Estimation for seasonal fractional ARIMA with stable innovations via the empirical characteristic function method

References

• Diongue AK, Diop A, Ndongo M. Seasonal fractional ARIMA with stable innovations. Statist Probab Lett. 2008;78:1404–1411. doi: 10.1016/j.spl.2007.12.011
   Web of Science ®Google Scholar
• Kokoszka PS, Taqqu MS. Fractional ARIMA with stable innovations. Stochastic Process Appl. 1995;60:19–47. doi: 10.1016/0304-4149(95)00034-8
   Web of Science ®Google Scholar
• Brockwell PJ, Davis RA. Time series: theory and methods. 2nd ed. New York: Springer Series in Statistics; 2006.
   Google Scholar
• Stuck BW, Kleiner B. A statistical analysis of telephone noise. Bell Syst Tech J. 1974;53:1263–1320. doi: 10.1002/j.1538-7305.1974.tb02791.x
   Google Scholar
• Fama EF. Behavior of stock market prices. J Bus. 1965;38(1):34–105. doi: 10.1086/294743
   Web of Science ®Google Scholar
• Ndongo M, Diongue AK, Diop A, Dossou-Gbété S. Estimation of long-memory parameters for seasonal fractional ARIMA with stable innovations. Stat Methodol. 2010;7:141–151. doi: 10.1016/j.stamet.2009.12.002
   Google Scholar
• Reisen VA, Rodrigues AL, Palma W. Estimation of seasonal fractionally integrated processes. Comput Statist Data Anal. 2006;50:568–582. doi: 10.1016/j.csda.2004.08.004
   Web of Science ®Google Scholar
• Calder M, Davis RA. Inferences for linear processes with stable noise. In: Adler RJ, Feldman RE, Taqqu MS, editors. A practical guide to heavy tails. Boston: Birkhiuser; 1998. p. 159–176.
   Google Scholar
• Knight JL, Yu J. The empirical characteristic function in time series estimation. Econometric Theory. 2002;18:691–721. doi: 10.1017/S026646660218306X
   Web of Science ®Google Scholar
• Hosking JRM. Modeling persistence in hydrological time series using fractional differencing. Water Resour Res. 1984;20(12):1898–1908. doi: 10.1029/WR020i012p01898
   Web of Science ®Google Scholar
• Alvarez A, Olivares P. Méthodes d'estimation pour des lois stables avec des applications en finance. Journal de la Société Française de Statistique. 2005;4(1):23–54.
   Google Scholar
• Porter-Hudak S. An application of the seasonal fractionally differenced model to the monetary aggregates. J Amer Statist Assoc. 1990;85(410):338–344. doi: 10.1080/01621459.1990.10476206
   Web of Science ®Google Scholar
• Granger CWJ, Joyeux R. An introduction to long-range time series models and fractional differencing. J Time Ser Anal. 1980;1:15–29. doi: 10.1111/j.1467-9892.1980.tb00297.x
   Google Scholar
• Hosking JRM. Fractional differencing. Biometrika. 1981;68:165–176. doi: 10.1093/biomet/68.1.165
   Web of Science ®Google Scholar
• Samorodnitsky G, Taqqu MS. Stable non-gaussian random processes: stochastic models with infinite variance. New York: Chapman & Hall; 1994.
   Google Scholar
• Giraitis L, Leipus R. A generalized fractionally differencing approach in long memory modelling. Lithuanian Math. Jl. 1995;35):65–81.
   Google Scholar
• Yu J. Empirical characteristic function estimation and its applications. Econometric Rev. 2004;23:93–123. doi: 10.1081/ETC-120039605
   Google Scholar
• Vinod HD. Maximum entropy ensembles for time series inference in economics. J Asian Econ. 2006;17(6):955–978. doi: 10.1016/j.asieco.2006.09.001
   Google Scholar
• Vinod HD, Lopez-de-Lacalle J. Maximum entropy bootstrap for time series: the meboot R package. J Statist Softw. 2009;29(5):1–19.
   Web of Science ®Google Scholar
• Heathcote CR. The integrated squared error estimation of parameters. Biometrika. 1977;64:255–264. doi: 10.1093/biomet/64.2.255
   Web of Science ®Google Scholar
• Newey WK, McFadden D. Large sample estimation and hypothesis testing. In: Engle RF, McFadden D, editors. Handbook of econometrics. Vol. 4. Amsterdam: North-Holland; 1994. p. 2113–2245.
   Google Scholar
• R Development Core Team R. A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing; 2008. Available from: http://www.R-project.org. ISBN 3-900051-07-0
   Google Scholar
• Stoev S, Taqqu MS. Simulation methods for linear fractional stable motion and FARIMA using the fast Fourier transform. Fractals. 2004;12(1):95–121. doi: 10.1142/S0218348X04002379
   Web of Science ®Google Scholar
• Chambers JM, Mallows CL, Stuck BW. A method for simulating stable random variables. J Amer Statist Assoc. 1976;71(354):340–344. Theory and Methods Section. doi: 10.1080/01621459.1976.10480344
   Web of Science ®Google Scholar
• Boutahar M, Marimoutou V, Nouira L. Estimation methods of the long memory parameter: Monte Carlo analysis and application. J Appl Stat. 2007;34(3):261–301. doi: 10.1080/02664760601004874
   Web of Science ®Google Scholar
• Diongue AK, Guégan D. Estimation of k-factor GIGARCH process: a Monte Carlo study. Comm Statist Simulation Comput. 2008;37:2037–2049. doi: 10.1080/03610910802304994
   Web of Science ®Google Scholar