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Simplified Spectral Analysis and Linear Filters for Analysis of Economic Time Series

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  • Supachoke Thawornkaiwong

Abstract

We develop and simplify spectral analysis of time series. The main focus is on the spectral representation theorem, Bochner's theorem, and some key results concerning time-invariant linear filters. We then show how to apply these key results to shed some light on various applications including Yule-Slutsky effects, seasonal adjustment and trend estimation. We also show how spectral analysis can indicate appropriateness of certain statistical models when applied with some economic time series.

Suggested Citation

  • Supachoke Thawornkaiwong, 2016. "Simplified Spectral Analysis and Linear Filters for Analysis of Economic Time Series," PIER Discussion Papers 25, Puey Ungphakorn Institute for Economic Research.
    • Handle: RePEc:pui:dpaper:25
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    References listed on IDEAS

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    1. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    2. Ghysels, Eric & Granger, Clive W J & Siklos, Pierre L, 1996. "Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process?," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 374-386, July.
    3. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-247, July-Sept.
    4. Ghysels, Eric & Granger, Clive W J & Siklos, Pierre L, 1996. "Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process? Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 396-397, July.
    5. Gomez, Victor, 2001. "The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 365-373, July.
    6. Phillips, Peter C. B., 1988. "The ET Interview: Professor James Durbin," Econometric Theory, Cambridge University Press, vol. 4(01), pages 125-157, April.
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    More about this item

    Keywords

    Spectral Analysis; Linear Filters; Exploratory Data Analysis; Yule-Slutzky Effect; Seasonality; Trend Estimation; HP Filters;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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