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A KPSS better than KPSS Rank tests for short memory stationarity
TLDR
In this article, a rank-test of the null hypothesis of short memory stationarity possibly after linear detrending was proposed, in which ranks substitute the original observations, and it was shown that the rank KPSS statistic shares the same limiting distribution as the standard kpsS statistic under the null and diverges under I(1) alternatives.Abstract:
We propose a rank-test of the null hypothesis of short memory stationarity possibly after linear detrending. For the level-stationarity hypothesis, the test statistic we propose is a modied version of the popular KPSS statistic, in which ranks substitute the original observations. We prove that the rank KPSS statistic shares the same limiting distribution as the standard KPSS statistic under the null and diverges under I(1) alternatives. For the trend-stationarity hypothesis, we apply the same rank KPSS statistic to the residual of a Theil-Sen regression on a linear trend. We derive the asymptotic distribution of the Theil-Sen estimator under short memory errors and prove that the Theil-Sen detrended rank KPSS statistic shares the same weak limit as the least-squares detrended KPSS. We study the asymptotic relative eciencyread more
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Book ChapterDOI
Convergence of probability measures
TL;DR: Weakconvergence methods in metric spaces were studied in this article, with applications sufficient to show their power and utility, and the results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables.
References
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ReportDOI
A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix
Whitney K. Newey,Kenneth D. West +1 more
TL;DR: In this article, a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction is described.
Journal ArticleDOI
Testing for a Unit Root in Time Series Regression
TL;DR: In this article, the authors proposed new tests for detecting the presence of a unit root in quite general time series models, which accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend.
Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Journal ArticleDOI
Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?
TL;DR: In this paper, a test of the null hypothesis that an observable series is stationary around a deterministic trend is proposed, where the series is expressed as the sum of deterministic trends, random walks, and stationary error.
Journal ArticleDOI
Conditional heteroskedasticity in asset returns: a new approach
TL;DR: In this article, an exponential ARCH model is proposed to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987, which is an improvement over the widely-used GARCH model.