In the
existing Statistics and Econometrics literature, there does not exist a
statistical test which may test for all kinds of roots of the characteristic
polynomial leading to an unstable dynamic response, i.e., positive and negative real unit roots, complex unit roots and
the roots lying inside the unit circle. This paper develops a test which is
sufficient to prove dynamic stability (in the context of roots of the
characteristic polynomial) of a univariate as well as a multivariate time
series without having a structural break. It covers all roots (positive and
negative real unit roots, complex unit roots and the roots inside the unit circle
whether single or multiple) which may lead to an unstable dynamic response.
Furthermore, it also indicates the number of roots causing instability in the
time series. The test is much simpler in its application as compared to the
existing tests as the series is strictly stationary under the null (C01, C12).
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