Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors

Abstract Johansen’s (2000. “A Bartlett Correction Factor for Tests of on the Cointegrating Relations.” Econometric Theory 16: 740–78) Bartlett correction factor for the LR test of linear restrictions on cointegrated vectors is derived under the i.i.d. Gaussian assumption for the innovation terms. However, the distribution of most data relating to financial variables is fat-tailed and often skewed; there is therefore a need to examine small sample inference procedures that require weaker assumptions for the innovation term. This paper suggests that using the non-parametric bootstrap to approximate a Bartlett-type correction provides a statistic that does not require specification of the innovation distribution and can be used by applied econometricians to perform a small sample inference procedure that is less computationally demanding than it’s analytical counterpart. The procedure involves calculating a number of bootstrap values of the LR test statistic and estimating the expected value of the test statistic by the average value of the bootstrapped LR statistic. Simulation results suggest that the inference procedure has good finite sample property and is less dependent on the parameter space of the data generating process.

Download Full-text

A BARTLETT CORRECTION FACTOR FOR TESTS ON THE COINTEGRATING RELATIONS

Econometric Theory ◽

10.1017/s0266466600165065 ◽

2000 ◽

Vol 16 (5) ◽

pp. 740-778 ◽

Cited By ~ 82

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.

Download Full-text

Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽

10.3390/econometrics9010010 ◽

2021 ◽

Vol 9 (1) ◽

pp. 10

Author(s):

Šárka Hudecová ◽

Marie Hušková ◽

Simos G. Meintanis

Keyword(s):

Goodness Of Fit ◽

Probability Generating Function ◽

Parametric Bootstrap ◽

Real Data ◽

Data Sets ◽

Test Statistics ◽

Finite Sample ◽

Generalized Poisson ◽

Goodness Of Fit Tests ◽

Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

Download Full-text

A Test for Functional Form Against Nonparametric Alternatives

Econometric Theory ◽

10.1017/s0266466600013165 ◽

1992 ◽

Vol 8 (4) ◽

pp. 452-475 ◽

Cited By ~ 72

Author(s):

Jeffrey M. Wooldridge

Keyword(s):

Alternative Model ◽

Regression Models ◽

Functional Form ◽

Parametric Model ◽

Finite Sample ◽

Test Statistic ◽

Sieve Estimation ◽

Finite Sample Properties ◽

Standard Normal ◽

Nonparametric Alternatives

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

Download Full-text

A NONPARAMETRIC TEST OF SIGNIFICANT VARIABLES IN GRADIENTS

Econometric Theory ◽

10.1017/s0266466620000407 ◽

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.

Download Full-text

TESTING HOMOGENEITY IN PANEL DATA MODELS WITH INTERACTIVE FIXED EFFECTS

Econometric Theory ◽

10.1017/s0266466613000017 ◽

2013 ◽

Vol 29 (6) ◽

pp. 1079-1135 ◽

Cited By ~ 47

Author(s):

Liangjun Su ◽

Qihui Chen

Keyword(s):

Panel Data ◽

Fixed Effects ◽

Data Models ◽

Development Economic ◽

Strong Mixing ◽

Panel Data Models ◽

Finite Sample ◽

Test Statistic ◽

Lm Test ◽

Interactive Fixed Effects

This paper proposes a residual-based Lagrange Multiplier (LM) test for slope homogeneity in large-dimensional panel data models with interactive fixed effects. We first run the panel regression under the null to obtain the restricted residuals and then use them to construct our LM test statistic. We show that after being appropriately centered and scaled, our test statistic is asymptotically normally distributed under the null and a sequence of Pitman local alternatives. The asymptotic distributional theories are established under fairly general conditions that allow for both lagged dependent variables and conditional heteroskedasticity of unknown form by relying on the concept of conditional strong mixing. To improve the finite-sample performance of the test, we also propose a bootstrap procedure to obtain the bootstrap p-values and justify its validity. Monte Carlo simulations suggest that the test has correct size and satisfactory power. We apply our test to study the Organization for Economic Cooperation and Development economic growth model.

Download Full-text

Monitoring Persistence Change in Heavy-Tailed Observations

Symmetry ◽

10.3390/sym13060936 ◽

2021 ◽

Vol 13 (6) ◽

pp. 936

Author(s):

Dan Wang

Keyword(s):

Kernel Method ◽

Alternative Hypothesis ◽

Null Distribution ◽

Real Data ◽

Ratio Test ◽

Finite Sample ◽

Test Statistic ◽

Bootstrap Approximation ◽

Heavy Tailed ◽

Better Than

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

Download Full-text

TESTING FOR SEASONAL UNIT ROOTS IN PERIODIC INTEGRATED AUTOREGRESSIVE PROCESSES

Econometric Theory ◽

10.1017/s0266466608080420 ◽

2008 ◽

Vol 24 (4) ◽

pp. 1093-1129 ◽

Cited By ~ 5

Author(s):

Tomas del Barrio Castro ◽

Denise R. Osborn

Keyword(s):

Unit Root ◽

Unit Roots ◽

Finite Sample ◽

Test Statistic ◽

Important Special Case ◽

Frequency Unit ◽

Annual Frequency ◽

Fixed Order ◽

Fuller Distribution ◽

Zero Frequency

This paper examines the implications of applying the Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238) (HEGY) seasonal root tests to a process that is periodically integrated. As an important special case, the random walk process is also considered, where the zero-frequency unit root t-statistic is shown to converge to the Dickey–Fuller distribution and all seasonal unit root statistics diverge. For periodically integrated processes and a sufficiently high order of augmentation, the HEGY t-statistics for unit roots at the zero and semiannual frequencies both converge to the same Dickey–Fuller distribution. Further, the HEGY joint test statistic for a unit root at the annual frequency and all joint test statistics across frequencies converge to the square of this distribution. Results are also derived for a fixed order of augmentation. Finite-sample Monte Carlo results indicate that, in practice, the zero-frequency HEGY statistic (with augmentation) captures the single unit root of the periodic integrated process, but there may be a high probability of incorrectly concluding that the process is seasonally integrated.

Download Full-text

Cause-specific quantile residual life regression

Statistical Methods in Medical Research ◽

10.1177/0962280215592426 ◽

2015 ◽

Vol 26 (4) ◽

pp. 1912-1924 ◽

Cited By ~ 2

Author(s):

Jeong Youn Lim ◽

Jong-Hyeon Jeong

Keyword(s):

Residual Life ◽

Fixed Time ◽

Estimating Equation ◽

Simulation Studies ◽

Finite Sample ◽

Test Statistic ◽

Life Distribution ◽

Finite Sample Properties ◽

Quantile Residual Life ◽

Log Linear

We propose a cause-specific quantile residual life regression where the cause-specific quantile residual life, defined as the inverse of the cumulative incidence function of the residual life distribution of a specific type of events of interest conditional on a fixed time point, is log-linear in observable covariates. The proposed test statistic for the effects of prognostic factors does not involve estimation of the improper probability density function of the cause-specific residual life distribution under competing risks. The asymptotic distribution of the test statistic is derived. Simulation studies are performed to assess the finite sample properties of the proposed estimating equation and the test statistic. The proposed method is illustrated with a real dataset from a clinical trial on breast cancer.

Download Full-text

A test statistic to quantify treelikeness in phylogenetics

10.1101/2021.02.16.431544 ◽

2021 ◽

Author(s):

Caitlin Cherryh ◽

Bui Quang Minh ◽

Rob Lanfear

Keyword(s):

Evolutionary History ◽

Incomplete Lineage Sorting ◽

Phylogenetic Analyses ◽

Phylogenetic Network ◽

Parametric Bootstrap ◽

Lineage Sorting ◽

Test Statistic ◽

Sequence Alignments ◽

Wide Range ◽

History Of

AbstractMost phylogenetic analyses assume that the evolutionary history of an alignment (either that of a single locus, or of multiple concatenated loci) can be described by a single bifurcating tree, the so-called the treelikeness assumption. Treelikeness can be violated by biological events such as recombination, introgression, or incomplete lineage sorting, and by systematic errors in phylogenetic analyses. The incorrect assumption of treelikeness may then mislead phylogenetic inferences. To quantify and test for treelikeness in alignments, we develop a test statistic which we call the tree proportion. This statistic quantifies the proportion of the edge weights in a phylogenetic network that are represented in a bifurcating phylogenetic tree of the same alignment. We extend this statistic to a statistical test of treelikeness using a parametric bootstrap. We use extensive simulations to compare tree proportion to a range of related approaches. We show that tree proportion successfully identifies non-treelikeness in a wide range of simulation scenarios, and discuss its strengths and weaknesses compared to other approaches. The power of the tree-proportion test to reject non-treelike alignments can be lower than some other approaches, but these approaches tend to be limited in their scope and/or the ease with which they can be interpreted. Our recommendation is to test treelikeness of sequence alignments with both tree proportion and mosaic methods such as 3Seq. The scripts necessary to replicate this study are available at https://github.com/caitlinch/treelikeness

Download Full-text

Pengaruh Model Pembelajaran ASSURE TERHADAP Hasil Belajar Siswa pada Materi Suhu dan Kalor

Musamus Journal of Science Education ◽

10.35724/mjose.v1i1.874 ◽

2018 ◽

Vol 1 (1) ◽

pp. 009-020

Author(s):

Sunartih Sunartih ◽

Marungkil Pasaribu ◽

Amiruddin Hatibe

Keyword(s):

Standard Deviation ◽

Hypothesis Testing ◽

Student Learning ◽

Learning Outcomes ◽

Student Learning Outcomes ◽

Learning Model ◽

T Test ◽

Test Statistic ◽

Model Learning ◽

Average Value

This study aims to determine whether there is an influence of ASSURE learning model on student learning outcomes in temperature and heat material of class XI SMA. The method used is quasi-experimental with equivalent pretest-posttest design. The population of this study were all students of class XI SMA . Sampling was carried out by purposive sampling with the sample of the study being class XI Mipa 2 as the experimental class and class X1 Mipa 5 as the control class. The research instrument in the form of learning outcomes tests and observation sheets that have been validated by the validator and field tested. Data analysis used inferential statistics is normality, homogeneity, hypothesis testing (2-party t test). Based on the results of research and analysis of research data, obtained the value of student learning outcomes at posttest average value of the experimental class is 14.90 with a standard deviation of 3.23 and for the control class of 11.57 with a standard deviation of 2.99. The test results of the t test statistic of 2 parties from hypothesis testing obtained the price thitung(4,11)>ttabel(1,67) or thitung(-4,11)>ttabel(-1,67) so that H1 is accepted and H0 is rejected. This result states that there are differences in student learning outcomes in physics subjects between classes taught with the ASSURE learning model and Direct Intruction learning models. It can be concluded that there is an influence of the ASSURE learning model on student learning outcomes in temperature and heat material in class XI of SMA. Keywords: assure learning model, learning outcomes, temperature and heat

Download Full-text