An exact test for a column of the covariance matrix based on a single observation

In this paper, we derive an exact test for a column of the covariance matrix. The test statistic is calculated by using a single observation. The exact distributions of the test statistic are derived under both the null and alternative hypotheses. We also obtain an analytical expression of the power function of the test for the equality of a column of the covariance matrix to a given vector. It is shown that the information contained in a single vector is large enough to ensure a good performance of the test. Moreover, the suggested test can be applied for time-dependent multivariate Gaussian processes. Copyright Springer-Verlag Berlin Heidelberg 2013