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Smoothing Non-Stationary Time Series Using the Discrete Cosine Transform

Journal of Systems Science & Complexity 2016年第2期29卷 382-404页

作者： THOMAKOS Dimitrios Department of Economics University of PeloponneseGreece22100 & Rimini Center for Economic Analysis

This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found fruitful applications in filtering and smoothing as it can closely approximate the optimal Karhunen-Loeve transform(KLT).In fact,it is known that it almost corresponds to the KLT for first-order autoregressive processes with a root close to unity:This is the case with most economic and financial time series.A number of new results are derived in the paper:(a) The explicit form of the linear smoother based on the DCT,which is found to have time-varying weights and that uses all observations;(b) the extrapolation of the DCT-smoothed series;(c) the form of the average frequency response function,which is shown to approximate the frequency response of the ideal low pass filter;(d) the asymptotic distribution of the DCT coefficients under the assumptions of deterministic or stochastic trends;(e) two news method for selecting an appropriate degree of smoothing,in general and under the assumptions in(d).These findings are applied and illustrated using several real world economic and financial time *** results indicate that the DCT-based smoother that is proposed can find many useful applications in economic and financial time series.

关键词： Discrete cosine transform non-stationary time series order selection singular spectrumanalysis smoothing trend extraction unit root.

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