Bartlett correction in the stable second‐order autoregressive model with intercept and trend. (16th August 2013)

• Record Type: Journal Article
• Authors: van, Noud P.A.
• Is Part Of: Statistica Neerlandica. Volume 67:Number 4(2013:Nov.)
• Page Start: 482
• Page End: 498
• Publication Date: 2013-08-16
• Subjects: Statistics -- Periodicals; 519.5; 314.92
• DOI: 10.1111/stan.12018
• Languages: English
• ISSNs: 0039-0402

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>This paper derives the Bartlett factors that can be used to obtain higher‐order improvements for testing hypotheses about the autoregressive (AR) parameters in the stable AR(2) model with possible intercept and linear trend. The factors are obtained for testing hypotheses about individual parameters (<italic>φ</italic>₁ and <italic>φ</italic>₂) as well as their sum. Moreover, the effect of deterministic terms on the correction factors is found explicitly. All corrections are non‐decreasing in the AR parameters. Furthermore, the Bartlett corrections for <italic>φ</italic>₁ and <italic>φ</italic>₂ tend to infinity as <italic>φ</italic>₂ approaches 1, whereas the correction for <italic>φ</italic>₁ + <italic>φ</italic>₂ tends to infinity as <italic>φ</italic>₁ + <italic>φ</italic>₂ is close to 1. The effectiveness of these Bartlett corrections in finite samples is evaluated by simulations.</p> </abstract>