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Maximum likelihood estimation for nonGaussian nonminimum phase ARMA sequences. (English) Zbl 0839.62085

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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F10 Point estimation
62F12 Asymptotic properties of parametric estimators