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On the empirical importance of periodicity in the volatility of financial time series

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  • Blazej Mazur

    (Economic Institute, National Bank of Poland and Department of Econometrics and Operations Research, Cracow University of Economics)

  • Mateusz Pipien

    (Economic Institute, National Bank of Poland and Department of Econometrics and Operations Research, Cracow University of Economics)

Abstract

We discuss the empirical importance of long term cyclical effects in the volatility of financial returns. Following ˘Ci˘zek and Spokoiny (2009), Amado and Teräsvirta (2012) and others, we consider a general conditionally heteroscedastic process with stationarity property distorted by a deterministic function that governs the possible variability in time of 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)-t- GARCH(1,1) 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. This may be interpreted as empirical evidence in favour of a linkage between the business cycle in the US economy and long term changes in the volatility of the basic stock market index.

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Bibliographic Info

Paper provided by National Bank of Poland, Economic Institute in its series National Bank of Poland Working Papers with number 124.

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Length: 29
Date of creation: 2012
Date of revision:
Handle: RePEc:nbp:nbpmis:124

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Keywords: Periodically correlated stochastic processes; GARCH models; Bayesian inference; volatility; unconditional variance;

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  1. Osiewalski, Jacek & Pipien, Mateusz, 2004. "Bayesian comparison of bivariate ARCH-type models for the main exchange rates in Poland," Journal of Econometrics, Elsevier, vol. 123(2), pages 371-391, December.
  2. Susmel, Raul, 2000. "Switching Volatility in Private International Equity Markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 5(4), pages 265-83, October.
  3. Ming-Yuan Leon Li & Hsiou-wei William Lin, 2004. "Estimating value-at-risk via Markov switching ARCH models - an empirical study on stock index returns," Applied Economics Letters, Taylor & Francis Journals, vol. 11(11), pages 679-691.
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