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Modified Gaussian likelihood estimators for ARMA models on \(\mathbb Z^d\). (English) Zbl 1178.62096

Summary: For observations from an autoregressive moving-average process of any dimension, we propose a modification of the Gaussian likelihood, which when maximized corrects the edge-effects and fixes the order of the bias for the estimators derived. We show that the new estimators are not only consistent but also asymptotically normal for any dimension. A classical one-dimensional time series result for the variance matrix is established for any dimension that guarantees the efficiency of the estimators, if the original process is Gaussian. We followed a model-based approach and used finite numbers for the corrections per dimension, which are especially made for the case of autoregressive moving-average models of fixed order.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
62M09 Non-Markovian processes: estimation
62H12 Estimation in multivariate analysis
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