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Vector autoregressions and causality. (English) Zbl 0796.62104

The asymptotic properties of Granger-type causality tests in unrestricted and nonstationary vector autoregression models are discussed. A sufficiency condition involving a rank condition on the submatrix of the cointegrating matrix is developed under which the above causality tests are shown to be valid asymptotically as chi-square criteria.
In the case when there is no cointegration, the Wald test statistic for causality is shown to have a nonstandard limiting distribution. For cointegrated systems the Wald tests for causality in error correction models are shown to be not always valid as chi-square criteria in an asymptotic sense.

MSC:

62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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