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Weak Convergence to a Matrix StochasticIntegral with Stable Processes

Published online by Cambridge University Press:  11 February 2009

Mehmet Caner
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Abstract

This paper generalizes the univariate results of Chanand Tran (1989, Econometric Theory5, 354–362) and Phillips (1990, EconometricTheory 6, 44–62) to multivariate timeseries. We develop the limit theory for theleast-squares estimate of a VAR(l) for a random walkwith independent and identically distributed errorsand for I(1) processes with weakly dependent errorswhose distributions are in the domain of attractionof a stable law. The limit laws are represented byfunctional of a stable process. A semiparametriccorrection is used in order to asymptoticallyeliminate the “bias” term in the limit law. Theseresults are also an extension of the multivariatelimit theory for square-integrable disturbancesderived by Phillips and Durlauf (1986,Review of Economic Studies 53,473–495). Potential applications include tests formultivariate unit roots and cointegration.

Information

Type
Research Article
Information
Econometric Theory , Volume 13 , Issue 4 , February 1997 , pp. 506 - 528
Copyright
Copyright © Cambridge University Press 1997

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References

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