scholarly journals Adaptive Wild Bootstrap Tests for a Unit Root With Non‐Stationary Volatility

2018 ◽  
Vol 21 (2) ◽  
pp. 87-113 ◽  
Author(s):  
H. Peter Boswijk ◽  
Yang Zu
Keyword(s):  
Unit Root ◽  
Wild Bootstrap ◽  
Bootstrap Tests

Wild Bootstrap Tests

2007 ◽  
Vol 24 (4) ◽  
pp. 31-37 ◽  
Author(s):  
Jurgen Franke ◽  
Siana Halim
Keyword(s):  
Wild Bootstrap ◽  
Bootstrap Tests

HETEROSKEDASTIC TIME SERIES WITH A UNIT ROOT

2009 ◽  
Vol 25 (5) ◽  
pp. 1228-1276 ◽  
Author(s):  
Giuseppe Cavaliere ◽  
A.M. Robert Taylor
Keyword(s):  
Unit Root ◽  
Innovation Process ◽  
Partial Solution ◽  
Weak Dependence ◽  
Martingale Differences ◽  
Inference Problem ◽  
Finite Samples ◽  
Bootstrap Tests ◽  
Spot Volatility ◽  
Innovation Processes

In this paper we provide a unified theory, and associated invariance principle, for the large-sample distributions of the Dickey–Fuller class of statistics when applied to unit root processes driven by innovations displaying nonstationary stochastic volatility of a very general form. These distributions are shown to depend on both the spot volatility and the integrated variation associated with the innovation process. We propose a partial solution (requiring any leverage effects to be asymptotically negligible) to the identified inference problem using a wild bootstrap–based approach. Results are initially presented in the context of martingale differences and are later generalized to allow for weak dependence. Monte Carlo evidence is also provided that suggests that our proposed bootstrap tests perform very well in finite samples in the presence of a range of innovation processes displaying nonstationary volatility and/or weak dependence.

scholarly journals TESTING FOR UNIT ROOTS IN THE PRESENCE OF A POSSIBLE BREAK IN TREND AND NONSTATIONARY VOLATILITY

2011 ◽  
Vol 27 (5) ◽  
pp. 957-991 ◽  
Author(s):  
Giuseppe Cavaliere ◽  
David I. Harvey ◽  
Stephen J. Leybourne ◽  
A.M. Robert Taylor
Keyword(s):  
Unit Root ◽  
Unit Roots ◽  
Parametric Model ◽  
Unit Root Tests ◽  
Wild Bootstrap ◽  
Inference Problem ◽  
Large Sample ◽  
Null Distributions ◽  
The Impact

We analyze the impact of nonstationary volatility on the break fraction estimator and associated trend break unit root tests of Harris, Harvey, Leybourne, and Taylor (2009) (HHLT). We show that although HHLT’s break fraction estimator retains the same large-sample properties as demonstrated by HHLT for homoskedastic shocks, the limiting null distributions of unit root statistics based around this estimator are not pivotal under nonstationary volatility. A solution to the identified inference problem, which does not require the practitioner to specify a parametric model for volatility, is provided using the wild bootstrap and is shown to perform well in practice.

Determination of the Number of Common Stochastic Trends under Conditional Heteroskedasticity

2021 ◽  
Vol 28 (3) ◽  
pp. 519-552
Author(s):  
Giuseppe Cavaliere ◽  
Anders Rahbek ◽  
A. M. Robert Taylor
Keyword(s):  
Small Samples ◽  
Wild Bootstrap ◽  
Financial Variables ◽  
Finite Samples ◽  
Stochastic Trends ◽  
Sequential Procedures ◽  
Bootstrap Tests ◽  
The Business Cycle ◽  
Better Than

Permanent-transitory decompositions and the analysis of the time series properties of economic variables at the business cycle frequencies strongly rely on the correct detection of the number of common stochastic trends (co-integration). Standard techniques for the determination of the number of common trends, such as the well-known sequential procedure proposed in Johansen (1996), are based on the assumption that shocks are homoskedastic. This contrasts with empirical evidence which documents that many of the key macro-economic and financial variables are driven by heteroskedastic shocks. In a recent paper, Cavaliere et al., (2010, Econometric Theory) demonstrate that Johansen's (LR) trace statistic for co-integration rank and both its i.i.d. and wild bootstrap analogues are asymptotically valid in non-stationary systems driven by heteroskedastic (martingale difference) innovations, but that the wild bootstrap performs substantially better than the other two tests in finite samples. In this paper we analyse the behaviour of sequential procedures to determine the number of common stochastic trends present based on these tests. Numerical evidence suggests that the procedure based on the wild bootstrap tests performs best in small samples under a variety of heteroskedastic innovation processes.

scholarly journals SIGN-BASED UNIT ROOT TESTS FOR EXPLOSIVE FINANCIAL BUBBLES IN THE PRESENCE OF DETERMINISTICALLY TIME-VARYING VOLATILITY

2019 ◽  
Vol 36 (1) ◽  
pp. 122-169 ◽  
Author(s):  
David I. Harvey ◽  
Stephen J. Leybourne ◽  
Yang Zu
Keyword(s):  
International Economic ◽  
Unit Root ◽  
Financial Data ◽  
Unit Root Tests ◽  
Time Varying ◽  
Wild Bootstrap ◽  
Financial Bubbles ◽  
International Economic Review ◽  
Higher Power ◽  
Empirical Illustration

This article considers the problem of testing for an explosive bubble in financial data in the presence of time-varying volatility. We propose a sign-based variant of the Phillips, Shi, and Yu (2015, International Economic Review 56, 1043–1077) test. Unlike the original test, the sign-based test does not require bootstrap-type methods to control size in the presence of time-varying volatility. Under a locally explosive alternative, the sign-based test delivers higher power than the original test for many time-varying volatility and bubble specifications. However, since the original test can still outperform the sign-based one for some specifications, we also propose a union of rejections procedure that combines the original and sign-based tests, employing a wild bootstrap to control size. This is shown to capture most of the power available from the better performing of the two tests. We also show how a sign-based statistic can be used to date the bubble start and end points. An empirical illustration using Bitcoin price data is provided.

Unit root bootstrap tests under infinite variance

2011 ◽  
Vol 33 (1) ◽  
pp. 32-47 ◽  
Author(s):  
Marta Moreno ◽  
Juan Romo
Keyword(s):  
Unit Root ◽  
Infinite Variance ◽  
Bootstrap Tests

Unit root bootstrap tests for AR (1) models

Biometrika ◽  
1996 ◽  
Vol 83 (4) ◽  
pp. 849-860 ◽  
Author(s):  
N Ferretti
Keyword(s):  
Unit Root ◽  
Bootstrap Tests
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