A Note on the Test of Serial Correlation Coefficients

In this note the author points out that in the case of stationary Guassian Markov process, i.e., autoregressive stochastic process, we can test the serial correlation coefficients by a method based on normal regression theory. Particularly, in the case of simple Markov process, we can find the confidence limits for its autocorrelation coefficient. In this method, so far as random variables are concerned, not all the information in the original data is used, with a consequence reduction of degrees of freedom. However, the other part of information is introduced as parameters in the distribution functions of random variables and in the statistic useful for tests.