Accession Number:

ADA171416

Title:

The Stationary Autogressive Model

Descriptive Note:

Technical rept.

Corporate Author:

STANFORD UNIV CA DEPT OF STATISTICS

Personal Author(s):

• Anderson, T. W.

Report Date:

1986-07-01

Pagination or Media Count:

28.0

Abstract:

There are several ways of developing the autoregressive stochastic process as a finite-parameter model for time series analysis. This paper obtains the properties of the autoregressive process from a stationary stochastic process that satisfies the simple condition that a linear combination of current and past elements of the process is independent of or alternatively uncorrelated with all earlier elements of the process. This approach provides a coherent, clear, and rigorous exposition of the autoregressive model. The stationarity and independence imply that the roots of the associated polynomial equation are less than 1 in absolute value. The existence of the moving average representation is deduced and its form for distinct roots. The Yule-Walker equations, which are derived, determine the autocovariance sequence. Another set of parameters consists of the variance of the process and the partial autocorrelation sequence.

Descriptors:

• *REGRESSION ANALYSIS
• PARAMETERS
• RANDOM VARIABLES
• COVARIANCE
• STATIONARY
• POLYNOMIALS
• MATHEMATICAL MODELS
• TIME SERIES ANALYSIS

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE