Fast Bayesian Estimation for VARFIMA Processes with Stable Errors

Baillie, R.T., 1996. Long memory processes and fractional integration in econometrics. Journal of Econometrics, 73, 5–59. Beran, J., 1992. Statistical methods for data with long-range dependence. Statistical Science, 7, 404–427. Beran, J., 1993. Fitting long-memory models by generalized linear regression. Biometrika, 80, 4, 817–822. Beran, J., 1994. Statistics for long-memory processes. Chapman & Hall, New York. Beran, J., 1995. Maximum likelihood estimation of the differencing parameter for invertible short- and long-memory ARIMA models. Journal of the Royal Statistical Society Series B, 57, 4, 659–672. Bisaglia, L., Guegan, D., 1998. A comparison of techniques of estimation in long-memory processes. Computational Statistics & Data Analysis, 27, 61–81. Böttcher, A., Silbermann, B., 1999. Introduction to Large Truncated Toeplitz Matrices. Springer-Verlag, New York. Brockwell, P.J., Davis, R.A., 1991. Time Series: Theory and Methods. Springer-Verlag, New York. Brockwell, P.J., Mitchell, H., 1998. Linear prediction for a class of multivariate stable processes. Communications in Statistics-Stochastic Models, 14(1 & 2), 297–310. Buckle, D.J., 1995. Bayesian inference for stable distribution. J. Amer. Statist. Assoc., 90, 605–613. Chambers, M.J., 1996, The estimation of continuous parameter long-memory time series models. Econom. Theory. 12, 374–390. Chan, N.H., Palma, W., 1998. State space modeling of long-memory processes. Ann. Statist., 26, 719–740. Chan, T.F., 1988. An optimal circulant preconditioner for Toeplitz systems. Siam J. Sci. Stat. Comput. 9, 766–771. Chan, T.F., Olkin, J.A., 1994. Circulant preconditioners for Toeplitz-block matrices. Num. Algs., 6, 89–101. Chen, W.W., Hurvich, C.M., Lu, Y., 2006. On the correlation matrix of the discrete Fourier transform and the fast solution of large Toeplitz systems for long-memory time series. J. Amer. Statist. Assoc., 101, 812–822. Cheung, Y.W., Diebold, F.X., 1994. On maximum likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean. Journal of Econometrics, 62, 301–16. Chung, C.F., and Baillie, R., 1993. Small sample bias in conditional sum-of-squares estimators of fractionally integrated ARMA models. Empirical Economics, 18, 791–806. Dahlhaus, R., 1989. Efficient parameter estimation for self-similar processes. Ann. Statist., 17, 1749–1766. Devroye, L., 1986. Nonuniform Random Variate Generation. Springer-Verlag, New York. 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. Fox, R., Taqqu, M.S., 1986. Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist., 14, 517–532. Giriatis, L., Surgailis, D., 1990. A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotic normality of Whittle’s estimate. Probab. Theory Related Fields, 86, 87–104. Golub, G.H., Van Loan, C.F., 1996. Matrix Computations (3rd edition). Johns Hopkins University Press, Baltimore. Hannan, E., Deistler, M., 1988. The Statistical Theory of Linear Systems. J. Wiley & Sons, New York. Haslett, J., Raftery, A.E., 1989. Space-time modelling with long-memory dependence: Assessing Ireland’s wind power resource (with discussion). Applied Statistics, 38, 1–50. Heyde, C.C., Gay, R., 1993. Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence. Stoch. Proc. and their Appl., 45, 169–182. Hosking, J.R.M., 1981. Fractional differencing. Biometrika, 68, 165–176. Hosking, J.R.M., 1984. Modeling persistence in hydrological time series using fractional differencing. Water Resources Research, 20, 1898–1908. Hsu, N.J., Breidt, F.J., 2003. Bayesian analysis of fractionally integrated ARMA with additive noise. Journal of Forecasting, 22, 491–514. Jensen, M.J., 2000. An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets. J. of Economic Dynamics and Control, 24, 361–387. Kinderman, A.J., Monahan, J.F., 1977. Computer generation of random variables using the ratio of uniform deviates. ACM Trans. of Math. Software, 3, 257–260. Ko, K., Vannucci, M., 2006a. Bayesian wavelet analysis of autoregressive fractionally integrated moving-average processes. Journal of Statistical Planning and Inference, 136, 3415–3434. Ko, K., Vannucci, M., 2006b. Bayesian wavelet-based methods for the detection of multiple changes of the long memory parameter. IEEE Transactions on Signal Processing, 54, 4461–4470. Kokoszka, P.S., Taqqu, M.S., 1995. Fractional ARIMA with stable innovations. Stoch. Proc. and their Applns., 60, 19–47. Kokoszka, P.S., Taqqu, M.S., 1996. Infinite variance stable moving averages with long memory. Journal of Econometrics, 73, 79–99. Koop, G., Ley E., Osiewalski J., Steel M.F.J., 1997. Bayesian analysis of long memory and persistence using ARFIMA models. Journal of Econometrics, 76, 149–169. Liseo, B., Marinucci, D., Petrella, L., 2001. Bayesian semiparametric inference on long-range dependence. Biometrika, 88(4), 1089–1104. Luceno, A., 1996. A fast likelihood approximation for vector general linear processes with long series: Application to fractional differencing. Biometrika, 83(3), 603–614. Martin, V.L., Wilkins, N.P., 1999. Indirect estimation of ARFIMA and VARFIMA models. J. Econometrics, 93, 149–175. McCoy, E.J., Walden, A.T., 1996. Wavelet Analysis and Synthesis of Stationary Long-Memory Processes. Journal of Computational and Graphical Statistics, 5, 1–31. Pai, J.S., Ravishanker, N., 2009. A multivariate preconditioned conjugate gradient approach for maximum likelihood estimation in vector long memory processes. Statistics and Probability Letters, 79(9), 1282–1289. Palma, W., 2007. Long-Memory Time Series. John Wiley and Sons, New York. Qiou, Z., Ravishanker, N., 1998a. Bayesian inference for time series with stable innovations. J. Time Series Analysis, 19, 235–249. Qiou, Z., Ravishanker, N., 1998b. Bayesian inference for multivariate time series with stable innovations. Sankhya Series A, 60, 459–475. Ravishanker, N., Ray, B.K., 1997. Bayesian analysis of vector ARFIMA processes. Aus. J. Statist., 39, 295–312. Robert, C.P., 2001. Bayesian Choice (2nd edition). Springer-Verlag, New York. Robinson, P.M., 1995. Log periodogram regression of time series with long-range dependence. Ann. Statist., 23, 1048–1072. Robinson, P.M., 2003. Time Series With Long Memory. Oxford University Press, Oxford. Samorodnitsky, G., Taqqu, M.S., 1994. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman & Hall, New York. Sowell, F.B., 1989. Maximum likelihood estimation of fractionally integrated time series models. Carnegie-Mellon University. Sowell, F.B., 1992a. Maximum likelihood estimation of stationary univariate fractionally integrated time series models. Journal of Econometrics, 53, 165–188. Sowell, F.B., 1992b. Modeling long run behavior with the fractional ARIMA model. Journal of Monetary Economics, 29, 277–302. Spiegelhalter, D.J., Best, N.G., Carlin, B.R., van der Linde, A., 2002. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society Series B, 64, 583–616. Tsay, W.-J., 2010. Maximum likelihood estimation of stationary multivariate ARFIMA processes, J. Statist. Comp. and Simul., 80, 729–745. Velasco, C., Robinson, P.M., 2000. Whittle pseudo-maximum likelihood estimation for nonstationary time series. J. Amer. Statist. Assoc., 95(452), 1229–1243. Whittle, P., 1983. Prediction and Regulation by Linear Least-squares Methods (2nd edition, revised). University of Minnesota Press, Minneapolis, MN.