## Abstract

We derive a stochastic expansion of the error variance-covariance matrix estimator

for the linear regression model under Gaussian AR(1) errors. The higher order accuracy terms of the refined formula are not directly derived from formal Edgeworth-type expansions but instead, the paper adopts Magadalinos’ (1992) stochastic order of ω which is a convenient device to obtain the equivalent relation between the stochastic expansion and the asymptotic approximation of corresponding distribution functions. A Monte Carlo experiment compares tests based on the new estimator with others in the literature and shows that the new tests perform well.

for the linear regression model under Gaussian AR(1) errors. The higher order accuracy terms of the refined formula are not directly derived from formal Edgeworth-type expansions but instead, the paper adopts Magadalinos’ (1992) stochastic order of ω which is a convenient device to obtain the equivalent relation between the stochastic expansion and the asymptotic approximation of corresponding distribution functions. A Monte Carlo experiment compares tests based on the new estimator with others in the literature and shows that the new tests perform well.

Original language | English |
---|---|

Pages (from-to) | 54-59 |

Number of pages | 6 |

Journal | Statistics and Probability Letters |

Volume | 135 |

Early online date | 11 Dec 2017 |

DOIs | |

Publication status | Published - 1 Apr 2018 |

## Keywords

- AR(1) disturbances
- Asymptotic approximations
- Autocorrelation robust inference
- Linear regression
- Stochastic expansions

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty