On the empirical importance of periodicity in the volatility of financial time series
AbstractWe 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 InfoPaper provided by National Bank of Poland, Economic Institute in its series National Bank of Poland Working Papers with number 124.
Date of creation: 2012
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Periodically correlated stochastic processes; GARCH models; Bayesian inference; volatility; unconditional variance;
Find related papers by 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)
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-10-27 (All new papers)
- NEP-ECM-2012-10-27 (Econometrics)
- NEP-ETS-2012-10-27 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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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