The Annals of Mathematical Statistics

A Note on the Test of Serial Correlation Coefficients

Masami Ogawara

Full-text: Open access


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.

Article information

Ann. Math. Statist., Volume 22, Number 1 (1951), 115-118.

First available in Project Euclid: 28 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Ogawara, Masami. A Note on the Test of Serial Correlation Coefficients. Ann. Math. Statist. 22 (1951), no. 1, 115--118. doi:10.1214/aoms/1177729700.

Export citation