Unit Root Tests Based on M Estimators

1995 ◽  
Vol 11 (2) ◽  
pp. 331-346 ◽  
Author(s):  
André Lucas
Keyword(s):  
Linear Combination ◽  
Unit Root ◽  
Asymptotic Theory ◽  
Simulation Experiment ◽  
Unit Root Test ◽  
Ordinary Least Squares ◽  
Asymptotic Distributions ◽  
Unit Root Tests ◽  
Nuisance Parameters ◽  
M Estimator

This paper considers unit root tests based on M estimators. The asymptotic theory for these tests is developed. It is shown how the asymptotic distributions of the tests depend on nuisance parameters and how tests can be constructed that are invariant to these parameters. It is also shown that a particular linear combination of a unit root test based on the ordinary least-squares (OLS) estimator and on an M estimator converges to a normal random variate. The interpretation of this result is discussed. A simulation experiment is described, illustrating the level and power of different unit root tests for several sample sizes and data generating processes. The tests based on M estimators turn out to be more powerful than the OLS-based tests if the innovations are fat-tailed.

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.

ASYMPTOTIC DISTRIBUTIONS FOR UNIT ROOT TEST STATISTICS IN NEARLY INTEGRATED SEASONAL AUTOREGRESSIVE MODELS

2000 ◽  
Vol 16 (2) ◽  
pp. 200-230 ◽  
Author(s):  
Seiji Nabeya
Keyword(s):  
Least Squares ◽  
Unit Root ◽  
Linear Trend ◽  
Unit Root Test ◽  
Ordinary Least Squares ◽  
Asymptotic Distributions ◽  
Autoregressive Models ◽  
Test Statistics ◽  
Autoregressive Parameter ◽  
Ordinary Least Squares Estimator

Seasonal autoregressive models with an intercept or linear trend are discussed. The main focus of this paper is on the models in which the intercept or trend parameters do not depend on the season. One of the most important results from this study is the asymptotic distribution for the ordinary least squares estimator of the autoregressive parameter obtained under nearly integrated condition, and another is the approximation to the limiting distribution of the t-statistic under the null for testing the unit root hypothesis.

scholarly journals Asymptotic Distribution of Unit Root Tests Base on ESTAR Model with Flexible Fourier Form

2021 ◽  
pp. 41-51
Author(s):  
Murtala Adam Muhammad ◽  
Junjuan Hu
Keyword(s):  
Brownian Motion ◽  
Asymptotic Distribution ◽  
Unit Root ◽  
Asymptotic Distributions ◽  
Unit Root Tests ◽  
Nuisance Parameters ◽  
Not Given

In this paper, the asymptotic distribution of Fourier ESTAR model (FKSS) proposed by [1], which was not given in the original paper are derived. Result shows that the asymptotic distributions are functions of brownian motion, only depends on K and free from nuisance parameters.

A revisit of the unemployment rate, interest rate, GDP growth and Inflation of Pakistan: Whether Structural break or unit root?

2021 ◽  
Vol 3 (2) ◽  
pp. 80-92
Author(s):  
Sara Muhammadullah ◽  
Amena Urooj ◽  
Faridoon Khan
Keyword(s):  
Interest Rate ◽  
Unemployment Rate ◽  
Unit Root ◽  
Structural Breaks ◽  
Inflation Rate ◽  
Structural Break ◽  
Unit Root Test ◽  
Unit Root Tests ◽  
Gdp Growth ◽  
Macroeconomic Indicators

The study investigates the query of structural break or unit root considering four macroeconomic indicators; unemployment rate, interest rate, GDP growth, and inflation rate of Pakistan. The previous studies create ambiguity regarding the stationarity and non-stationarity of these variables. We employ Zivot & Andrews (1992) unit root test and Step Indicator Saturation (SIS) method for multiple break detection in mean. GDP growth and inflation rate are stationary at level whereas unit root tests fail to reject the null hypothesis of the unemployment rate and interest rate at level. However, Zivot and Andrew unit root test with a single endogenous break indicates that the unemployment rate and interest rate are stationary at level with a single endogenous break. On the other hand, the SIS method reveals that the series are stationary with multiple structural breaks. It is inferred that it is inappropriate to take the first difference of the unemployment rate and interest rate to attain stationarity. The results of this study confirmed that there exist multiple breaks in the macroeconomic variables considered in the context of Pakistan.

M-estimator based unit root tests in the ESTAR framework

2014 ◽  
Vol 56 (4) ◽  
pp. 1115-1135 ◽  
Author(s):  
Rickard Sandberg
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
M Estimator

scholarly journals Synergy between an Improved Covariate Unit Root Test and Cross-sectionally Dependent Panel Data Unit Root Tests

2014 ◽  
Vol 83 (6) ◽  
pp. 676-700 ◽  
Author(s):  
Kaddour Hadri ◽  
Eiji Kurozumi ◽  
Daisuke Yamazaki
Keyword(s):  
Panel Data ◽  
Unit Root ◽  
Unit Root Test ◽  
Unit Root Tests

Testing the Unemployment Hysteresis for G-20 Countries

2018 ◽  
pp. 375-382 ◽  
Author(s):  
Veli Yilanci ◽  
Mahmut Unsal Sasmaz
Keyword(s):  
South Africa ◽  
United Kingdom ◽  
Unit Root ◽  
Unit Root Test ◽  
Unit Root Tests ◽  
Unemployment Rates

In this chapter, the authors analyze the validity of unemployment hysteresis for G-20 countries, namely Australia, Brazil, Canada, France, Germany, Indonesia, Italy, Japan, Korea, Mexico, Russia, South Africa, Turkey, United Kingdom, and USA for the 1960–2014 period. For this purpose, they examine the stationarity of the unemployment rates by using ADF unit root test and Fourier ADF (FADF) unit root tests. FADF unit root test is a recently introduced test whose power is not affected by the number, location, and form of the breaks. The results of the tests show that the unemployment hysteresis is valid for some of the countries.

scholarly journals ON AUGMENTED HEGY TESTS FOR SEASONAL UNIT ROOTS

2012 ◽  
Vol 28 (5) ◽  
pp. 1121-1143 ◽  
Author(s):  
Tomás del Barrio Castro ◽  
Denise R. Osborn ◽  
A.M. Robert Taylor
Keyword(s):  
Unit Root ◽  
Unit Roots ◽  
Linear Process ◽  
Unit Root Tests ◽  
Nuisance Parameters ◽  
Martingale Difference ◽  
Linear Processes ◽  
Seasonal Unit Roots ◽  
Null Distributions ◽  
Augmented Dickey Fuller

In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, whereas those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T1/2) rate is shown to be sufficient.

scholarly journals A Different Look at Cointegration Relationship between Quarterly Inflation Rates and Growth via Seasonal Integration Tests

2019 ◽  
Author(s):  
Sera Şanlı ◽  
Mehmet Özmen
Keyword(s):  
Economic Growth ◽  
Unit Root ◽  
Unit Root Test ◽  
Unit Root Tests ◽  
Maximum Order ◽  
Unit Root Testing ◽  
Testing Sequence ◽  
Inflation Rates ◽  
Cointegration Relationship ◽  
Integration Analysis

Detecting the direction of inflation-growth relationship has been a controversial issue in terms of the theoretical framework, notedly since the rise of Mundell-Tobin effect which is based upon the assumption of substitutability between money and capital. In this study, it has been aimed to investigate the cointegrating relationship and its direction between inflation and economic growth covering the period 1998Q1:2014Q4 for Turkey as grounded on the testing sequence that is illustrated by Ilmakunnas (1990) in order to handle unit root testing in a seasonal context by testing the appropriate order of differencing and concerns with the case where SI(2,1) (seasonally integrated of order (2,1)) is the maximum order of seasonal integration. It has been also utilized from ADF unit root test and DHF, HEGY & OCSB seasonal unit root tests in seasonal integration analysis. In the study, five cointegration regressions have been considered in the level, seasonally averaged, quarterly differenced, first differenced and twice differenced forms and two series have been found to have the same degree of seasonal integration as SI(1,1). Applying various residual tests have revealed the presence of a cointegrating relationship between two variables. In addition, the inflation-growth relationship in Turkey has been concluded to perform in an opposite direction.

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