A note on the limit theory of a Dickey–Fuller unit root test with heavy tailed innovations

2017 ◽  
Vol 126 ◽  
pp. 198-204 ◽  
Author(s):  
Stelios Arvanitis
Keyword(s):  
Unit Root ◽  
Unit Root Test ◽  
Limit Theory ◽  
Heavy Tailed

PANEL UNIT ROOT TESTS WITH CROSS-SECTION DEPENDENCE: A FURTHER INVESTIGATION

2009 ◽  
Vol 26 (4) ◽  
pp. 1088-1114 ◽  
Author(s):  
Jushan Bai ◽  
Serena Ng
Keyword(s):  
Cross Section ◽  
Unit Root ◽  
Linear Trend ◽  
Unit Root Test ◽  
Panel Unit Root ◽  
Limit Theory ◽  
Sample Moment ◽  
The Common ◽  
Using Data ◽  
Joint Limit

An effective way to control for cross-section correlation when conducting a panel unit root test is to remove the common factors from the data. However, there remain many ways to use the defactored residuals to construct a test. In this paper, we use the panel analysis of nonstationarity in idiosyncratic and common components (PANIC) residuals to form two new tests. One estimates the pooled autoregressive coefficient, and one simply uses a sample moment. We establish their large-sample properties using a joint limit theory. We find that when the pooled autoregressive root is estimated using data detrended by least squares, the tests have no power. This result holds regardless of how the data are defactored. All PANIC-based pooled tests have nontrivial power because of the way the linear trend is removed.

scholarly journals Limit Theory for Stationary Autoregression with Heavy-Tailed Augmented GARCH Innovations

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 816
Author(s):  
Eunju Hwang
Keyword(s):  
Unit Root ◽  
Stable Distribution ◽  
Asymptotic Properties ◽  
Tail Index ◽  
Asymptotic Distributions ◽  
Uniform Limit ◽  
Limit Theory ◽  
Heavy Tailed ◽  
Heteroscedastic Variance ◽  
Ar Models

This paper considers stationary autoregressive (AR) models with heavy-tailed, general GARCH (G-GARCH) or augmented GARCH noises. Limit theory for the least squares estimator (LSE) of autoregression coefficient ρ=ρn is derived uniformly over stationary values in [0,1), focusing on ρn→1 as sample size n tends to infinity. For tail index α∈(0,4) of G-GARCH innovations, asymptotic distributions of the LSEs are established, which are involved with the stable distribution. The convergence rate of the LSE depends on 1−ρn2, but no condition on the rate of ρn is required. It is shown that, for the tail index α∈(0,2), the LSE is inconsistent, for α=2, logn/(1−ρn2)-consistent, and for α∈(2,4), n1−2/α/(1−ρn2)-consistent. Proofs are based on the point process and the asymptotic properties in AR models with G-GARCH errors. However, this present work provides a bridge between pure stationary and unit-root processes. This paper extends the existing uniform limit theory with three issues: the errors have conditional heteroscedastic variance; the errors are heavy-tailed with tail index α∈(0,4); and no restriction on the rate of ρn is necessary.

Convergence in per capita carbon footprint and ecological footprint for G7 countries: Evidence from panel Fourier threshold unit root test

2021 ◽  
pp. 0958305X2110114
Author(s):  
Veli Yilanci ◽  
Muhammed Sehid Gorus ◽  
Sakiru Adebola Solarin
Keyword(s):  
Unit Root ◽  
Structural Breaks ◽  
Structural Changes ◽  
Unit Root Test ◽  
G7 Countries ◽  
Convergence Hypothesis ◽  
International Climate ◽  
Per Capita ◽  
Nonlinear Behaviors ◽  
Nonlinear Unit Root Tests

This paper aims to explore the convergence of per capita carbon and ecological footprints in G7 countries during 1961–2016. For this purpose, we propose a new unit root test in the panel setting–the panel Fourier threshold unit root test. This test takes into consideration both multiple smooth structural changes and nonlinearity. According to the literature, the power of the nonlinear unit root tests is reduced in the case of ignoring structural breaks. Therefore, we expect to get more reliable empirical findings by utilizing this methodology. The empirical results of this paper show that these series have nonlinear behaviors for the period 1961–2016. Furthermore, they demonstrate that the absolute convergence hypothesis is valid in G7 countries for both regimes. Thus, governments can conduct common environmental policies, including international climate summits and agreements, instead of national-based policies to mitigate environmental deterioration in their countries.

A New Unit Root Test for Unemployment Hysteresis Based on the Autoregressive Neural Network*

2021 ◽  
Author(s):  
OlaOluwa S. Yaya ◽  
Ahamuefula E. Ogbonna ◽  
Fumitaka Furuoka ◽  
Luis A. Gil‐Alana
Keyword(s):  
Neural Network ◽  
Unit Root ◽  
Unit Root Test ◽  
Autoregressive Neural Network

scholarly journals Dynamic Relationship Between Real Export, Real Import, Real Exchange Rate, Labor Force and Real Gross Domestic Product in Malaysia

2019 ◽  
Vol 10 (5) ◽  
pp. 20
Author(s):  
Emilda Hashim ◽  
Norimah Rambeli ◽  
Asmawi Hashim ◽  
Norasibah Abdul Jalil ◽  
Shahrun Nizam Abdul Aziz ◽  
...  
Keyword(s):  
Exchange Rate ◽  
Labor Force ◽  
Open Economy ◽  
Unit Root ◽  
Correction Term ◽  
Unit Root Test ◽  
Real Effective Exchange Rate ◽  
Global Changes ◽  
Real Gdp ◽  
Long Run

This study examined short run and long run relationship between endogenous and exogenous variables. Specifically, it studied the relationship between real export, real import, labor force participation and real effective exchange rate (REER) and real GDP in Malaysia from 1988 to 2017. These variables were tested in various tests, namely, unit root test, granger causality test, vector autoregressive (VAR), Johansen Juselius test and Error Correction Term (ECT). The result revealed that all variables were non-stationary at the level form and stationary at first difference in ADF unit root test. The findings also exhibited the existence of bilateral relationships between real export and real GDP, real import and real GDP, as well as labor and real GDP. Nonetheless, there were no relationship found between REER and real GDP. On the other hand, in VAR, the lag optimum was lag 10 because it indicated the smallest value of AIC. Moreover, for Johansen Juselius cointegration test, it showed two cointegrated vector at both, 5% and 1%, level in trace test. In addition, Max-Eigen value test indicated two cointegrated vector at 0.05 and one cointegrated vector at 0.01. As for the Wald test, there were long run cointegration relationship between real GDP and its determinants, namely real export, real import, labor and REER. Apparently, Malaysia, as a small open economy, has relied heavily on foreign trade. Consequently, our domestic economic performance is susceptible to the changes in international markets and exchange rate. Therefore, suitable international policy implementation is vital to ensure Malaysian economy will be able to adjust to current global changes.

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