The Sampling Distribution of the Serial Correlation Coefficient

The Probability Content of Cones in Isotropic Random Fields

“…In the third case, the distribution and the moments of the square of the norm are obtained from the density of the norm W which is given in Mathai et al [26], Section 3.2. Additional results on the moments of sample serial covariances may be found for example in Provost and Rudiuk [28] and Sutradhar [30] for the Gaussian case.…”

“…As an example, one may take the lag-k sample serial correlation coefficient, that is, P k ( yÄ )ÂP 0 ( yÄ ), with P k ( yÄ )=(y$VA k V y)ÂT according to (28), noting that P 0 ( yÄ )=(y$V y)ÂT and V is idempotent.…”

On the distribution of the sample autocorrelation coefficients

“…Although this exact distribution is well known (see Ali (1984) and Provost and Rudiuk (1995)), its practical use has been very limited. The main obstacle in its computation is obtaining the eigenvalues of a symmetric n × n matrix, where n is the length of the time series.…”

The exact distribution of indefinite quadratic forms in noncentral normal vectors

“…Such ratios arise for example in regression and analysis of variance problems associated with linear models. The sample serial correlation coeËficient as defined in Anderson (1990) and discussed in Provost and Rudiuk (1995) also has this structure.…”