Brendan McCabe

A Consistent Test for a Unit Root

This article investigates several U.S. macroeconomic time series for the presence of a unit root using a newly developed test. This test has stationarity as its null hypothesis, and the alternative is a unit-root process. The test is shown to be consistent, and its asymptotic null distribution is determined. Our findings contrast sharply with those obtained via the standard unit-root tests.

Can Economic Time Series Be Differenced to Stationarity

This article considers a class of nonstationary varying-coefficient autoregressive models that allow stochastic variability in the autoregressive root. It is argued that such models provide a better description of the behavior of macroeconomic variables than fixed-unit-root autoregressive models because they allow more general forms of nonstationarity. We construct a test of the null hypothesis of a fixed unit root against the alternative of a randomized root with unit mean and derive its asymptotic distribution. The test is applied to several U.S. macroeconomic series generally considered to contain fixed unit roots. We find that for about half of the series the fixed-unit-root null is rejected.

Modified Stationarity Tests with Data-Dependent Model-Selection Rules

We describe some simple methods for improving the performance of stationarity tests (i.e., tests that have a stationary null and a unit-root alternative). Specifically, we increase the rate of convergence of the test under the unit-root alternative from O p(T) to O p (T 2), then suggest an optimal method of selecting the order of the autoregressive component in the fitted autoregressive integrated moving average model on which the test is based. Simulation evidence suggests that these modifications work well. We apply the modified procedure to U.S. monthly macroeconomic data and uncover new evidence of a unit root in unemployment.

A Parametric approach to testing the null of cointegration

A residual‐based test for cointegration is proposed where a parametric adjustment is made to account for the possible stationarity of the disturbance vector. Allowance is also made for the regressor variables to be cointegrated among themselves. The parametric adjustment turns out to be more robust and powerful than tests based on long‐run variance estimators according to theoretical and simulation evidence.

ON ESTIMATING AN ARMA MODEL WITH AN MA UNIT ROOT

This paper investigates the behavior of the maximum likelihood estimator of a Gaussian autoregressive moving average model with a unit root in the moving average polynomial. The results are primarily of interest in testing hypotheses that involve moving average unit roots as, for example, when testing for stationarity of a series.

The power of some tests for difference stationarity under local heteroscedastic integration

Abstract This article considers the power properties of the McCabe and Tremayne (MT) test for the difference stationarity of a time series. The limiting distribution of the MT test is derived under sequences of locally heteroscedastic and locally explosive autoregressive (AR) alternatives. The limiting distribution of Dickey–Fuller (DF) statistics is also considered under a sequence of locally heteroscedastic alternatives. Whereas the MT test possesses asymptotic power against both forms of nonstationary local alternative, the DF tests set up to test against explosive AR alternatives display little or no ability to reject difference stationarity under local heteroscedastic integration.

On the moments of certain stochastic integrals

The moments of certain stochastic integrals with respect to Brownian motion are well known. In this paper the mean and variance of some integrals involving Brownian bridges are found.

A simple test for parameter constancy in a nonlinear time series regression model

Abstract This paper develops a test for parameter constancy in a nonlinear regression model where the parameters follow a random walk under the alternative. The test is derived assuming normality, and supposing that a first order Taylor series expansion of the nonlinear function holds valid. This yields a test with a simple stucture and tractable asymptotic distribution. Simulation evidence suggests that the test performs well in more general circumstances.