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On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process


  • Błażej Mazur

    () (Cracow University of Economics)

  • Mateusz Pipień

    () (Cracow University of Economics)


We discuss the empirical importance of long term cyclical effects in the volatility of financial returns. Following Amado and Terasvirta (2009), Cizek and Spokoiny (2009) and others, we consider a general conditionally heteroscedastic process with stationarity property distorted by a deterministic function that governs the possible time variability of the unconditional variance. The function proposed in this paper can be interpreted as a finite Fourier approximation of an Almost Periodic (AP) function as defined by Corduneanu (1989). The resulting model has a particular form of a GARCH process with time varying parameters, intensively discussed in the recent literature. In the empirical analyses we apply a generalisation of the Bayesian AR(1)-GARCH model for daily returns of S&P500, covering the period of sixty years of US postwar economy, including the recently observed global financial crisis. The results of a formal Bayesian model comparison clearly indicate the existence of significant long term cyclical patterns in volatility with a strongly supported periodic component corresponding to a 14 year cycle. Our main results are invariant with respect to the changes of the conditional distribution from Normal to Student-t and to the changes of the volatility equation from regular GARCH to the Asymmetric GARCH.

Suggested Citation

  • Błażej Mazur & Mateusz Pipień, 2012. "On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 4(2), pages 95-116, June.
  • Handle: RePEc:psc:journl:v:4:y:2012:i:2:p:95-116

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    References listed on IDEAS

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    Cited by:

    1. Silvennoinen Annastiina & Teräsvirta Timo, 2016. "Testing constancy of unconditional variance in volatility models by misspecification and specification tests," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 347-364, September.
    2. repec:psc:journl:v:9:y:2017:i:3:p:173-200 is not listed on IDEAS
    3. Ewa Ratuszny, 2013. "Robust Estimation in VaR Modelling - Univariate Approaches using Bounded Innovation Propagation and Regression Quantiles Methodology," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 5(1), pages 35-63, March.
    4. Łukasz Lenart, 2016. "Generalized Resampling Scheme With Application to Spectral Density Matrix in Almost Periodically Correlated Class of Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 369-404, May.
    5. Escribano, Alvaro & Sucarrat, Genaro, 2016. "Equation-by-Equation Estimation of Multivariate Periodic Electricity Price Volatility," MPRA Paper 72736, University Library of Munich, Germany.
    6. Ewa Ratuszny, 2015. "Risk Modeling of Commodities using CAViaR Models, the Encompassing Method and the Combined Forecasts," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 15, pages 129-156.
    7. Cristina Amado & Annastiina Silvennoinen & Timo Terasvirta, 2017. "Modelling and Forecasting WIG20 Daily Returns," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 9(3), pages 173-200, September.
    8. Annastiina Silvennoinen & Timo Teräsvirta, 3108. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," CREATES Research Papers 2017-28, Department of Economics and Business Economics, Aarhus University.

    More about this item


    GARCH models; Bayesian inference; periodically correlated stochastic processes; volatility; unconditional variance;

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)


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