Breidt, F. Jay; Davis, Richard A.; Lii, Keh-Shin; Rosenblatt, Murray Maximum likelihood estimation for noncausal autoregressive processes. (English) Zbl 0711.62072 J. Multivariate Anal. 36, No. 2, 175-198 (1991). Summary: We discuss a maximum likelihood procedure for estimating parameters in possibly noncausal autoregressive processes driven by i.i.d. non-Gaussian noise. Under appropriate conditions, estimates of the parameters that are solutions to the likelihood equations exist and are asymptotically normal. The estimation procedure is illustrated with a simulation study for AR(2) processes. Cited in 1 ReviewCited in 26 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M09 Non-Markovian processes: estimation 62E20 Asymptotic distribution theory in statistics 60F05 Central limit and other weak theorems Keywords:asymptotic normality; nonminimum phase; maximum likelihood procedure; noncausal autoregressive processes; i.i.d. non-Gaussian noise; simulation study; AR(2) processes Software:UNCMND; pchip × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Beran, R., Adaptive estimates for autoregressive processes, Ann. Inst. Statist. Math., 28, 77-89 (1976) · Zbl 0362.62093 [2] Breidt, F. J.; Davis, R. A., Time-reversibility, identifiability, and independence of innovations for stationary time series (1990), Preprint · Zbl 0753.62058 [3] Brockwell, P. J.; Davis, R. A., (Time Series: Theory and Methods (1987), Springer-Verlag: Springer-Verlag New York) · Zbl 0604.62083 [4] Dennis, J. E.; Schnabel, R. B., (Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1983), Prentice-Hall: Prentice-Hall New York) · Zbl 0579.65058 [5] Kahaner, D.; Moler, C.; Nash, S., (Numerical Methods and Software (1988), Prentice-Hall: Prentice-Hall New York) [6] Kreiss, J., On adaptive estimation in stationary ARMA processes, Ann. Statist., 15, 112-133 (1987) · Zbl 0616.62042 [7] Lehmann, E. L., (Theory of Point Estimation (1983), Wiley: Wiley New York) · Zbl 0522.62020 [8] Lii, K. S.; Rosenblatt, M., Deconvolution and estimation of transfer function phase and coefficients for non-Gaussian linear processes, Ann. Statist., 10, 1195-1208 (1982) · Zbl 0512.62090 [9] Nikias, C. L.; Raghuveer, M. R., Bispectrum estimation: A digital signal processing framework, (Proc. IEEE, 75 (1987)), 869-891 [10] Rosenblatt, M., (Stationary Sequences and Random Fields (1985), Birkhäuser: Birkhäuser Boston) · Zbl 0597.62095 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.