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BIASES OF ESTIMATORS IN MULTIVARIATE NON‐GAUSSIAN AUTOREGRESSIONS
Author(s) -
Pope Alun Lloyd
Publication year - 1990
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/j.1467-9892.1990.tb00056.x
Subject(s) - mathematics , estimator , martingale difference sequence , gaussian , autoregressive model , multivariate statistics , martingale (probability theory) , moment (physics) , statistics , physics , classical mechanics , quantum mechanics
Abstract. Expressions for the bias of the least‐squares and modified Yule‐Walker estimators in a correctly specified multivariate autoregression of arbitrary order are obtained without assuming that the innovations are Gaussian. Instead, the innovations are assumed to form a martingale difference sequence which is stationary up to sixth order and which has finite sixth moments. The errors in the expressions are shown to be O( n ‐3/2 ), as the sample size n under some moment conditions. The expressions obtained are the same in the Gaussian and non‐Gaussian cases.