Use of Time-Frequency Representations in the Analysis of Stock Market Data
The analysis of economic/financial time series in the frequency domain is a relatively underexplored area of the literature, particularly when the statistical properties of a time series are time-variant (evolutionary). In this case, the spectral content of the series varies as time progresses, rendering the conventional Fourier theory inadequate in describing the cyclical characteristics of the series fully. The joint Time-Frequency Representation (TFR) techniques overcome this problem, as they are capable of analyzing a given (continuous or discrete) function of time in time and frequency domains simultaneously.
To illustrate the potential of some of the TFR techniques widely used in various fields of science and engineering for use in the analysis of stock market data, the behavior of ISE-100 index of the Istanbul Stock Exchange is analyzed first, using two linear (the Gabor Transformation and the Short Time Fourier Transform) and two quadratic (the Wigner Distribution and the Page Distribution) TFRs. The performance of each TFR in detecting and decoding cycles that may be present in the original ISE data is evaluated by utilizing a specially synthesized time series whose trend and/or cycle components can be analytically specified and computed. This series is constructed in such a way to roughly mimic the pattern of a stock index series such as the original ISE series and is used as a benchmark for comparative performance analysis. The results indicate that the performance of the Page distribution, used for the first time in economics/finance literature, is significantly superior to the other TFRs considered. The analysis is then repeated using NASDAQ-100 index data recorded over the last 15 years so as to see if the results are robust to a change in the source of stock data from an emerging to a well-established market. The results point to a superior performance by the Page distribution once again, demonstrating the robustness of our previous results.
KeywordsBusiness cycles Time-frequency representations Stock index series Page distribution Wigner distribution Gabor transformation Short time Fourier transform
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