Robust Inference for Near-Unit Root Processes with Time-Varying Error Variances

2014 ◽  
Vol 35 (5) ◽  
pp. 751-781 ◽  
Author(s):  
Matei Demetrescu ◽  
Christoph Hanck
Keyword(s):  
Unit Root ◽  
Robust Inference ◽  
Time Varying ◽  
Near Unit Root

scholarly journals A Residual-Based Cointegration Test for Near Unit Root Variables

2007 ◽  
Vol 2007 (907) ◽  
pp. 1-31 ◽  
Author(s):  
Erik Hjalmarsson ◽  
◽  
Pär Österholm
Keyword(s):  
Unit Root ◽  
Cointegration Test ◽  
Near Unit Root

scholarly journals EXPLOITING INFINITE VARIANCE THROUGH DUMMY VARIABLES IN NONSTATIONARY AUTOREGRESSIONS

2013 ◽  
Vol 29 (6) ◽  
pp. 1162-1195 ◽  
Author(s):  
Giuseppe Cavaliere ◽  
Iliyan Georgiev
Keyword(s):  
Unit Root ◽  
Asymptotic Properties ◽  
Ordinary Least Squares ◽  
Infinite Variance ◽  
Local Power ◽  
Test Statistic ◽  
Asymptotically Normal ◽  
Normal Test ◽  
Order Of Magnitude ◽  
Near Unit Root

We consider estimation and testing in finite-order autoregressive models with a (near) unit root and infinite-variance innovations. We study the asymptotic properties of estimators obtained by dummying out “large” innovations, i.e., those exceeding a given threshold. These estimators reflect the common practice of dealing with large residuals by including impulse dummies in the estimated regression. Iterative versions of the dummy-variable estimator are also discussed. We provide conditions on the preliminary parameter estimator and on the threshold that ensure that (i) the dummy-based estimator is consistent at higher rates than the ordinary least squares estimator, (ii) an asymptotically normal test statistic for the unit root hypothesis can be derived, and (iii) order of magnitude gains of local power are obtained.

scholarly journals On the Distribution of the Nearly Unstable AR(1) Process with Heavy Tails

2010 ◽  
Vol 42 (01) ◽  
pp. 106-136 ◽  
Author(s):  
Mariana Olvera-Cravioto
Keyword(s):  
Real Line ◽  
Uniform Approximation ◽  
Unit Root ◽  
Heavy Tails ◽  
Gaussian Approximation ◽  
Heavy Tail ◽  
Tail Asymptotics ◽  
Precise Description ◽  
Entire Real Line ◽  
Near Unit Root

We consider a nearly unstable, or near unit root, AR(1) process with regularly varying innovations. Two different approximations for the stationary distribution of such processes exist: a Gaussian approximation arising from the nearly unstable nature of the process and a heavy-tail approximation related to the tail asymptotics of the innovations. We combine these two approximations to obtain a new uniform approximation that is valid on the entire real line. As a corollary, we obtain a precise description of the regions where each of the Gaussian and heavy-tail approximations should be used.

Weak convergence in the near unit root setting

2013 ◽  
Vol 83 (5) ◽  
pp. 1411-1415
Author(s):  
N. Bailey ◽  
L. Giraitis
Keyword(s):  
Weak Convergence ◽  
Unit Root ◽  
Near Unit Root

Asymptotic Distributions of the Least-Squares Estimators and Test Statistics in the Near Unit Root Model with Non-Zero Initial Value and Local Drift and Trend

1994 ◽  
Vol 10 (5) ◽  
pp. 937-966 ◽  
Author(s):  
Seiji Nabeya ◽  
Bent E. Sørensen
Keyword(s):  
Characteristic Function ◽  
Asymptotic Distribution ◽  
Unit Root ◽  
Stochastic Integral ◽  
Integral Representations ◽  
Characteristic Functions ◽  
General Interest ◽  
Initial Value ◽  
Stochastic Integral Representations ◽  
Near Unit Root

This paper considers the distribution of the Dickey-Fuller test in a model with non-zero initial value and drift and trend. We show how stochastic integral representations for the limiting distribution can be derived either from the local to unity approach with local drift and trend or from the continuous record asymptotic results of Sørensen [29]. We also show how the stochastic integral representations can be utilized as the basis for finding the corresponding characteristic functions via the Fredholm approach of Nabeya and Tanaka [16,17], This “link” between those two approaches may be of general interest. We further tabulate the asymptotic distribution by inverting the characteristic function. Using the same methods, we also find the characteristic function for the asymptotic distribution for the Schmidt-Phillips [26] unit root test. Our results show very clearly the dependence of the various tests on the initial value of the time series.

Panel Unit-root Tests for Heteroskedastic Panels

2018 ◽  
Vol 18 (1) ◽  
pp. 184-196 ◽  
Author(s):  
Helmut Herwartz ◽  
Simone Maxand ◽  
Fabian H. C. Raters ◽  
Yabibal M. Walle
Keyword(s):  
Unit Root ◽  
Serial Correlation ◽  
Unit Root Tests ◽  
Order Selection ◽  
Time Varying ◽  
Development Research ◽  
Computational Statistics ◽  
Panel Unit Root Tests ◽  
Panel Unit Root ◽  
European Governance

In this article, we describe the command xtpurt, which implements the heteroskedasticity-robust panel unit-root tests suggested in Herwartz and Siedenburg (2008, Computational Statistics and Data Analysis 53: 137–150), Demetrescu and Hanck (2012a, Economics Letters 117: 10–13), and, recently, Herwartz, Maxand, and Walle (2017, Center for European, Governance and Economic Development Research Discussion Papers 314). While the former two tests are robust to time-varying volatility when the data contain only an intercept, the latter test is unique because it is asymptotically pivotal for trending heteroskedastic panels. Moreover, xtpurt incorporates lag-order selection, prewhitening, and detrending procedures to account for serial correlation and trending data.

Estimating cointegrating vectors using near unit root variables

2004 ◽  
Vol 11 (12) ◽  
pp. 781-784 ◽  
Author(s):  
Aaron D. Smallwood * ◽  
Stefan C. Norrbin
Keyword(s):  
Unit Root ◽  
Near Unit Root
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