### Abstract

We consider a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter ^{ρn} and the distribution of the time series of innovations. In particular, we consider the full range of cases in which ^{ρn} satisfies n(1- ^{ρn})→∞ and n(1- ^{ρn})→ ^{h1}∈[0,∞) as n→∞, where n is the sample size. Results of this type are needed to establish the uniform asymptotic properties of the LS and quasi-GLS statistics.

Original language | English (US) |
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Pages (from-to) | 196-210 |

Number of pages | 15 |

Journal | Journal of Econometrics |

Volume | 169 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Economics and Econometrics

### Cite this

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*Journal of Econometrics*, vol. 169, no. 2, pp. 196-210. https://doi.org/10.1016/j.jeconom.2012.01.017

**Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity.** / Andrews, Donald W.K.; Guggenberger, Patrik.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity

AU - Andrews, Donald W.K.

AU - Guggenberger, Patrik

PY - 2012/8/1

Y1 - 2012/8/1

N2 - We consider a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter ρn and the distribution of the time series of innovations. In particular, we consider the full range of cases in which ρn satisfies n(1- ρn)→∞ and n(1- ρn)→ h1∈[0,∞) as n→∞, where n is the sample size. Results of this type are needed to establish the uniform asymptotic properties of the LS and quasi-GLS statistics.

AB - We consider a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter ρn and the distribution of the time series of innovations. In particular, we consider the full range of cases in which ρn satisfies n(1- ρn)→∞ and n(1- ρn)→ h1∈[0,∞) as n→∞, where n is the sample size. Results of this type are needed to establish the uniform asymptotic properties of the LS and quasi-GLS statistics.

UR - http://www.scopus.com/inward/record.url?scp=84862701351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862701351&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2012.01.017

DO - 10.1016/j.jeconom.2012.01.017

M3 - Article

AN - SCOPUS:84862701351

VL - 169

SP - 196

EP - 210

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 2

ER -