A $t$-Test for the Serial Correlation Coefficient

Abstract

Let $r$ be the sample serial correlation coefficient computed from a sample of size $N$ drawn from a serially correlated process with parameter $\rho$. It is shown that the statistic $$t = \frac{(r - \rho) \sqrt{N + 1}}{\sqrt{1 - r^2}}$$ is approximately distributed as Student's $t$ with $N + 1$ degrees of freedom.