Residuals Modeling with AR and ARMA Representations

Guillaume Mercère ()
Additional contact information
Guillaume Mercère: Université de Poitiers

Chapter Chapter 5 in Data Driven Model Learning for Engineers, 2023, pp 121-157 from Springer

Abstract: Abstract After some time spent on the transition between the Wold decomposition transfer function and the AR and ARMA model parameterizations, this chapter focuses on AR and ARMA parameter estimation, i.e., describes (i) standard numerical solutions for computing the AR and ARMA coefficients, (ii) the main statistical properties of these estimation techniques. More precisely, in this chapter, it is shown that By assuming that the residuals time series Is a realization of a zero mean weak stationary stochastic sequence which does not contain linearly singular components anymore. Has been generated by a stable, causal, linear, and time invariant system. The modeling of the residuals boils down to the estimation of ARMA model coefficients, i.e., a finite number of constant weights thanks to the Wold decomposition theorem. The computation of AR model parameters from residuals realizations can be carried out by using a linear least squares algorithm. The computation of ARMA model parameters from residuals realizations can be carried out by using a pseudolinear least squares or a nonlinear least squares algorithm. Both AR and ARMA model parameters can be estimated consistently under mild practical conditions. The autocorrelation and partial autocorrelation functions are easy-to-implement tools to determine if an AR or ARMA model structure should be considered for residuals time series modeling. Prediction with confidence intervals can be carried out once reliable AR or ARMA model parameters are available.

Date: 2023
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-31636-4_5

Ordering information: This item can be ordered from
http://www.springer.com/9783031316364

DOI: 10.1007/978-3-031-31636-4_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().