Weak Convergence of Marked Empirical Processes for Focused Inference on AR(p) vs AR(p + 1) Stationary Time Series

Alejandra Cabaña (), Enrique M. Cabaña and Marco Scavino
Additional contact information
Alejandra Cabaña: Universitat Autònoma de Barcelona
Enrique M. Cabaña: Universidad de la República
Marco Scavino: Universidad de la República

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 3, 793-810

Abstract: Abstract The technique applied by the authors to construct consistent and focused tests of fit for i.i.d. samples and regression models is extended to AR models for stationary time series. This approach leads to construct a consistent goodness-of-fit test for the null hypothesis that a stationary series is governed by an autoregressive model of a given order p. In addition of the consistency, the test is focused to detect efficiently the alternative of an AR(p + 1) model. The basic functional statistic conveying the information provided by the series is the process of accumulated sums of the residuals computed under the model of the null hypothesis of fit, reordered as concomitants of the conveniently delayed process. This process is transformed in order to obtain a new process with the same limiting Gaussian law encountered in earlier applications of the technique. Therefore, a Watson type quadratic statistic computed from this process has the same asymptotic laws under the null hypothesis of fit, and also under the alternatives of focusing, than the test statistics used in those applications. As a consequence, the resulting test has the same desirable performance as the tests previously developed by applying the same kind of transformations of processes.

Keywords: Goodness-of-fit; Autoregressive processes; Marked processes; Transformations of processes in inference; 62G10; 62M10 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-011-9270-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9270-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-011-9270-7

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().