A Sufficient Statistical Test for Dynamic Stability

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