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Exact tests for serial correlation in vector processes

Published online by Cambridge University Press:  24 October 2008

E. J. Hannan
E. J. Hannan
Affiliation:
Australian National UniversityCanberra, A.C.T.
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Abstract

Exact tests for serial independence in vector Markoff processes have been obtained by considering the system of regressions of the vectors observed at time 2t on the vectors observed at times (2t − 1) and (2t + 1). The tests then reduce to those obtained from canonical correlation procedures in multivariate analysis. Two particular cases are

(1) The test for serial independence of a vector of residuals from a system of regressions in which the regressors are all independent of the residuals. At the same time a test of the hypothesis that the regressor and regrediend vectors are independent is obtained.

(2) The test for serial correlation or partial serial correlation in a multiple Markoff process (autoregressive process).

An investigation of the efficiency of the test so obtained, of the hypothesis that a process is a simple Markoff process (against the alternative that the process is a second-order auto-regression) suggests that the efficiency of all of these tests will be low.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 3 , July 1956 , pp. 482 - 487
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1)Bartlett, M. S.Proc. Camb. phil. Soc. 30 (1938), 327.CrossRefGoogle Scholar
(2)Bartlett, M. S.Suppl. J. R. statist. Soc. 6 (1947), 176.CrossRefGoogle Scholar
(3)Hannan, E. J.Biometrika, 42 (1955), 133.CrossRefGoogle Scholar
(4)Hannan, E. J.Biometrika, 42 (1955), 316.CrossRefGoogle Scholar
(5)Marriott, F. H. C.Biometrika, 39 (1952), 58.CrossRefGoogle Scholar
(6)Ogawara, M.Ann. math. Statist. 22 (1951), 115.CrossRefGoogle Scholar
(7)Pitman, E. J. G.Lecture notes on non-parametric inference (University of North Carolina, 1948).Google Scholar
(8)Rao, C. R.Biometrika, 35 (1948), 58.CrossRefGoogle Scholar
(9)Rao, C. R.Advanced statistical methods in biometric research (New York, 1952).Google Scholar