scholarly journals THE IMPACT OF PERSISTENT CYCLES ON ZERO FREQUENCY UNIT ROOT TESTS

2013 ◽  
Vol 29 (6) ◽  
pp. 1289-1313 ◽  
Author(s):  
Tomás del Barrio Castro ◽  
Paulo M.M. Rodrigues ◽  
A.M. Robert Taylor
Keyword(s):  
Unit Root ◽  
Unit Root Test ◽  
American Statistical Association ◽  
Unit Root Tests ◽  
Statistical Association ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Augmented Dickey Fuller ◽  
Frequency Unit ◽  
The Impact

In this paper we investigate the impact of persistent (nonstationary or near nonstationary) cycles on the asymptotic and finite-sample properties of standard unit root tests. Results are presented for the augmented Dickey–Fuller (ADF) normalized bias and t-ratio-based tests (Dickey and Fuller, 1979, Journal of the American Statistical Association 745, 427–431; Said and Dickey, 1984; Biometrika 71, 599–607). the variance ratio unit root test of Breitung (2002, Journal of Econometrics 108, 343–363), and the M class of unit-root tests introduced by Stock (1999, in Engle and White (eds.), A Festschrift in Honour of Clive W.J. Granger) and Perron and Ng (1996, Review of Economic Studies 63, 435–463). We show that although the ADF statistics remain asymptotically pivotal (provided the test regression is properly augmented) in the presence of persistent cycles, this is not the case for the other statistics considered and show numerically that the size properties of the tests based on these statistics are too unreliable to be used in practice. We also show that the t-ratios associated with lags of the dependent variable of order greater than two in the ADF regression are asymptotically normally distributed. This is an important result as it implies that extant sequential methods (see Hall, 1994, Journal of Business & Economic Statistics 17, 461–470; Ng and Perron, 1995, Journal of the American Statistical Association 90, 268–281) used to determine the order of augmentation in the ADF regression remain valid in the presence of persistent cycles.

Unit-root tests for explosive behavior

2021 ◽  
Vol 21 (4) ◽  
pp. 999-1020
Author(s):  
Christopher F. Baum ◽  
Jesús Otero
Keyword(s):  
International Economic ◽  
Unit Root ◽  
American Statistical Association ◽  
Unit Root Tests ◽  
Statistical Association ◽  
International Economic Review ◽  
Augmented Dickey Fuller ◽  
Using Data ◽  
The Right ◽  
Rolling Windows

We present a new command, radf, that tests for explosive behavior in time series. The command computes the right-tail augmented Dickey and Fuller (1979, Journal of the American Statistical Association 74: 427–431) unitroot test and its further developments based on supremum statistics derived from augmented Dickey–Fuller-type regressions estimated using recursive windows (Phillips, Wu, and Yu, 2011, International Economic Review 52: 201–226) and recursive flexible windows (Phillips, Shi, and Yu, 2015, International Economic Review 56: 1043–1078). It allows for the lag length in the test regression and the width of rolling windows to be either specified by the user or determined using data-dependent procedures, and it performs the date-stamping procedures advocated by Phillips, Wu, and Yu (2011) and Phillips, Shi, and Yu (2015) to identify episodes of explosive behavior. It also implements the wild bootstrap proposed by Phillips and Shi (2020, Handbook of Statistics: Financial, Macro and Micro Econometrics Using R, Vol. 42, 61–80) to lessen the potential effects of unconditional heteroskedasticity and account for the multiplicity issue in recursive testing. The use of radf is illustrated with an empirical example.

scholarly journals Simulation Analysis of Threshold Autoregressive Unit Root Tests

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Steve Cook
Keyword(s):  
Unit Root ◽  
Simulation Analysis ◽  
Unit Root Tests ◽  
Robust Methods ◽  
Finite Sample ◽  
Threshold Estimation ◽  
Matrix Estimation ◽  
Threshold Autoregressive ◽  
Finite Sample Properties ◽  
The Impact

Using numerical simulation, the finite-sample properties of threshold autoregressive (TAR) and momentum-threshold (MTAR) autoregressive-based unit root tests under both deterministic and consistent methods of threshold estimation are examined in the presence of generalised autoregressive conditional heteroskedasticity (GARCH). Previous research is extended by considering both the impact of alternative robust methods of covariance matrix estimation and the behaviour of the secondary tests of asymmetry associated with the TAR and MTAR models. The results obtained reveal many interesting features, in particular the distortionary effects of consistent-threshold estimation. In summary, the findings presented indicate that caution should be exercised when interpreting the results of these frequently employed threshold-based testing methods.

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.

scholarly journals Impact of Public Capital Expenditure on Inflation Rate in Nigeria

2021 ◽  
Vol 2 (4) ◽  
pp. 30-39
Author(s):  
Jideofor Nnennaya Joy ◽  
Michah Chukwuemeka Okafor ◽  
Eke Onyekachi Abaa
Keyword(s):  
Unit Root ◽  
Inflation Rate ◽  
Capital Expenditure ◽  
Unit Root Test ◽  
Public Capital ◽  
Distributed Lag ◽  
Autoregressive Distributed Lag ◽  
Mixed Order ◽  
Augmented Dickey Fuller ◽  
The Impact

This paper examines the impact of public capital expenditure on inflation rate in Nigeria. The data for the study were sourced from various issues of the Central Bank of Nigeria’s statistical bulletin. The data was subjected to unit root test using Augmented Dickey fuller (ADF) approach to ascertain the time series properties. Descriptive statistics was used to assess the socioeconomic characteristics of the variables. Due to the mixed order of integration witnessed in the unit root, ARDL- Autoregressive Distributed Lag approach was used for cointegration and regression analysis. The result found that Public capital expenditure is negatively and statistically significant (tcal = -2.903) in influencing Inflation Rate in Nigeria. This outcome is highly directional in the sense that prudent and productive spending will always subdue inflation in any economy; therefore, this study recommend that government should increase its investment in production sectors and encourage skilful and willing citizens to participate, since this would reduce the expenses being incurred on business as a result low currency value and raise the profitability of firms.

A family of nonparametric unit root tests for processes driven by infinite variance innovations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kemal Caglar Gogebakan
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
Tuning Parameter ◽  
Infinite Variance ◽  
Finite Sample ◽  
Power Performance ◽  
Finite Sample Size ◽  
Heavy Tailed ◽  
The Impact ◽  
Adf Test

Abstract This paper presents extensions to the family of nonparametric fractional variance ratio (FVR) unit root tests of Nielsen (2009. “A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic.” Econometric Theory 25: 1515–44) under heavy tailed (infinite variance) innovations. In this regard, we first develop the asymptotic theory for these FVR tests under this setup. We show that the limiting distributions of the tests are free of serial correlation nuisance parameters, but depend on the tail index of the infinite variance process. Then, we compare the finite sample size and power performance of our FVR unit root tests with the well-known parametric ADF test under the impact of the heavy tailed shocks. Simulations demonstrate that under heavy tailed innovations, the nonparametric FVR tests have desirable size and power properties.

scholarly journals RIPPLE EFFECT AND REGIONAL HOUSE PRICES DYNAMICS IN CHINA

2016 ◽  
Vol 20 (4) ◽  
pp. 397-408 ◽  
Author(s):  
Chi-Chuan LEE ◽  
Chien-Chiang LEE ◽  
Shu-Hen CHIANG
Keyword(s):  
Unit Root ◽  
House Prices ◽  
Unit Root Test ◽  
Unit Root Tests ◽  
Ripple Effect ◽  
Seemingly Unrelated Regressions ◽  
Long Run ◽  
Equilibrium Relationship ◽  
Augmented Dickey Fuller ◽  
Long Run Equilibrium

This paper examines the stationarity properties, the long-run equilibrium and the leadlag relationship among the regional house prices in China from December 2000 to July 2013. Unlike traditional unit-root tests, the panel seemingly unrelated regressions augmented Dickey-Fuller (SURADF) unit-root test reveals that the regional house prices in China are a mixture of I(0) and I(1) processes. There is concrete evidence in favor of the hypothesis of a long-run equilibrium relationship among all regions, except for Shanghai region, and supporting the price diffusion or ripple effect among these Chinese cities. Finally, we determine that these regional house prices exhibit uni-directional causalities running from Beijing, Chongqing, and Shenzhen to Guangzhou and Tianjin, respectively.

scholarly journals UNIT ROOT TEST IN A THRESHOLD AUTOREGRESSION: ASYMPTOTIC THEORY AND RESIDUAL-BASED BLOCK BOOTSTRAP

2008 ◽  
Vol 24 (6) ◽  
pp. 1699-1716 ◽  
Author(s):  
Myung Hwan Seo
Keyword(s):  
Unit Root ◽  
Null Hypothesis ◽  
Unit Root Test ◽  
Block Bootstrap ◽  
Finite Sample ◽  
Threshold Autoregression ◽  
Augmented Dickey Fuller ◽  
Simplifying Assumptions ◽  
Adf Test ◽  
Threshold Process

This paper develops a test of the unit root null hypothesis against a stationary threshold process. This testing problem is nonstandard and complicated because a parameter is unidentified and the process is nonstationary under the null hypothesis. We derive an asymptotic distribution for the test, which is not pivotal without simplifying assumptions. A residual-based block bootstrap is proposed to calculate the asymptoticp-values. The asymptotic validity of the bootstrap is established, and a set of Monte Carlo simulations demonstrates its finite-sample performance. In particular, the test exhibits considerable power gains over the augmented Dickey–Fuller (ADF) test, which neglects threshold effects.

scholarly journals Characterizing growth instability: new evidence on unit roots and structural breaks in countries’ long run trajectories

2021 ◽  
Author(s):  
Emanuele Russo ◽  
Neil Foster-McGregor
Keyword(s):  
Unit Root ◽  
Structural Breaks ◽  
Structural Changes ◽  
Alternative Hypothesis ◽  
Unit Root Test ◽  
Unit Roots ◽  
Finite Sample ◽  
Aggregate Shocks ◽  
Long Run ◽  
Finite Sample Properties

AbstractIn this paper we investigate whether long run time series of income per capita are better described by a trend-stationary model with few structural changes or by unit root processes in which permanent stochastic shocks are responsible for the observed growth discontinuities. For a group of advanced and developing countries in the Maddison database, we employ a unit root test that allows for an unspecified number of breaks under the alternative hypothesis (up to some ex ante determined maximum). Monte Carlo simulations studying the finite sample properties of the test are reported and discussed. When compared with previous findings in the literature, our results show less evidence against the unit root hypothesis. We find even fewer rejections when relaxing the assumption of Gaussian shocks. Our results are broadly consistent with the implications of evolutionary macro models which posit frequent growth shifts and fat-tailed distribution of aggregate shocks.

scholarly journals THE IMPACT OF EXPORTS ON ECONOMIC GROWTH OF PAKISTAN AND INDIA

2019 ◽  
Vol 2 (02) ◽  
pp. 77-89
Author(s):  
Rasheed Khan
Keyword(s):  
Economic Growth ◽  
Human Capital ◽  
Unit Root ◽  
Unit Root Test ◽  
Direct Foreign Investment ◽  
Ordinary Least Squares ◽  
Policy Makers ◽  
Augmented Dickey Fuller ◽  
The Impact ◽  
Adf Test

The aim of this study is to investigate the impact of exports on economic growth of Pakistan and India for the period of 1990 to 2016. The unit root test namely Augmented Dickey Fuller (ADF) test was used to identify stationarity in the data. The method of Fully Modified Ordinary Least Squares (FMOLS) was employed to estimate the coefficient of the variables. The FMOLS results exhibit that exports is having positive and significant impact on economic growth in both countries. Moreover, the empirical results reveal that Foreign Direct Investment (FDI) inflow and human capital have also positive and significant effect on the economic growth. The findings of this study suggest that policy makers need to make effective policies in order to increase the volume of exports as well as attract direct foreign investment and encourage human capital in order to stimulate economic growth.

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