Approximations to the distribution of the least squares estimator in a first order stationary autoregressive model

Abstract

This study investigates the adequacy of approximations to the distribution of the least squares estimator in a first order stationary autoregressive model by the normal distribution, Edgeworth-type expansions, Cornish-Fisher-type expansions and the four-parameter Pearson distributions. Accuracy of these approximations is found to depend substantially on sample size and values of the autoregressive coefficient. Only the Pearson approximations appear to be reliable for both large and moderately small samples. Convenient algorithms by Tsui and Ali (1991a) are used to obtain the exact moments of the related estimator, thereby lifting the major blockage to applying such approximations.

Keywords:

• Approximating distributions
• Cornish-Fisher expansion
• Edge-worth expansion
• Pearson distributions