In this paper the asymptotic properties of ARMA processes with complex-conjugate unit roots in the AR lag polynomial are studied. These processes behave quite di¤erently from regular unit root processes (with a single root equal to 1). In particular, the asymptotic properties of a standardized version of the periodogram for such processes are analyzed, and a nonparametric test of the complex un...

This paper analyzes the mean reversion and unit root properties of general diffusion models and their discrete samples. In particular, we find that the Dickey-Fuller unit root test applied to discrete samples from a diffusion model becomes a test of no mean reversion rather than a unit root, or more generally, nonstationarity in the underlying diffusion. The unit root test has a well defined li...

The Phillips-Perron unit root test was used to test for unit roots, using level or trend nonstationarity as the null [1]. (A unit root tests whether a variable y evolves as a random walk, i.e., with the dynamic relation yt = yt-1 + constant + deterministic trend + errort.) The KPSS test [1,2], which uses level or trend stationarity as the null, was used to confirm the results of the Phillips-Pe...

The paper introduces order of integration test (OIT) which serves as a simple alternative to unit root built generally using auxiliary autoregressive AAR(3) model. parametric boundary conditions necessary and sufficient for testing the null hypothesis that non-stationary variable under is integrated zero I(0) were estimated via generalized least squares (GLS). decision on evaluated t-statistic....