×

Testing for a unit root nonstationarity in multivariate autoregressive time series. (English) Zbl 0674.62055

Summary: The characteristic equation of a multiple autoregressive time series involves the eigenvalues of a matrix equation which determine if the series is stationary. Suppose one eigenvalue is 1 and the rest are less than 1 in magnitude. We show that ordinary least squares may be used to estimate the matrices involved and that the largest estimated eigenvalue has distributional properties that allow us to test this unit root hypothesis using critical values tabulated by the second author in his Ph. D. dissertation [Estimation and hypothesis testing in nonstationary time series, Iowa State Univ. (1976)]. If a single unit root is suspected, a model can be fit whose parameters are constrained to produce an exact unit root. This is the vector analog of differencing in the univariate case. In the fitting process, canonical series can be computed.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M02 Markov processes: hypothesis testing
Full Text: DOI