The Student's t Approximation in a Stationary First Order Autoregressive Model

The exact distribution of the regression t statistic for testing the value of the AR parameter in a Gaussian first ord er autoregressive model is investigated by Monte Carlo methods. The S tudent's t distribution is not a satisfactory approximation for sampl es typical in economic applications. The main problem is the location of the distribution of the t statistic rather than the shape. Once t he t statistic is adjusted so that it has the same mean and standard deviation as Student's t, the distribution of the adjusted t statisti c is accurately approximated by Student's t. Techniques are presented for mak-ing these adjustments in practice.