Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Processes

Chan, Ngai Hang; Wei, Ching-Zong

doi:10.1214/aos/1176350711

Cited by 532 publications

(345 citation statements)

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“…These results are in line with those developed in Chan and Wei (1988), in which limiting distributions of the least squares estimator were considered. On the other hand, it is worth mentioning that the (normalized) regressors and the (normalized) estimators used for prediction are not asymptotically independent in nonstationary autoregressions; see Ing and Sin (2006) for simple random walk models.…”

Section: Moment Bounds For the Inverse Of The Normalized Fisher Inforsupporting

confidence: 91%

“…When d ≥ 1 and sup 0<t<∞ E|ε t | q < ∞, q > 2, following the arguments used in Phillips (1987) and Chan and Wei (1988), it can be shown that )) . However, the limiting value of E(N f 2 1,n (d)) remains unclear.…”

Section: Asymptotic Expressions For the Mspementioning

confidence: 99%

“…, and k is a constant fixed with n, Theorem 3.5.1 of Chan and Wei (1988) and the continuous mapping theorem can be applied to show that…”

Section: Moment Bounds For the Inverse Of The Normalized Fisher Informentioning

confidence: 99%

See 2 more Smart Citations

Prediction Errors in Nonstationary Autoregressions of Infinite Order

Ing¹,

Sin²,

Yu³

2009

Econom. Theory

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Assume that observations are generated from a nonstationary autoregressive (AR) processes of infinite order. We adopt a finite-order approximation model to predict future observations and obtain an asymptotic expression for the mean-squared prediction error (MSPE) of the least squares predictor. This expression provides the first exact assessment of the impacts of nonstationarity, model complexity and model misspecification on the corresponding MSPE. It not only provides a deeper understanding of the least squares predictors in nonstationary time series, but also forms the theoretical foundation for a companion paper by the same authors, which obtains asymptotically efficient order selection in nonstationary AR processes of possibly infinite order.

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Section: Moment Bounds For the Inverse Of The Normalized Fisher Inforsupporting

confidence: 91%

Section: Asymptotic Expressions For the Mspementioning

confidence: 99%

See 1 more Smart Citation

Prediction Errors in Nonstationary Autoregressions of Infinite Order

Ing¹,

Sin²,

Yu³

2009

Econom. Theory

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“…In all cases, the differences of V, are assumed to be strong mixing. The first example assumes that the differences of U, are strong mixing, which has applications in the theory of multivariate unit roots [4] and cointegration among I(1) variables [8,12]. The second example assumes that U, is the product of processes whose differences are strong mixing, which has applications in the theory of heteroskedastic cointegration [6] and nonstationary variances [7].…”

Section: Introductionmentioning

confidence: 99%

Convergence to Stochastic Integrals for Dependent Heterogeneous Processes

1992

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This paper provides conditions to establish the weak convergence of stochastic integrals. The theorems are proved under the assumption that the innovations are strong mixing with uniformly bounded 2+ moments. Several applications of the results are given, relevant for the theories of estimation with I(1) processes, I(2) processes, processes with nonstationary variances, nearintegrated processes, and continuous time approximations.

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“…errors. Some related results on estimating and testing unit roots can be found in Phillips and Durlauf (1986), Phillips (1987), Chan and Wei (1988), Lucas (1995), and Herce (1996), and the references cited therein. When the error term follows a GARCH process, estimation and testing for a unit root involves intrinsic problems, an issue that was first raised by Pantula (1989).…”

Section: Introductionmentioning

confidence: 99%

Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence

Ling

McAleer

2003

Econometric Reviews

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Michael McAleer Department of Economics University of Western Australia Revised: June 2001Abstract Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition α+β < 1. The former has the usual unit root distribution and the latter is a functional of a bivariate Brownian motion, as in Ling and Li (1998). Several unit root tests based on LS estimators, ML estimators, and mixing LS and ML estimators, are constructed. Simulation results show that tests based on mixing LS and ML estimators perform better than Dickey-Fuller tests which are based on LS estimators, and that tests based on the ML estimators perform better than the mixed estimators.

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Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Processes

Cited by 532 publications

References 0 publications

Prediction Errors in Nonstationary Autoregressions of Infinite Order

Prediction Errors in Nonstationary Autoregressions of Infinite Order

Convergence to Stochastic Integrals for Dependent Heterogeneous Processes

Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence

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