Heteroscedasticity in non-stationary time series,some Monte Carlo evidence |
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Authors: | N Haldrup |
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Institution: | 1. Institute of Economics, University of Aarhus, DK-8000, Aarhus C, Denmark
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Abstract: | A frequent question raised by practitioners doing unit root tests is whether these tests are sensitive to the presence of
heteroscedasticity. Theoretically this is not the case for a wide range of heteroscedastic models. However, for some limiting
cases such as degenerate and integrated heteroscedastic processes it is not obvious whether this will have an effect. In this
paper we report a Monte Carlo study analyzing the implications of various types of heteroscedasticity on three types of unit
root tests: The usual Dickey-Fuller test, Phillips' (1987) semi-parametric test and finally a Dickey-Fuller type test using
White's (1980) heteroscedasticity consistent standard errors. The sorts of heteroscedasticity we examine are the GARCH model
of Bollerslev (1986) and the Exponential ARCH model of Nelson (1991). In particular, we call attention to situations where
the conditional variances exhibit a high degree of persistence as is frequently observed for returns of financial time series,
and the case where, in fact, the variance process for the first class of models becomes degenerate. |
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