Abstract
We consider the calculation of confidence intervals for the correlation parameter, based on observations of a large number of short Gaussian first-order autoregressive processes with different means but common correlation and variance. Ordinary profile likelihood gives very misleading answers. The approximate conditional likelihood of Cox & Reid (1987) is calculated and shown to lead to consistent estimation of the correlation. Simulations verify that the usual asymptotic properties of the statistics derived from the conditional likelihood are quite satisfactory. In this example the approximate conditional likelihood is the same as the marginal likelihood for the standardized residuals, although this is not true in general.
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