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Bartlett correction in the stable second‐order autoregressive model with intercept and trend
Author(s) -
Giersbergen Noud P.A.
Publication year - 2013
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12018
Subject(s) - autoregressive model , mathematics , infinity , star model , order (exchange) , statistics , econometrics , mathematical analysis , autoregressive integrated moving average , time series , economics , finance
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 ( φ 1 and φ 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 φ 1 and φ 2 tend to infinity as φ 2 approaches 1, whereas the correction for φ 1 + φ 2 tends to infinity as φ 1 + φ 2 is close to 1. The effectiveness of these Bartlett corrections in finite samples is evaluated by simulations.