Publication:
Weak convergence to a matrix stochastic integral with stable processes

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English

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This paper generalizes the univariate results of Chan and Tran (1989, Econometric Theory 5, 354-362) and Phillips (1990, Econometric Theory 6, 44-62) to multivariate time series. We develop the limit theory for the least-squares estimate of a VAR(1) 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 functionals of a stable process. A semiparametric correction is used in order to asymptotically eliminate the ''bias'' 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.

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Econometric Theory

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Cambridge Univ Press

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Economics, Mathematics, Social sciences, Mathematical methods, Statistics, Probability

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