Time Series Filtering through Chebyshev Polynomials

This paper comparatively evaluates performances of widely-used filters employed to separate the trend of a given non-stationary time series from its cyclical components, against a Chebyshev polynomial-based filter designed for this purpose. The performances of detrending techniques under consideration are measured by their ability to capture cyclical components of a special series with known properties, constructed to serve as a benchmark. We demonstrate that detrending performances of conventional techniques such as the line fitting method, Hodrick-Prescott and Band-Pass filters can easily be matched by fitting a Chebyshev polynomial to the given time series. This approach offers an additional advantage as the smoothness of the extracted trend –and hence, the frequency content of the detrended series– can effectively be controlled by changing the highest order of the polynomial. As 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.