A recently proposed approximate maximum-likelihood estimator (MLE) of multiple exponentials converts the frequency estimation problem into a problem of estimating the coefficients of a :-polynomial with roots at the desired frequencies. Theoretically, the roots of the estimated polynomial should fall on the unit circle, but MLE, as originally proposed, does not guarantee unit circle roots. This...

In econometric literatures, a number of tests for unit roots have been proposed in the presence of structural changes in I(1) and I(0) model when the numbers of break points are or are not known (though their locations are unknown). Recently [2] proposed a unit root test consisted of two steps: estimating break points and testing a unit root, but their methods resulted in remarkable negative bi...

New methods are developed for identifying, estimating, and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit-root (UR), local (LUR), mildly integrated (MI), explosive (ME) specifications in the new model formulation. It is shown how a parameterization involving localizing rate sequence characterizes departures from unity ca...

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...