Weak Convergence to a Matrix Stochastic Integral with Stable Processes

Mehmet Caner ()

Econometric Theory, 1997, vol. 13, issue 04, pages 506-528

Abstract: This paper generalizes the univariate results of Chan and Tran (1989, Econometric Theory 5, 354 62) to multivariate time series. We develop the limit theory for the least-squares estimate of a VAR(l) for a random walk with independent and identically distributed errors and for I(1) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. The limit laws are represented by functional of a stable process. A semiparametric correction is used in order to asymptotically eliminate the term in the limit law. These results are also an extension of the multivariate limit theory for square-integrable disturbances derived by Phillips and Durlauf (1986, Review of Economic Studies 53, 473 495). Potential applications include tests for multivariate unit roots and cointegration.

Date: 1997
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