457 Long Memory Discrete-Valued Time Series
Beran, J. (1994). Statistical methods for data with long-range dependence, Statistical Science, 7,
404–416.
Brockwell, A.E. (2007). Likelihood-based analysis of a class of generalized long-memory time series
models. Journal of Time Series Analysis, 28, 386–407.
Brockwell, P.J. and Davis, R.A. (1991), Time Series: Theory and Methods, 2nd edn., Springer-Verlag,
New York.
Chen, W.W., Hurvich, C.M., and Lu, Y. (2006). On the correlation matrix of the discrete Fourier trans-
form and the fast solution of large Toeplitz systems for long memory time series, Journal of the
American Statistical Association, 101, 812–822.
Creal, D., Koopman, S.J., and Lucas, A. (2013). Generalized autoregressive score models with
applications, Journal of Applied Econometrics, 28, 777–795.
Cui, Y. and Lund, R.B. (2009). A new look at time series of counts, Biometrika, 96, 781–792.
Feller, W. (1968). An Introduction to Probability Theory and its Applications, 3rd edn., John Wiley & Sons,
New York.
Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series
models, Journal of Time Series Analysis, 4, 221–238.
Granger, C.W.J. and Joyeux, R. (1980). An introduction to long-memory time series models and
fractional differencing, Journal of Time Series Analysis, 1, 15–29.
Guégan, D. (2005). How can we dene the concept of long memory? An econometric survey,
Econometric Reviews, 24, 113–149.
Heathcote, C.R. (1967). Complete exponential convergence and some related topics, Journal of Applied
Probability, 4, 217–256.
Holan, S., McElroy, T., and Chakraborty, S. (2009). A Bayesian approach to estimating the long
memory parameter, Bayesian Analysis, 4, 159–190.
Holan, S.H. and McElroy, T.S. (2012). Bayesian seasonal adjustment of long memory time series.
In: Economic Time Series: Modeling and Seasonality, Bell W.R., Holan S.H., McElroy T.S. (eds).
Chapman & Hall/CRC Press: Boca Raton, FL.
Hosking, J.R.M. (1981). Fractional differencing, Biometrika, 68, 165–176.
Jacobs, P.A. and Lewis, P.A.W. (1978a). Discrete time series generated by mixtures I: Correlational
and runs properties, Journal of the Royal Statistical Society, Series B, 40, 94–105.
Jacobs, P.A. and Lewis, P.A.W. (1978b). Discrete time series generated by mixtures II: Asymptotic
properties, Journal of the Royal Statistical Society, Series B, 40, 222–228.
Ko, K. and Vannucci, M. (2006). Bayesian wavelet analysis of autoregressive fractionally
integrated moving-average processes, Journal of Statistical Planning and Inference, 136,
3415–3434.
Lund, R. and Livsey, J. (2015). Renewal-based count time series. In R. A. Davis, S. H. Holan, R. Lund
and N. Ravishanker, eds., Handbook of Discrete-Valued Time Series, pp. 101–120. Chapman & Hall,
Boca Raton, FL.
MacDonald, I.L. and Zucchini, W. (2015). Hidden Markov models for discrete-valued time series. In
R.
A. Davis, S. H. Holan, R. Lund and N. Ravishanker, eds., Handbook of Discrete-Valued Time
Series, pp. 267–286. Chapman & Hall, Boca Raton, FL.
McElroy, T.S. and Holan, S.H. (2012). On the computation of autocovariances for generalized
Gegenbauer processes, Statistica Sinica, 22, 1661–1687.
McKenzie, E. (1985). Some simple models for discrete variate time series, Water Resources Bulletin, 21,
645–650.
McKenzie, E. (1986). Autoregressive-moving average processes with negative-binomial and geomet-
ric marginal distributions, Advances in Applied Probability, 18, 679–705.
McKenzie, E. (1988). Some ARMA models for dependent sequences of Poisson counts, Advances in
Applied Probability, 20, 822–835.
Pai, J.S. and Ravishanker, N. (1996). Bayesian modeling of ARFIMAprocesses by Markov chain Monte
Carlo methods, Journal of Forecasting, 15, 63–82.
Pai, J.S. and Ravishanker, N. (1998). Bayesian analysis of autoregressive fractionally integrated
moving-average processes, Journal of Time Series Analysis, 19, 99–112.