Abstract
We build upon the class of beta regressions introduced by Ferrari and Cribari-Neto (J. Appl. Stat. 31:799–815, 2004) to propose a dynamic model for continuous random variates that assume values in the standard unit interval (0,1). The proposed βARMA model includes both autoregressive and moving average dynamics, and also includes a set of regressors. We discuss parameter estimation, hypothesis testing, goodness-of-fit assessment and forecasting. In particular, we give closed-form expressions for the score function and for Fisher’s information matrix. An application that uses real data is presented and discussed.
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References
Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petroc BN, Kaski F (eds) Second international symposium in information theory. Akademiai Kiado, Budapest, pp 267–281
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Control AC-19:716–723
Benjamin MA, Rigby RA, Stasinopoulos M (2003) Generalized autoregressive moving average models. J Am Stat Assoc 98:214–223
Choi B (1992) ARMA model identification. Springer, New York
Cribari-Neto F, Vasconcellos KLP (2002) Nearly unbiased maximum likelihood estimation for the beta distribution. J Stat Comput Simul 72:107–118
Ferrari SLP, Cribari-Neto F (2004) Beta regression for modelling rates and proportions. J Appl Stat 31:799–815
Fokianos K, Kedem B (2004) Partial likelihood for time series following generalized linear models. J Time Ser Anal 25:173–197
Li WK (1991) Testing model adequacy for some Markov regression models for time series. Biometrika 78:83–89
Li WK (1994) Time series models based on generalized linear models: some further results. Biometrics 50:506–511
McCullagh P, Nelder JA (1989) Generalized linear models, 2nd edn. Chapman and Hall, London
Nelder JA, Wedderburn RWM (1972) Generalized linear models. J R Stat Soc A 135:370–384
Nocedal J, Wright SJ (1999) Numerical optimization. Springer, New York
Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464
Shephard N (1995). Generalized linear autoregressions. Technical report, Nuffield College, Oxford University. Manuscript available at http://www.nu.ox.ac.uk/economics/papers/1996/w8/glar.ps
Vasconcellos KLP, Cribari-Neto F (2005) Improved maximum likelihood estimation in a new class of beta regression models. Braz J Probab Stat 19:13–31
Zeger SL, Qaqish B (1988) Markov regression models for time series: a quasi-likelihood approach. Biometrics 44:1019–1031
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An erratum to this article is available at http://dx.doi.org/10.1007/s11749-017-0528-4.
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Rocha, A.V., Cribari-Neto, F. Beta autoregressive moving average models. TEST 18, 529–545 (2009). https://doi.org/10.1007/s11749-008-0112-z
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DOI: https://doi.org/10.1007/s11749-008-0112-z