The Annals of Statistics

Consistency Properties of Least Squares Estimates of Autoregressive Parameters in ARMA Models

George C. Tiao and Ruey S. Tsay

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Abstract

A unified treatment of the consistency properties of the ordinary least squares estimates in an autoregressive fitting of time series from nonstationary or stationary autoregressive moving average models is given. For a given model, the orders of autoregressions which produce consistent estimates are obtained and the limiting values, hence the biases, of the estimates of other autoregressions are investigated.

Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 856-871.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346252

Digital Object Identifier
doi:10.1214/aos/1176346252

Mathematical Reviews number (MathSciNet)
MR707936

Zentralblatt MATH identifier
0523.62076

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62J05: Linear regression

Keywords
ARMA time series autoregression consistency least squares nonstationarity

Citation

Tiao, George C.; Tsay, Ruey S. Consistency Properties of Least Squares Estimates of Autoregressive Parameters in ARMA Models. Ann. Statist. 11 (1983), no. 3, 856--871. doi:10.1214/aos/1176346252. https://projecteuclid.org/euclid.aos/1176346252


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