Pascalau, Razvan and Thomann, Christian and Gregoriou, Greg N. (2010): Unconditional mean, Volatility and the Fourier-Garch representation. Published in: Aestimatio No. 1 (December 2010): pp. 1-20.
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This paper proposes a new model called Fourier-GARCH that is a modification of the popular GARCH(1,1). This modification allows for time-varying first and second moments via means of Flexible Fourier transforms. A nice feature of this model is its ability to capture both short and long run dynamics in the volatility of the data, requiring only that the proper frequencies of the Fourier transform be specified. Several simulations show the ability of the Fourier series to approximate breaks of an unknown form, irrespective of the time or location of breaks. The paper shows that the main cause of the long run memory effect seen in stock returns is the result of a time varying first moment. In addition, the study suggests that allowing only the second moment to vary over time is not sufficient to capture the high persistence observed in lagged returns.
|Item Type:||MPRA Paper|
|Original Title:||Unconditional mean, Volatility and the Fourier-Garch representation|
|English Title:||Unconditional mean, Volatility and the Fourier-Garch representation|
|Keywords:||ARCH/GARCH, Structural change, Unconditional volatility|
|Subjects:||G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing; Trading volume; Bond Interest Rates
G - Financial Economics > G2 - Financial Institutions and Services > G29 - Other
|Depositing User:||IEB Research Department|
|Date Deposited:||17. Jan 2012 07:33|
|Last Modified:||02. Mar 2013 16:45|
Becker, R., Enders, W. and Hurn, S. (2001). Modelling structural change in money demand using a Fourierseries approximation, Research Paper Series 67, Quantitative Finance Research Centre, University of Technology, Sydney.
Becker, R., Enders, W. and Lee, J. (2006). A stationarity test in the presence of an unknwon number of smooth breaks, Journal of Time Series Analysis, 27, pp. 381–409.
Bollerslev, T. (1987). A conditionally heteroskedastic time series model for speculative prices and rates of return, The Review of Economics and Statistics, 69, pp. 542–47.
Diebold, F. X. and Inoue, A. (2001). Long memory and regime switching, Journal of Econometrics, 105, pp. 131–159.
Enders, W. and Lee, J. (2006). Testing for a unit root with a nonlinear Fourier function. Mimeo, University of Alabama.
Engle, R. and Bollerslev, T. (1986). Modeling the persistence of conditional variances, Econometric Reviews, 5, pp. 1–50.
Engle, R. F. and Rangel, J. G. (2008). The spline-garch model for low-frequency volatility and its global macroeconomic causes, Review of Financial Studies, 21, pp. 1187–1222.
Gallant, R. (1981). On the basis in flexible functional form and an essentially unbiased form: the flexible fourier form, Journal of Econometrics, 15, pp. 211–353.
Granger, C. W. J. (1980). Long memory relationships and the aggregation of dynamic models, Journal of Econometrics, 14, pp. 227–238.
Granger, C. W. J. and Joyeux, R. (1980). An introduction to long memory time series and fractional differencing, Journal of Time Series Analysis, 1, pp. 15–30.
Granger, C. W. J. and Joyeux, R. (1986). Modeling the persistence of the conditional variances: a comment, Econometric Reviews, 5, pp. 51–56.
Kapetianos, G., Shin, Y. and Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework, Journal of Econometrics, 112, pp. 359–379.
Lamoureux, C. G. and Lastrapes, W. D. (1990). Persistence in variance, structural change, and the GARCH model, Journal of Business & Economic Statistics, 8(2), pp. 225–235
Leybourne, S., Newbold, P. and Vougas, D. (1998). Unit roots and smooth transitions, Journal of Time Series Analysis, 19, pp. 83–97.
Maddala, G. and Kim, I.-M. (1998). Unit roots,cointegration and structural change, Cambridge University Press, Cambridge (UK).
Mikosch, T. and Starica, C. (2004). Non-stationarities in financial time series, the long range dependence and the IGARCH effects, Econometrics 0412005, EconWPA.
Perron, P. and Qu, Z. (2007). An analytical evaluation of the log-periodogram estimate in the presence of level shifts. Available at http://people.bu.edu/perron/.
Starica, C. and Granger, C. (2005). Nonstationarities in stock returns, The Review of Economics and Statistics, 87, pp. 503–522.