scholarly journals A POWERFUL TEST OF THE AUTOREGRESSIVE UNIT ROOT HYPOTHESIS BASED ON A TUNING PARAMETER FREE STATISTIC

2009 ◽  
Vol 25 (6) ◽  
pp. 1515-1544 ◽  
Author(s):  
Morten Ørregaard Nielsen
Keyword(s):  
Asymptotic Distribution ◽  
Unit Root ◽  
Linear Time ◽  
Nonparametric Test ◽  
Tuning Parameter ◽  
Ratio Test ◽  
Local Power ◽  
Finite Sample ◽  
Power Of The Test ◽  
The Family

This paper presents a family of simple nonparametric unit root tests indexed by one parameter,d, and containing the Breitung (2002,Journal of Econometrics108, 342–363) test as the special cased= 1. It is shown that (a) each member of the family withd> 0 is consistent, (b) the asymptotic distribution depends ondand thus reflects the parameter chosen to implement the test, and (c) because the asymptotic distribution depends ondand the test remains consistent for alld> 0, it is possible to analyze the power of the test for different values ofd. The usual Phillips–Perron and Dickey–Fuller type tests are indexed by bandwidth, lag length, etc., but have none of these three properties.It is shown that members of the family withd< 1 have higher asymptotic local power than the Breitung (2002) test, and whendis small the asymptotic local power of the proposed nonparametric test is relatively close to the parametric power envelope, particularly in the case with a linear time trend. Furthermore, generalized least squares (GLS) detrending is shown to improve power whendis small, which is not the case for the Breitung (2002) test. Simulations demonstrate that when applying a sieve bootstrap procedure, the proposed variance ratio test has very good size properties, with finite-sample power that is higher than that of the Breitung (2002) test and even rivals the (nearly) optimal parametric GLS detrended augmented Dickey–Fuller test with lag length chosen by an information criterion.

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 GENERALIZED LAPLACE INFERENCE IN MULTIPLE CHANGE-POINTS MODELS

2021 ◽  
pp. 1-31
Author(s):  
Alessandro Casini ◽  
Pierre Perron
Keyword(s):  
Asymptotic Distribution ◽  
Structural Changes ◽  
Linear Time ◽  
Bayesian Estimator ◽  
Change Points ◽  
Finite Sample ◽  
Time Series Regression ◽  
Long Span ◽  
Inference Methods ◽  
Theoretical Side

Under the classical long-span asymptotic framework, we develop a class of generalized laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998,Econometrica66, 47–78). The GL estimator is defined by an integration rather than optimization-based method and relies on the LS criterion function. It is interpreted as a classical (non-Bayesian) estimator, and the inference methods proposed retain a frequentist interpretation. This approach provides a better approximation about the uncertainty in the data of the change-points relative to existing methods. On the theoretical side, depending on some input (smoothing) parameter, the class of GL estimators exhibits a dual limiting distribution, namely the classical shrinkage asymptotic distribution or a Bayes-type asymptotic distribution. We propose an inference method based on highest density regions using the latter distribution. We show that it has attractive theoretical properties not shared by the other popular alternatives, i.e., it is bet-proof. Simulations confirm that these theoretical properties translate to good finite-sample performance.

scholarly journals Avaliações numéricas das inferências no modelo Beta-Skew-t-EGARCH

2015 ◽  
Vol 13 (1) ◽  
pp. 40
Author(s):  
Fernanda Maria Muller ◽  
Fábio Mariano Bayer
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Likelihood Method ◽  
Ratio Test ◽  
Finite Sample ◽  
Sample Sizes ◽  
Monte Carlo Simulation Study ◽  
Power Of The Test ◽  
Component Test ◽  
Two Component

The Beta-Skew-t-EGARCH model was recently proposed in literature to model the volatility of financial returns. The inferences over the parameters of the model are based on maximum likelihood method. These estimators have good asymptotic properties, however in finite sample sizes their performance can be poor. With the purpose of evaluating the finite sample performance of point estimators and of the likelihood ratio test proposed to the presence of two components of volatility, we present a Monte Carlo simulation study. Numerical results indicate that the maximum likelihood estimators of some parameters of the model are considerably biased in sample sizes smaller than 3000. The evaluation results of the proposed two-component test, in terms of size and power of the test, showed its practical usefulness in sample sizes greater than 3000. At the end of the work we present an application in a real data of the proposed two-component test and the model Beta-Skew-t-EGARCH.

scholarly journals SUP-TESTS FOR LINEARITY IN A GENERAL NONLINEAR AR(1) MODEL

2009 ◽  
Vol 26 (4) ◽  
pp. 965-993 ◽  
Author(s):  
Christian Francq ◽  
Lajos Horvath ◽  
Jean-Michel Zakoïan
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Null Hypothesis ◽  
Nuisance Parameter ◽  
Time Series Models ◽  
Ratio Test ◽  
Finite Sample ◽  
Chi Square ◽  
Finite Sample Properties ◽  
Linearity Testing

We consider linearity testing in a general class of nonlinear time series models of order one, involving a nonnegative nuisance parameter that (a) is not identified under the null hypothesis and (b) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the likelihood ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chi-square processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite-sample properties of the sup-tests are studied by simulations.

scholarly journals A BARTLETT CORRECTION FACTOR FOR TESTS ON THE COINTEGRATING RELATIONS

2000 ◽  
Vol 16 (5) ◽  
pp. 740-778 ◽  
Author(s):  
Søren Johansen
Keyword(s):  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Correction Factor ◽  
Likelihood Ratio Tests ◽  
Ratio Test ◽  
Finite Sample ◽  
Bartlett Correction ◽  
Simulation Experiments ◽  
Sample Distribution

Likelihood ratio tests for restrictions on cointegrating vectors are asymptotically χ2 distributed. For some values of the parameters this asymptotic distribution does not give a good approximation to the finite sample distribution. In this paper we derive the Bartlett correction factor for the likelihood ratio test and show by some simulation experiments that it can be a useful tool for making inference.

scholarly journals Quantile inference for nonstationary processes with infinite variance innovations

2021 ◽  
Vol 36 (3) ◽  
pp. 443-461
Author(s):  
Qi-meng Liu ◽  
Gui-li Liao ◽  
Rong-mao Zhang
Keyword(s):  
Unit Root ◽  
Brownian Bridge ◽  
Consumer Price Index ◽  
Infinite Variance ◽  
Finite Variance ◽  
Ratio Test ◽  
Finite Sample ◽  
Kolmogorov Smirnov ◽  
Von Mises ◽  
Quantile Inference

AbstractBased on the quantile regression, we extend Koenker and Xiao (2004) and Ling and McAleer (2004)’s works from finite-variance innovations to infinite-variance innovations. A robust t-ratio statistic to test for unit-root and a re-sampling method to approximate the critical values of the t-ratio statistic are proposed in this paper. It is shown that the limit distribution of the statistic is a functional of stable processes and a Brownian bridge. The finite sample studies show that the proposed t-ratio test always performs significantly better than the conventional unit-root tests based on least squares procedure, such as the Augmented Dick Fuller (ADF) and Philliphs-Perron (PP) test, in the sense of power and size when infinite-variance disturbances exist. Also, quantile Kolmogorov-Smirnov (QKS) statistic and quantile Cramer-von Mises (QCM) statistic are considered, but the finite sample studies show that they perform poor in power and size, respectively. An application to the Consumer Price Index for nine countries is also presented.

scholarly journals LOCAL ASYMPTOTIC POWER OF THE IM-PESARAN-SHIN PANEL UNIT ROOT TEST AND THE IMPACT OF INITIAL OBSERVATIONS

2009 ◽  
Vol 26 (1) ◽  
pp. 311-324 ◽  
Author(s):  
David Harris ◽  
David I. Harvey ◽  
Stephen J. Leybourne ◽  
Nikolaos D. Sakkas
Keyword(s):  
Unit Root ◽  
Initial Conditions ◽  
Unit Root Test ◽  
Finite Sample ◽  
Asymptotic Power ◽  
Panel Unit Root ◽  
Practical Applications ◽  
Power Of The Test ◽  
Local Asymptotic Power ◽  
The Impact

In this note we derive the local asymptotic power function of the standardized averaged Dickey–Fuller panel unit root statistic of Im, Pesaran, and Shin (2003, Journal of Econometrics, 115, 53–74), allowing for heterogeneous deterministic intercept terms. We consider the situation where the deviation of the initial observation from the underlying intercept term in each individual time series may not be asymptotically negligible. We find that power decreases monotonically as the magnitude of the initial conditions increases, in direct contrast to what is usually observed in the univariate case. Finite-sample simulations confirm the relevance of this result for practical applications, demonstrating that the power of the test can be very low for values of T and N typically encountered in practice.

A NONPARAMETRIC TEST OF SIGNIFICANT VARIABLES IN GRADIENTS

2020 ◽  
pp. 1-45
Author(s):  
Feng Yao ◽  
Taining Wang
Keyword(s):  
Null Distribution ◽  
Monte Carlo Study ◽  
Nonparametric Test ◽  
Hedonic Price ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Test ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation ◽  
Mean Function

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.

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