A Comparative Evaluation of the Performances of Different Filtering Techniques in Business Cycle Identification

This paper presents a comparative evaluation of different filtering techniques employed to separate the trend of a given non-stationary time series from its cyclical components in identifying the business cycles. The performances of detrending techniques under consideration can be compared by constructing a special time series with known analytical features so as to mimic the pattern of actually observed series of interest. We demonstrate that detrending performances of conventional techniques such as the line fitting method and Hodrick-Prescott filters can easily be matched through an alternative approach based on fitting a polynomial to the given time series. This approach offers an additional advantage as the smoothness of the extracted trend Òand hence, the frequency content of the detrended seriesÒ can effectively be controlled by changing the highest order of fitting polynomial. \tAs an illustration of the use of this approach in the analysis of stock market data, we analyze the behavior of ISE-100 index of Istanbul Stock Exchange, a highly volatile series, over the period from July 9, 1990 to date. For this purpose, we process the series that is detrended through alternative filtering techniques we consider, by using the Page Distribution (PD). We show that the PD, a quadratic time-frequency representation technique that allows for a given function of time be analyzed in time and frequency domains simultaneously, is particularly suitable for this problem.