Higher order residual analysis for nonlinear time series with autoregressive correlation structures
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Authors
Lewis, Peter A. W.
Lawrence, A. J.
Subjects
Advisors
Date of Issue
1984-09
Date
Publisher
Monterey, CA; Naval Postgraduate School
Language
Abstract
The paper considers nonlinear time series whose second order autocorrelations satisfy autoregressive Yule-Walker equations. The usual linear residuals are then uncorrelated, but not independent, as would be the case for linear autoregressive processes. Two such types of nonlinear model are treated in some detail; random coefficient autoregression and multiplicative autoregression. The proposed analysis involves crosscorrelation of the usual linear residuals and their squares. This function is obtained for the two types of model considered, and allows differentiation between models with the same autocorrelation structure in the same class. For the random coefficient models it is shown that one side of the crosscorrelation function is zero, giving a useful signature of these processes. The non-zero features of the crosscorrelations are informative of the higher order dependency structure. In applications this residual analysis requires only standard statistical calculations, and extends rather than replaces the usual second order analysis
Type
Technical Report
Description
Series/Report No
Department
Organization
Identifiers
NPS Report Number
NPS55-84-022
Sponsors
Prepared for: Chief of Naval Research
Arlington, VA
Funding
N00014R4WR 24004
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.