEco.monash.edu.au

Keywords: Band Pass Filter, Cycle, Simulate, Sensitivity Analysis.

JEL Classifications: C22, E32.

Abstract:
The aim of this paper is to examine the ability of the Band Pass (BP) filter to extract "business cycles" from non-stationary data. A "business cycle" is defined as a completed cyclical movement of 6 to 32 quarters' duration. We simulate time series from data generating processes (DGPs) that have stochastic trends and 6-period to 32-period cycles, pass them through the BP filter and compare the filter output with the actual cycle. Using the four estimated models in Harvey and Jaeger (Journal of Applied Econometrics, 1993) as the basis of our Monte Carlo simulations, we find no significant correlation between the actual cycles and BP filter outputs for three out of the four DGPs. This finding entices further research into the relationship between the success of BP filter in isolating the cyclical component and specific features of the DGP. Sensitivity analysis is conducted with respect to four characteristics of the DGP: the amplitude of the cycle, the duration of the cycle, the ratio of the variance of the trend innovation to the variance of cycle innovation, and the relative variance of measurement noise. The relative size of the trend error appears to impede the ability of the BP filter greatly. The relative size of the irregular dispersion significantly deteriorates the accuracy of the BP filter, however less severely than the trend counterpart. There is a positive relationship between the accuracy of the BP filter and the amplitude of the cycle. The relationship between duration of the cycle and BP filter's success in extracting it is non-monotone. Other things equal, the BP filter is most successful when the true cycle has a period of 10 quarters.

PDF file of paper: desilva.pdf

Session: Filtering and Forecasting

Time: Friday, 6 July, 8:45am - 10:15am

Room: C