Estimating and forecasting generalized fractional Long memory stochastic volatility models

dc.contributor.authorPeiris, Shelton
dc.contributor.authorAsai, Manabu
dc.contributor.authorMcAleer, Michael
dc.description.abstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model.
dc.description.facultyFac. de Ciencias Económicas y Empresariales
dc.description.facultyInstituto Complutense de Análisis Económico (ICAE)
dc.identifier.citationAndersen, T.G., Bollerslev, T., Diebold, F.X., Labys, P. (2001). The distribution of realized exchange rate volatility, Journal of the American Statistical Association, 96, 42-55. Andersen, T.G., Bollerslev, T., Diebold, F.X., Labys, P., (2003). Modeling and forecasting realized volatility, Econometrica, 71, 529-626. Arteche, J. (2004). Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models, Journal of Econometrics, 119, 131-154. Asai, M., McAleer, M., Medeiros, M.C. (2012). Asymmetry and long memory in volatility modeling, Journal of Financial Econometrics, 10, 495-512. Baillie R.T., Bollerslev, T., Mikkelsen, H.O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 74, 3–30. Barndorff-Nielsen, O.E., Shephard, N. (2002). Econometric analysis of realized volatility and its use inestimating stochastic volatility models, Journal of the Royal Statistical Society, Series B, 64, 253-280. Bollerslev, T., Zhou, H. (2002). Estimating stochastic volatility diffusion using conditional moments of integrated volatility, Journal of Econometrics, 109, 33-65. Bollerslev, T., Mikkelsen, H.O. (1996). Modeling and pricing long-memory in stock market volatility, Journal of Econometrics, 73, 151–184. Breidt, F.J., Crato, N., de Lima, P. (1998). The detection and estimation of long memory, Journal of Econometrics, 83, 325–348. Candelon, B., Colletaz, G., Hurlin, C., Tokpavi, S. (2011), Backtesting value-at-risk: A GMM duration-based approach, Journal of Financial Econometrics, 9, 314-343. Christoffersen, P. (1998). Evaluating interval forecasts, International Economic Review, 39, 841-862. Christoffersen, P., Pelletier, D. (2004). Backtesting value-at-risk: A duration-based approach, Journal of Financial Econometrics, 2, 84-108. Chung, C.F. (1996a). Estimating a generalized long memory process, Journal of Econometrics, 73, 237–259. Chung, C.F. (1996b). A generalized fractionally integrated autoregressive moving-average process, Journal of Time Series Analysis, 17, 111–140. Clark, P.K. (1973). A subordinated stochastic process model with fixed variance for speculative prices. Econometrica, 41, 135–156. Deo, R.S., Hurvich, C.M. (2001). On the log periodogram regression estimator of the memory parameter in long memory stochastic volatility models, Econometric Theory, 17, 686–710. Dissanayake, G., Peiris, S., Proietti, T. (2016). State space modeling of Gegenbauer processes with long memory, Computational Statistics & Data Analysis, 100, 115–130. Doornik J.A. Ooms, M. (2003). Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models, Computational Statistics & Data Analysis, 42, 333–348. Engle, R. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007. Granger, C.W.J., Morris, M. (1976). Time series modeling and interpretation, Journal of the Royal Statistical Society, Series A, 139, 246-257. Gray, H.L., Zhang, N., Woodward, W.A. (1989). On generalized fractional processes, Journal of Time Series Analysis, 10, 233-257. Hansen, P.R., Z. Huang, and H.H. Shek (2012). Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility, Journal of Applied Econometrics, 27, 877–906. Harvey, A. (1998). Long memory in stochastic volatility, in: Knight, J. and S. Satchell (eds.), Forecasting Volatility in Financial Markets, Oxford: Butterworth-Haineman, 307–320. Hosoya, Y. (1997). A limit theory for long-range dependence and statistical inference on related models, Annals of Statistics, 25, 105–137. Koopman, S.J., Jungbacker, B., Hol, E. (2005). Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements, Journal of Empirical Finance, 12, 445-475. McAleer, M. (2005). Automated inference and learning in modeling financial volatility, Econometric Theory, 21, 232-261. McElroy, T.S., Holan, S.H. (2012). On the computation of autocovariances for generalized Gegenbauer processes, Statistica Sinica, 22, 1661–1687. Pong S., Shackelton, M.B., Taylor, S.J., Xu, X. (2004). Forecasting currency volatility: a comparison of implied volatilities and AR(FI)MA models, Journal of Banking and Finance, 28, 2541-2563. Sandmann, G., Koopman, S.J. (1998). Estimation of stochastic volatility models via Monte Carlo maximum likelihood, Journal of Econometrics, 87, 271–301. Shephard, N. (2005). General introduction, in N. Shephard (ed.), Stochastic Volatility, Oxford University Press, Oxford, pp.1–33. Shitan, M., Peiris, M. (2008). Generalized autoregressive (GAR) model: A comparison of maximum likelihood and Whittle estimation procedures using a simulation study, Communications in Statistics - Theory and Methods, 37(3), 560–570. Shitan, M., Peiris, M. (2013). Approximate asymptotic variance-covariance matrix for the Whittle estimators of GAR(1) parameters, Communications in Statistics - Theory and Methods, 42(5), 756–770. So, M.K.P. (1999). Time series with additive noise, Biometrika, 86, 474–482. So, M.K.P. (2002). Bayesian analysis of long memory stochastic volatility models, Sankhya¯, 24, 1–10. Taniguchi, M. (1982). On estimation of the integrals of the fourth order cumulant spectral density, Biometrika, 69, 117–122. Taniguchi, M., Kakizawa, Y. (2000). Asymptotic Theory of Statistical Inference for Time Series, New York: Springer-Verlag. Taylor, S.J. (1982). Financial returns modeled by the product of two stochastic processes - a study of daily sugar prices 1961-79, in: Anderson, O.D. (ed.), Time Series Analysis: Theory and Practice, vol.1, Amsterdam: North-Holland, 203-226. Taylor, S.J. (1986). Modelling Financial Time Series, Chichester: Wiley. Zaffaroni, P. (2009). Whittle estimation of EGARCH and other exponential volatility models, Journal of Econometrics, 151, 190–200.
dc.publisherFacultad de Ciencias Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE)
dc.relation.ispartofseriesDocumentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
dc.rights.accessRightsopen access
dc.subject.keywordStochastic volatility
dc.subject.keywordGARCH models
dc.subject.keywordGegenbauer Polynomial
dc.subject.keywordLong Memory
dc.subject.keywordSpectral Likelihood
dc.subject.ucmProbabilidades (Estadística)
dc.subject.ucmEconometría (Economía)
dc.subject.unesco1208 Probabilidad
dc.subject.unesco5302 Econometría
dc.titleEstimating and forecasting generalized fractional Long memory stochastic volatility models
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