@ARTICLE{Mazur_Błażej_On_2012,
 author={Mazur, Błażej and Pipień, Mateusz},
 number={No 2},
 journal={Central European Journal of Economic Modelling and Econometrics},
 pages={95-116},
 howpublished={online},
 year={2012},
 publisher={Oddział PAN w Łodzi},
 abstract={We discuss the empirical importance of long term cyclical effects in the volatility of financial returns. Following Amado and Teräsvirta (2009), ČiŽek 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-tand to the changes of the volatility equation from regular GARCH to the Asymmetric GARCH.},
 type={Artykuły / Articles},
 title={On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process},
 URL={http://journals.pan.pl/Content/103772/PDF-MASTER/mainFile.pdf},
 doi={10.24425/cejeme.2012.119278},
 keywords={GARCH Models, Bayesian inference, periodically correlated stochastic processes, volatility, unconditional variance},
}