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Time-spectral density and wavelets approaches. Comparative study. Applications to SP500 returns and US GDP

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  • Ahamada, Ibrahim
  • Jolivaldt, Philippe

Abstract

Various forms of instability can be observed in macroeconomic and financial data including changes in variance, changes in cycle properties, or both. Traditional tests do not allow to distinguish between these different cases. This paper proposes and compares two alternative approaches. The comparison is based on Monte Carlo simulations. The first approach is based on windowed-estimate of the time-spectral density, while the second method is the wavelets theory. We show that the wavelets approach is particularly powerful to detect changes in cyclical properties, while the first approach fails in such a case. In contrast, the wavelets method fails to capture time–interaction effects, while the first approach is more powerful regarding this point. Hence the two methods are complementary. A first application on the SP500 returns shows that there are only changes in variance without altering the cyclical properties of the series. A second application on the US growth rate allows to conclude that there are simultaneous changes in the time and frequency domain.

Suggested Citation

  • Ahamada, Ibrahim & Jolivaldt, Philippe, 2013. "Time-spectral density and wavelets approaches. Comparative study. Applications to SP500 returns and US GDP," Economic Modelling, Elsevier, vol. 31(C), pages 460-466.
    • Handle: RePEc:eee:ecmode:v:31:y:2013:i:c:p:460-466
    DOI: 10.1016/j.econmod.2012.12.007
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    1. repec:zbw:bofrdp:2005_001 is not listed on IDEAS
    2. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
    3. Patrick M. Crowley, 2005. "An intuitive guide to wavelets for economists," GE, Growth, Math methods 0508009, University Library of Munich, Germany.
    4. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    5. Marianne Sensier & Dick van Dijk, 2004. "Testing for Volatility Changes in U.S. Macroeconomic Time Series," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 833-839, August.
    6. W.‐Y. T. Chan & H. Tong, 1975. "A Simulation Study of the Estimation of Evolutionary Spectral Functions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(3), pages 333-341, November.
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    Cited by:

    1. Marczak, Martyna & Gómez, Víctor, 2015. "Cyclicality of real wages in the USA and Germany: New insights from wavelet analysis," Economic Modelling, Elsevier, vol. 47(C), pages 40-52.

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    More about this item

    Keywords

    Time–frequency domain; Time-spectral density; Wavelets; Covariance-stationarity; Monte Carlo simulation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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