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Journal of the American Statistical Association Volume 79, 1984 - Issue 385
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Theory and Method

Consistent Estimates of Autoregressive Parameters and Extended Sample Autocorrelation Function for Stationary and Nonstationary ARMA Models

Ruey S. Tsay Department of Statistics, Carnegie-Mellon University, Pittsburgh, PA, 15213, USA
&
George C. Tiao Graduate School of Business, University of Chicago, Chicago, IL, 60637, USA
Pages 84-96 | Received 01 Jul 1982, Published online: 12 Mar 2012
 
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Abstract

A unified approach for the tentative specification of the order of mixed stationary and nonstationary ARMA models is proposed. For the ARMA models, an iterative regression procedure is given to produce consistent estimates of the autoregressive parameters. An extended sample autocorrelation function based on these consistent estimates is then defined and used for order determination. One of the advantages of this new approach is that it eliminates the need to determine, usually rather arbitrarily, the order of differencing to produce stationarity in modeling time series. Comparisons with other existing identification methods are discussed, and several samples are given.

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