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Full-Text Articles in Social and Behavioral Sciences
Testing For A Unit Root In The Presence Of Deterministic Trends, Peter C.B. Phillips, Peter Schmidt
Testing For A Unit Root In The Presence Of Deterministic Trends, Peter C.B. Phillips, Peter Schmidt
Cowles Foundation Discussion Papers
This paper provides a new unit root test based on an alternative parameterization which has previously been considered by Bhargava (1986). This parameterization allows for trend under both the null and the alternative, without introducing any parameters that are irrelevant under either. This is not so in the Dickey-Fuller parameterizations. The new test is extracted from the score or LM principle under the assumption that the errors are iid N(0, sigma squared (epsilon)), but our asymptotics hold under more general assumptions about the errors. Two forms of the test (a coefficient test and at t-test) are derived.
An Empirical Process Central Limit Theorem For Dependent Non-Identically Distributed Random Variables, Donald W.K. Andrews
An Empirical Process Central Limit Theorem For Dependent Non-Identically Distributed Random Variables, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper establishes a central limit theorem (CLT) for empirical processes indexed by smooth functions. The underlying random variables may be temporally dependent and non-identically distributed. In particular, the CLT holds for near epoch dependent (i.e., functions of mixing processes) triangular arrays, which include strong mixing arrays, among others. The results apply to classes of functions that have series expansions. The proof of the CLT is particularly simple; no chaining argument is required. The results can be used to establish the asymptotic normality of semiparametric estimators in time series contexts. An example is provided.
Time Series Regression With A Unit Root And Infinite Variance Errors, Peter C.B. Phillips
Time Series Regression With A Unit Root And Infinite Variance Errors, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Chan and Tran give the limit theory for the least squares coefficient in a random walk with the iid errors that are in the domain of attraction of a stable law. This note discusses their results and provides generalizations to the case of I(q) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. General unit root tests are also studied. It is shown that the semiparametric corrections suggested by the author for the finite variance case continue to work when the errors have infinite variance. The limit laws are expressed in terms …
The Durbin-Watson Ratio Under Infinite Variance Errors, Peter C.B. Phillips, Mico Loretan
The Durbin-Watson Ratio Under Infinite Variance Errors, Peter C.B. Phillips, Mico Loretan
Cowles Foundation Discussion Papers
This paper studies the properties of the von Neumann ratio for time series with infinite variance. The asymptotic theory is developed using recent results on the weak convergence of partial sums of time series with infinite variance to stable processes and of sample serial correlations to functions of stable variables. Our asymptotics cover the null of iid variates and general moving average (MA) alternatives. Regression residuals are also considered. In the static regression model the Durbin-Watson statistic has the same limit distribution as the von Neumann ratio under general conditions. However, the dynamic models, the results are more complex and …