Time Series Filtering through Chebyshev Polynomials
AbstractThis 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 â€“and hence, the frequency content of the detrended seriesâ€“ 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.
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Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 287.
Date of creation: 11 Aug 2004
Date of revision:
Filtering and time-frequency representation techniques; Chebyshev polynomials;
Find related papers by JEL classification:
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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