Data cloning estimation of GARCH and COGARCH models

References

• Mandelbrot B. The variation of certain speculative prices. J Bus. 1963;36:394–419. doi: 10.1086/294632
   Web of Science ®Google Scholar
• Engle R. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica. 1982;50:987–1008. doi: 10.2307/1912773
   Web of Science ®Google Scholar
• Bollerslev T. Generalized autoregressive conditional heteroskedasticity. J Econ. 1986;31:307–327. doi: 10.1016/0304-4076(86)90063-1
   Web of Science ®Google Scholar
• Nelson D. ARCH models as diffusion approximations. J Econ. 1990;45:7–38. doi: 10.1016/0304-4076(90)90092-8
   Web of Science ®Google Scholar
• Wang Y. Asymptotic nonequivalence of GARCH models and diffusions. Ann Stat. 2002;30:754–783. doi: 10.1214/aos/1028674841
   Web of Science ®Google Scholar
• Corradi V. Reconsidering the continuous time limit of the GARCH(1,1) process. J Econ. 2000;96:145–153. doi: 10.1016/S0304-4076(99)00053-6
   Web of Science ®Google Scholar
• Kallsen J, Taqqu M. Option pricing in ARCH-type models. Math Financ. 8 (1998), pp. 13–26. doi: 10.1111/1467-9965.00042
   Web of Science ®Google Scholar
• Kazmerchuk Y, Swishchuk A, Wu J. A continuous-time GARCH model for stochastic volatility with delay. Can Appl Math Q. 2005;13:123–149.
   Google Scholar
• Lorenz R. Weak approximation of stochastic delay differential equations with bounded memory by discrete time series [PhD thesis]. Berlin, Germany: Humbold University of Berlin; 2006.
   Google Scholar
• Klüppelberg C, Lindner A, Maller R. A continuous-time GARCH process driven by a Lévy process: stationarity and second-order behaviour. J Appl Probab. 2004;41:601–622. doi: 10.1239/jap/1091543413
   Web of Science ®Google Scholar
• Bollerslev T. Glossary to ARCH (GARCH). Russell J Bertrand Russell Arch. 2008;49:1–42.
   Google Scholar
• Haug S, Klüppelberg C, Lindner A, Zapp M. Method of moment estimation in the COGARCH(1, 1) model. Econ J. 2007;10:320–341. doi: 10.1111/j.1368-423X.2007.00210.x
   Web of Science ®Google Scholar
• Maller R, Müller G, Szimayer A. GARCH modelling in continuous time for irregularly spaced time series data. Bernoulli. 2008;14:519–542. doi: 10.3150/07-BEJ6189
   Web of Science ®Google Scholar
• Müller G. MCMC estimation of the COGARCH(1, 1) model. J Financ Econ. 2010;8:481–510.
   Web of Science ®Google Scholar
• Lele S, Dennis B, Lutscher F. Data cloning: easy maximum likelihood estimation for complex ecological models using Bayesian Markov Chain monte Carlo methods. Ecol Lett. 2007;10,551–563. doi: 10.1111/j.1461-0248.2007.01047.x
   PubMed Web of Science ®Google Scholar
• Lele S, Nadeem K, Schmuland B. Estimability and likelihood inference for generalized linear mixed models using data cloning. J Am Stat Assoc. 2010;105:1617–1625. doi: 10.1198/jasa.2010.tm09757
   Web of Science ®Google Scholar
• Francq C, Zakoian J. GARCH models: structure, statistical inference and financial applications. Chichester: Wiley; 2010.
   Google Scholar
• Ardia D. Financial risk management with Bayesian estimation of GARCH models: theory and applications. Vol. 612. Berlin Heidelberg: Springer; 2008.
   Google Scholar
• Lindner AM. Stationarity, mixing, distributional properties and moments of GARCH(p, q)-processes. In: Andersen TG, Davis RA, Kreib JP, Mikosch TV, editors. Handbook of financial time series. Berlin Heidelberg: Springer; 2009. p. 43–69.
   Google Scholar
• Nelson DB. Stationarity and persistence in the GARCH(1, 1) model. Econom Theory. 1990;6:318–334. doi: 10.1017/S0266466600005296
   Web of Science ®Google Scholar
• Sólymos P. dclone: Data Cloning in R. R J. 2010;2:29–37.
   Google Scholar
• R Core Team. R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2012. ISBN 3-900051-07-0
   Google Scholar
• Chan KS, Ripley B. TSA: time series analysis, R package version 1.01, 2012. Available from: http://CRAN.R-project.org/package=TSA
   Google Scholar
• Brooks S, Gelman A. General methods for monitoring convergence of iterative simulations. J Comput Graph Stat. 1998;7:434–455.
   Web of Science ®Google Scholar
• Plummer M. JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling, 2003. Available from: http://citeseer.ist.psu.edu/plummer03jags
   Google Scholar
• Denwood MJ, Runjags: Run Bayesian MCMC Models in the BUGS syntax from Within R, R package version 0.9.9-2, 2011. Available from: http://cran.r-project.org/web/packages/runjags
   Google Scholar
• Nakatsuma T. A Markov-chain sampling algorithm for GARCH models. Stud Nonlinear Dyn Econ. 1998;3:107–117.
   Web of Science ®Google Scholar
• Godfrey L. Testing against general autoregressive and moving average error models when the regressors include lagged dependent variables. Econometrica: J Econom Soc. 1978:1293–1301. doi: 10.2307/1913829
   Google Scholar
• Breusch T. Testing for autocorrelation in dynamic linear models*. Aust Econ Pap. 1978;17:334–355. doi: 10.1111/j.1467-8454.1978.tb00635.x
   Web of Science ®Google Scholar
• Akaike H. A new look at the statistical model identification. IEEE Trans Autom Control, 1974;19:716–723. doi: 10.1109/TAC.1974.1100705
   Web of Science ®Google Scholar
• Schwarz G. Estimating the dimension of a model. Ann Stat. 1978;6:461–464. doi: 10.1214/aos/1176344136
   Web of Science ®Google Scholar