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AN EXPLICIT NEARLY UNBIASED ESTIMATE OF THE AR(1) PARAMETER FOR REPEATED MEASUREMENTS
Author(s) -
Azzalini A.,
Frigo A. C.
Publication year - 1991
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.1467-9892.1991.tb00083.x
Subject(s) - mathematics , statistics , autocorrelation , series (stratigraphy) , autoregressive model , value (mathematics) , covariate , paleontology , biology
. It is assumed that n ( n ≥ 1) independent time series, each of length T. have the same autocorrelation function of the AR(1) type, but they may differ in mean value, with the mean value of the i th series equal to a linear combination of a set of covariates associated with the series. To estimate the common autoregressive parameter, Daniels' method is extended to the present case. As, for small T , this gives a severely biased estimate, a formula for its mean value is obtained. A modified estimate which has a substantially smaller bias is found using this formula.