An expression for the joint distribution of serial correlation coefficients, circularly defined, has been derived. It has been shown that this distribution possesses properties similar to those already encountered in the distribution of a single serial correlation coefficient, i.e. it is defined by different function forms for various subregions. The distribution thus found is of little use for computational purposes. Consequently, approximate forms have been investigated and the suitability of the ordinary partial correlation coefficient for large-sample testing has been inferred.
"The Joint Distribution of Serial Correlation Coefficients." Ann. Math. Statist. 20 (4) 561 - 571, December, 1949. https://doi.org/10.1214/aoms/1177729948