Accession Number:

ADA056214

Title:

The Autocovariance Function Determined Via the Z-Transform, with Application to Box Jenkins Forecasting Models.

Descriptive Note:

Research rept.,

Corporate Author:

FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING

Personal Author(s):

• Muth,Eginhard J.

Report Date:

1978-05-01

Pagination or Media Count:

41.0

Abstract:

A Method is presented which yields the autocovariance function of a stationary discrete-time stochastic process in closed form. Special reference is made to the Box Jenkins forecasting methodology in which the underlying process is generated by passing white noise through a linear filter. The impulse response of the filter and its Z-transform, the transfer function, are obtained from the equation which defines the filter. The bilateral Z-transform of the autocovariance function is then derived from the transfer function, and is inverted following a partially fraction expansion. Several examples of this procedure are worked out in detail, and a summary of solutions for a number of cases is given. Author

Descriptors:

• *FORECASTING
• *TIME SERIES ANALYSIS
• MATHEMATICAL MODELS
• STOCHASTIC PROCESSES
• TRANSFER FUNCTIONS
• WHITE NOISE
• COVARIANCE
• LAPLACE TRANSFORMATION

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE