Lii, Keh-Shin; Rosenblatt, Murray Maximum likelihood estimation for nonGaussian nonminimum phase ARMA sequences. (English) Zbl 0839.62085 Stat. Sin. 6, No. 1, 1-22 (1996). Summary: We consider an approximate maximum likelihood procedure for estimating parameters of possibly noncausal and noninvertible autoregressive moving average processes driven by independent identically distributed nonGaussian noise. It is shown that the normalized approximate likelihood has a global maximum at true parameter values in the nonGaussian case. Under appropriate conditions, estimates of parameters that are solutions of likelihood equations exist, are consistent and asymptotically normal. An asymptotic covariance matrix is given. The procedure is illustrated with simulation examples of ARMA(1,1) processes. Cited in 11 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F10 Point estimation 62F12 Asymptotic properties of parametric estimators Keywords:asymptotic normality; approximate maximum likelihood procedure; noncausal; noninvertible; autoregressive moving average processes; nonGaussian noise; global maximum; asymptotic covariance matrix; ARMA(1,1) processes × Cite Format Result Cite Review PDF