Bounded integrated processes and unit root tests

Cavaliere, Giuseppe

doi:10.1007/bf02511445

Cited by 4 publications

(1 citation statement)

References 24 publications

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“…To answer this question, Chan and Wei (1987) as well as Phillips (1987a,b) proposed the triangular array framework, so-called nearly nonstationary AR(1) model, and established the limiting distributions of the least squares estimator for θ n under the assumption that the conditional variance of the model ε t is finite. Further results of the least squares estimate for the near-integrated AR(1) model are presented by Chan (1988Chan ( , 1990, Chan and Tran (1989), Knight (1987), Rao (1978), Lai and Wei (1982), Cox and Llatas (1991), Larsson (1995) as well as by Cavaliere (2002).…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Theory for Moderate Deviations from the Unit Boundary in Quantile Autoregressive Time Series

Katsouris¹

2022

Preprint

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We establish the asymptotic theory in quantile autoregression when the model parameter is specified with respect to moderate deviations from the unit boundary such that ρ n = 1 + c kn where (k n ) n∈N is a nonrandom sequence that diverges at a rate slower than the sample size n. Then, extending the framework proposed by Phillips and Magdalinos (2007), we consider the limit theory for the near-stationary and the near-explosive cases when the model is estimated with a conditional quantile specification function and model parameters are quantile-dependent. Additionally, a Bahadur-type representation and limiting distributions based on the M-estimators of the model parameters are derived. Specifically, we show that the serial correlation coefficient converges in distribution to a ratio of two independent random variables. Monte Carlo simulations illustrate the finite-sample performance of the estimation procedure under investigation.

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