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On Residual Variance Estimation in Autoregressive Models
Author(s) -
Mentz Raul P.,
Morettin Pedro A.,
Toloi Clélia
Publication year - 1998
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00085
Subject(s) - autoregressive model , mathematics , estimator , residual , variance (accounting) , statistics , series (stratigraphy) , normality , econometrics , moment (physics) , asymptotic distribution , star model , time series , autoregressive integrated moving average , algorithm , accounting , paleontology , physics , classical mechanics , business , biology
In this paper we consider time series models belonging to the autoregressive (AR) family and deal with the estimation of the residual variance. This is important because estimates of the variance are involved in, for example, confidence sets for the parameters of the model, estimation of the spectrum, expressions for the estimated error of prediction and sample quantities used to make inferences about the order of the model. We consider the asymptotic biases for moment and least squares estimators of the residual variance, and compare them with known results when available and with those for maximum likelihood estimators under normality. Simulation results are presented for finite samples