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DETERMINANTS OF COVARIANCE MATRICES OF DIFFERENCED AR(1) PROCESSES

Published online by Cambridge University Press:  06 September 2007

Chirok Han
Chirok Han
Affiliation:
University of Auckland
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Abstract

In this note, determinants are explicitly calculated for the covariance matrices of differenced and double-differenced AR(1) variables.The author thanks Peter C.B. Phillips for introducing the author to Grenander and Szegö's book on Toeplitz matrices and giving useful comments. The author also thanks two anonymous referees for helpful comments on earlier drafts of the note.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 23 , Issue 6 , December 2007 , pp. 1248 - 1253
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Galbraith, R.F. & J.I. Galbraith (1974) On the inverses of some patterned matrices arising in the theory of stationary time series. Journal of Applied Probability 11, 63–71.Google Scholar
Grenander, U. & G. Szegö (1958) Toeplitz Forms and Their Applications. University of California Press.
Haddad, J.N. (2004) On the closed form of the covariance matrix and its inverse of the causal ARMA process. Journal of Time Series Analysis 25, 443–448.Google Scholar
Han, C. & P.C.B. Phillips (2006) GMM Estimation for Dynamic Panels with Fixed Effects and Strong Instruments at Unity. Cowles Foundation Discussion Paper no. 1599.
Hoy, M., J. Livernois, C. McKenna, R. Rees, & T. Stengos (1996) Mathematics for Economics. Addison-Wesley.
Hsiao, C., M.H. Pesaran, & A.K. Tahmiscioglu (2002) Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods. Journal of Econometrics 109, 107–150.Google Scholar
Karanasos, M. (1998) A new method for obtaining the autocovariance of an ARMA model: An exact form solution. Econometric Theory 14, 622–640.Google Scholar
McCabe, B.P.M. & S.J. Leybourne (1998) On estimating an ARMA model with an MA unit root. Econometric Theory 14, 326–338.Google Scholar
Ploberger, W. & P.C.B. Phillips (2002) Optimal Testing for Unit Roots in Panel Data. Mimeo, University of Rochester.
Zinde-Walsh, V. (1988) Some exact formulae for autoregressive moving average processes. Econometric Theory 4, 384–402.Google Scholar