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

Błażej Mazur () and Mateusz Pipień

No 124, NBP Working Papers from Narodowy Bank Polski

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.

Keywords: Periodically correlated stochastic processes; GARCH models; Bayesian inference; volatility; unconditional variance (search for similar items in EconPapers)
JEL-codes: C11 C58 G10 (search for similar items in EconPapers)
Pages: 29
Date: 2012
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (21)

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Persistent link: https://EconPapers.repec.org/RePEc:nbp:nbpmis:124

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