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GAUSSIAN INFERENCE IN AR(1) TIME SERIES WITH OR WITHOUT A UNIT ROOT

  • Peter C.B. Phillips (a1) and Chirok Han (a2)

Abstract

This paper introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite-sample bias and are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform rate of convergence. En route, a useful central limit theorem (CLT) for sample covariances of linear processes is given, following Phillips and Solo (1992, Annals of Statistics, 20, 971–1001). The approach also has useful extensions to dynamic panels.

Copyright

Corresponding author

Address correspondence to Peter Phillips, Cowles Foundation for Research in Economics, Yale University, Box 208281, New Haven, CT 06520-8281, USA; e-mail: peter.phillips@yale.edu.

References

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Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.
Karanasos, M. (1998) A new method for obtaining the autocovariance of an ARMA model: An exact form solution. Econometric Theory 14, 622640.
Paparoditis, E.Politis, D.N. (2000) Large-sample inference in the general AR(1) model. Test 9, 487509.
Phillips, P.C.B.Magdalinos, T. (2005) Limit Theory for Moderate Deviations from a Unit Root. Cowles Foundation Discussion paper 1471, Yale University.
Phillips, P.C.B.Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 9711001.
White, J.S. (1958) The limiting distribution of the serial correlation coefficient in the explosive case. Annals of Mathematical Statistics 29, 11881197.

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