scholarly journals UNIT ROOT TESTING IN PRACTICE: DEALING WITH UNCERTAINTY OVER THE TREND AND INITIAL CONDITION

2009 ◽  
Vol 25 (3) ◽  
pp. 587-636 ◽  
Author(s):  
David I. Harvey ◽  
Stephen J. Leybourne ◽  
A.M. Robert Taylor
Keyword(s):  
Decision Rule ◽  
Unit Root ◽  
Ordinary Least Squares ◽  
Unit Root Tests ◽  
Trend Detection ◽  
Initial Condition ◽  
Finite Sample ◽  
Testing Procedures ◽  
Unit Root Testing ◽  
Deterministic Trend

In this paper we focus on two major issues that surround testing for a unit root in practice, namely, (i) uncertainty as to whether or not a linear deterministic trend is present in the data and (ii) uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not. In each case simple testing procedures are proposed with the aim of maintaining good power properties across such uncertainties. For the first issue, if the initial condition is negligible, quasi-differenced (QD) detrended (demeaned) Dickey–Fuller-type unit root tests are near asymptotically efficient when a deterministic trend is (is not) present in the data generating process. Consequently, we compare a variety of strategies that aim to select the detrended variant when a trend is present, and the demeaned variant otherwise. Based on asymptotic and finite-sample evidence, we recommend a simple union of rejections-based decision rule whereby the unit root null hypothesis is rejected whenever either of the detrended or demeaned unit root tests yields a rejection. Our results show that this approach generally outperforms more sophisticated strategies based on auxiliary methods of trend detection. For the second issue, we again recommend a union of rejections decision rule, rejecting the unit root null if either of the QD or ordinary least squares (OLS) detrended/demeaned Dickey–Fuller-type tests rejects. This procedure is also shown to perform well in practice, simultaneously exploiting the superior power of the QD (OLS) detrended/demeaned test for small (large) initial conditions.

scholarly journals The Persistence of Suicides in G20 Countries between 1990 and 2017: an SPSM Approach to Three Generations of Unit Root Tests

2021 ◽  
Vol 24 (2) ◽  
pp. 153-173
Author(s):  
Izunna Anyikwa ◽  
Nicolene Hamman ◽  
Andrew Phiri
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
World Health ◽  
Health Concern ◽  
Economic Governance ◽  
Testing Procedures ◽  
Three Generations ◽  
Unit Root Testing ◽  
Health Organization ◽  
Global Economic Governance

Suicides represent an encompassing measure of psychological wellbeing, emotional stability as well as life satisfaction, and they have been recently identified by the World Health Organization (WHO) as a major global health concern. The G20 countries represent the powerhouse of global economic governance and hence possess the ability to influence the direction of global suicide rates. In applying the sequential panel selection method (SPSM) to three generations of unit root testing procedures, the study investigates the integration properties of suicides in G20 countries between 1990–2017. The results obtained from all three generations of tests provide rigid evidence of persistence within the suicides for most member states of the G20 countries, hence supporting the current strategic agenda pushed by the WHO in reducing suicides to a target rate of 10 percent. In addition, we further propose that such strategies should emanate from within G20 countries and spread globally thereafter.

scholarly journals Is It the Natural Rate Hypothesis or the Hysteresis Hypothesis for Unemployment Rates in Newly Industrialized Economies?

2019 ◽  
Vol 22 (4) ◽  
pp. 39-55
Author(s):  
Dieu Nsenga ◽  
Mirada Nach ◽  
Hlalefang Khobai ◽  
Clement Moyo ◽  
Andrew Phiri
Keyword(s):  
Unit Root ◽  
Structural Breaks ◽  
The Philippines ◽  
Unit Root Tests ◽  
Natural Rate ◽  
Unemployment Rates ◽  
Quarterly Data ◽  
Testing Procedures ◽  
Unit Root Testing ◽  
Conventional Unit

The focus of our study is on determining whether unemployment rates in 8 New Industrialized Economies conform to the natural rate hypothesis or the hysteresis hypothesis. To this end, we employ a variety of unit of unit root testing procedures to quarterly data collected between 2002:q1 and 2017:q1. Summarizing of our findings, conventional unit root tests which account neither for asymmetries nor structural breaks produce the most inconclusive results. On the other hand, tests which incorporate structural breaks while ignoring asymmetries tends to favour the natural rate hypothesis for our panel of countries. However, simultaneously accounting for asymmetries and unobserved structural breaks seemingly produces the most robust findings and confirms hysteresis in all unemployment rates except for Asian economies/countries of Thailand and the Philippines.

scholarly journals The Impact of the Initial Condition on Covariate Augmented Unit Root Tests

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Chrystalleni Aristidou ◽  
David I. Harvey ◽  
Stephen J. Leybourne
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
Initial Condition ◽  
Unit Root Testing ◽  
The Impact ◽  
Univariate Approach

AbstractWe examine the behaviour of OLS-demeaned/detrended and GLS-demeaned/detrended unit root tests that employ stationary covariates, as proposed by Hansen (1995, “Rethinking the Univariate Approach to Unit Root Testing.”

ASYMPTOTICALLY UMP PANEL UNIT ROOT TESTS—THE EFFECT OF HETEROGENEITY IN THE ALTERNATIVES

2014 ◽  
Vol 31 (3) ◽  
pp. 539-559 ◽  
Author(s):  
I. Gaia Becheri ◽  
Feike C. Drost ◽  
Ramon van den Akker
Keyword(s):  
Unit Root ◽  
Generalized Least Squares ◽  
Applied Economics ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Asymptotic Power ◽  
Optimal Tests ◽  
Independent Panel ◽  
Local Asymptotic Power ◽  
Uniformly Most Powerful

In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007, Journal of Econometrics 141, 416–459) present an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon et al. (2007, Journal of Econometrics 141, 416–459), a pooled generalized least squares (GLS) based test using the Breitung and Meyer (1994, Applied Economics 25, 353–361) device, and a new test based on the asymptotic structure of the model are all asymptotically UMP (Uniformly Most Powerful). Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.

Near Observational Equivalence and Theoretical size Problems with Unit Root Tests

1996 ◽  
Vol 12 (4) ◽  
pp. 724-731 ◽  
Author(s):  
Jon Faust
Keyword(s):  
Unit Root ◽  
Sufficient Conditions ◽  
Unit Root Test ◽  
Asymptotic Distributions ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Test Procedures ◽  
Asymptotic Size ◽  
Finite Sample Size ◽  
Topological Sense

Said and Dickey (1984,Biometrika71, 599–608) and Phillips and Perron (1988,Biometrika75, 335–346) have derived unit root tests that have asymptotic distributions free of nuisance parameters under very general maintained models. Under models as general as those assumed by these authors, the size of the unit root test procedures will converge to one, not the size under the asymptotic distribution. Solving this problem requires restricting attention to a model that is small, in a topological sense, relative to the original. Sufficient conditions for solving the asymptotic size problem yield some suggestions for improving finite-sample size performance of standard tests.

LIKELIHOOD-BASED INFERENCE IN TRENDING TIME SERIES WITH A ROOT NEAR UNITY

2001 ◽  
Vol 17 (6) ◽  
pp. 1082-1112 ◽  
Author(s):  
Zhijie Xiao
Keyword(s):  
Time Series ◽  
Joint Estimation ◽  
Unit Root Tests ◽  
Time Series Models ◽  
Least Squares Regression ◽  
Finite Sample ◽  
Testing Procedures ◽  
Monte Carlo Experiments ◽  
Autoregressive Parameter ◽  
Nonlinear Equation Systems

This paper studies likelihood-based estimation and tests for autoregressive time series models with deterministic trends and general disturbance distributions. In particular, a joint estimation of the trend coefficients and the autoregressive parameter is considered. Asymptotic analysis on the M-estimators is provided. It is shown that the limiting distributions of these estimators involve nonlinear equation systems of Brownian motions even for the simple case of least squares regression. Unit root tests based on M-estimation are also considered, and extensions of the Neyman–Pearson test are studied. The finite sample performance of these estimators and testing procedures is examined by Monte Carlo experiments.

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