### Abstract

For the AR(1) model, one implicitly assumes a specific variance on the initial observation, or that the process started a long time ago, to insure homoscedasticity. This paper investigates Anderson and Hsiao's (1982) suggestion of an arbitrary variance on the initial observation of the autoregressive process. This is done in a panel data framework. Regardless of when the AR(1) process started, one can translate this starting date into an 'effective' initial variance assumption. This 'effective' initial variance can be estimated with panel data and tested for departures from homoscedasticity. The consequences of this departure on various estimators is studied via Monte Carlo experiments. The following estimators are compared: OLS, Iterative Cochrane-Orcutt (ICO), and two maximum likelihood (mle) estimators, one corresponding to the usual stationary assumption denoted by BM [Beach and MacKinnon (1978)] and another mle corresponding to the arbitrary variance assumption on the initial observations. Both mle's can be achieved as iterative GLS - the former using a Prais-Winsten (PW) transformation and the latter using a Generalized PW transformation (GPW). Some of the major findings are the following: BM performs poorly for large departures of the variance of the initial observations from the usual homoscedastic assumption, whereas the mle corresponding to the GPW transformation is robust to various assumptions on the variance of the initial observations. ICO continues to perform poorly relative to estimators that use all time series observations, even though the CO estimator of ρ{variant} performs well compared to that of GPW. The t-statistic which tests the true value of the parameter may be misleading for OLS and BM depending upon the departure of the initial variance from the homoscedastic assumption. However, this t-statistic performs well for the GPW estimator. Finally, the likelihood ratio test which tests the usual homoscedastic assumption on the initial disturbances and a pre-test estimator based on this test perform well in Monte Carlo experiments, and are recommended.

Original language | English (US) |
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Pages (from-to) | 371-380 |

Number of pages | 10 |

Journal | Journal of Econometrics |

Volume | 52 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1992 |

Externally published | Yes |

### ASJC Scopus subject areas

- Economics and Econometrics

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## Cite this

*Journal of Econometrics*,

*52*(3), 371-380. https://doi.org/10.1016/0304-4076(92)90017-L