A Monte Carlo Study of Tests of Blockwise Weak Separability

Separability assumptions on functional structure have received a great deal of attention from econometricians and economic theorists because (a) separability provides the fundamental linkage between aggregation over goods and the maximization principles in economic theory, (b) separability provides the theoretical basis for partitioning the economy's structure into sectors, and (c) separability provides a theoretical hypothesis, which can produce parameter restrictions, permitting great simplification in estimation of large demand systems. The power of the various available tests for separability has never been determined, however. We conduct Monte Carlo studies to examine the capability of currently available methods to provide correct inferences about separability.     

Testing for heteroskedasticity in the tobit and probit models

Non-constant variance across observations (heteroskedasticity) results in the maximum likelihood estimators of tobit and probit model parameters being inconsistent. Some of the available tests for constant variance across observations (homoskedasticity) are discussed and examined in a small Monte Carlo experiment.     

蒙特卡罗方法下线性模型的异方差性检验方法

在已有的异方差性检验方法的基础上,运用蒙特卡罗方法,借助permutation检验思想,在不假定随机扰动项服从同一分布族的条件下,通过从大样本中提取大量的子样本,不断对线性模型进行拟合和检验,根据异方差为真的频率大小,给出了一种新的异方差检验方法。随机模拟表明本检验方法优于传统方法。     

Testing for the Equality of Two Nonparametric Regression Curves with Long Memory Errors

This article discusses the problem of testing the equality of two nonparametric regression functions against two-sided alternatives for uniform design on [0,1] with long memory moving average errors. The standard deviations and the long memory parameters are possibly different for the two errors. The article adapts the partial sum process idea used in the independent observations settings to construct the tests and derives their asymptotic null distributions. The article also shows that these tests are consistent for general alternatives and obtains their limiting distributions under a sequence of local alternatives. Since the limiting null distributions of these tests are unknown, we first conducted a Monte Carlo simulation study to obtain a few selected critical values of the proposed tests. Then based on these critical values, another Monte Carlo simulation is conducted to study the finite sample level and power behavior of these tests at some alternatives. The article also contains a simulation study that assesses the effect of estimating the nonparametric regression function on an estimate of the long memory parameter of the errors. It is observed that the estimate based on direct observations is generally preferable over the one based on the estimated nonparametric residuals.     

Testing for a change in repeated measures data

Four nonparametric test statistics for the change-point problem with repeated measures data are proposed. In a Monte Carlo simulation study, critical values for the proposed test statistics are simulated and the performances of the proposed tests are compared with the performances of some competitive tests in terms of asymptotic behavior and power. We provide appropriate recommendations for different occurrences of the change-point and illustrate the testing methods using a set of real data.     

Testing for the Equality of Two Autoregressive Functions Using Quasi-Residuals

This article discusses the problem of testing the equality of two nonparametric autoregressive functions against one-sided alternatives. The heteroscedastic errors and stationary densities of the two independent strong mixing strictly stationary time series can be possibly different. The article adapts the idea of using sum of quasi-residuals to construct the test and derives its asymptotic null distributions. The article also shows that the test is consistent for general alternatives and obtains its limiting distributions under a sequence of local alternatives. Then a Monte Carlo simulation is conducted to study the finite sample level and power behavior of these tests at some alternatives. We also compare the test to an existing lag matched test theoretically and by Monte Carlo experiments.     

Testing Fractional Order of Long Memory Processes: A Monte Carlo Study

Testing the fractionally integrated order of seasonal and nonseasonal unit roots is quite important for the economic and financial time series modeling. In this article, the widely used Robinson's (1994 Robinson , P. M. ( 1994 ). Efficient tests of nonstationary hypotheses . J. Am. Stat. Assoc. 89 ( 428 ): 1420 – 1437 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) test is applied to various well-known long memory models. Via Monte Carlo experiments, we study and compare the performances of this test using several sample sizes.     

Testing the Equality of Two Exponential Distributions

This paper proposes an overlapping-based test statistic for testing the equality of two exponential distributions with different scale and location parameters. The test statistic is defined as the maximum likelihood estimate of the Weitzman's overlapping coefficient, which estimates the agreement of two densities. The proposed test statistic is derived in closed form. Simulated critical points are generated for the proposed test statistic for various sample sizes and significance levels via Monte Carlo Simulations. Statistical powers of the proposed test are computed via simulation studies and compared to those of the existing Log likelihood ratio test.     

Testing for spherical symmetry via the empirical characteristic function

Kolmogorov–Smirnov-type and Cramér–von Mises-type goodness-of-fit tests are proposed for the null hypothesis that the distribution of a random vector X is spherically symmetric. The test statistics utilize the fact that X has a spherical symmetric distribution if, and only if, the characteristic function of X is constant over surfaces of spheres centred at the origin. Both tests come in convenient forms that are straightforwardly applicable with the computer. The asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions. Since both the finite sample and the asymptotic null distribution depend on the unknown distribution of the Euclidean norm of X, a conditional Monte Carlo procedure is used to actually carry out the tests. Results on the behaviour of the test in finite-samples are included along with a real-data example.     

A Meta Analytic Approach to Testing for Panel Cointegration

We propose new tests for panel cointegration by extending the panel unit root tests of Choi (2001 Choi , I. ( 2001 ). Unit root tests for panel data . Journal of International Money and Finance 20 ( 2 ): 249 – 272 .[Crossref], [Web of Science ®] , [Google Scholar]) and Maddala and Wu (1999 Maddala , G. , Wu , S. ( 1999 ). A comparative study of unit root tests with panel data and a new simple test . Oxford Bulletin of Economics and Statistics 61 ( S1 ): 631 – 652 .[Crossref] , [Google Scholar]) to the panel cointegration case. The tests are flexible, intuitively appealing, and relatively easy to compute. We investigate the finite sample behavior in a simulation study. Several variants of the tests compare favorably in terms of both size and power with other widely used panel cointegration tests.     

A Comparison of Significance Testing Procedures for the Intraclass Correlation from Family Data

Different procedures for testing problems concerning intraclass correlation from familial data are considered in the case of varying number of siblings per family. Under the assumption of multivariate normality, the hypotheses that the intraclass correlation is equal to a specified value are tested. To assess the performance of the tests, Monte Carlo simulations are designed to compare their powers. The Neyman's (1959) C(α) test and the test based on the modified ANOVA F statistic are shown to be consistently more powerful than other procedures.     

On the Value of derivative evaluations and random walk suppression in Markov Chain Monte Carlo algorithms

Two strategies that can potentially improve Markov Chain Monte Carlo algorithms are to use derivative evaluations of the target density, and to suppress random walk behaviour in the chain. The use of one or both of these strategies has been investigated in a few specific applications, but neither is used routinely. We undertake a broader evaluation of these techniques, with a view to assessing their utility for routine use. In addition to comparing different algorithms, we also compare two different ways in which the algorithms can be applied to a multivariate target distribution. Specifically, the univariate version of an algorithm can be applied repeatedly to one-dimensional conditional distributions, or the multivariate version can be applied directly to the target distribution.     

Exploring the Impact of Multivariate GARCH Innovations on Hypothesis Testing for Cointegrating Vectors

This article investigates the impact of multivariate generalized autoregressive conditional heteroskedastic (GARCH) errors on hypothesis testing for cointegrating vectors. The study reviews a cointegrated vector autoregressive model incorporating multivariate GARCH innovations and a regularity condition required for valid asymptotic inferences. Monte Carlo experiments are then conducted on a test statistic for a hypothesis on the cointegrating vectors. The experiments demonstrate that the regularity condition plays a critical role in rendering the hypothesis testing operational. It is also shown that Bartlett-type correction and wild bootstrap are useful in improving the small-sample size and power performance of the test statistic of interest.     

Testing for stationarity in heterogeneous panel data in the presence of cross-section dependence

The panel variant of the KPSS tests developed by Hadri [Hadri, K., 2000, Testing for stationarity in heterogeneous panels. Econometrics Journal, 3, 148–161] for the null of stationarity suffers from size distortions in the presence of cross-section dependence. However, applying the bootstrap methodology, we find that these tests are approximately correctly sized.     

Exact Goodness‐of‐Fit Testing for the Ising Model

The Ising model is one of the simplest and most famous models of interacting systems. It was originally proposed to model ferromagnetic interactions in statistical physics and is now widely used to model spatial processes in many areas such as ecology, sociology, and genetics, usually without testing its goodness of fit. Here, we propose various test statistics and an exact goodness‐of‐fit test for the finite‐lattice Ising model. The theory of Markov bases has been developed in algebraic statistics for exact goodness‐of‐fit testing using a Monte Carlo approach. However, finding a Markov basis is often computationally intractable. Thus, we develop a Monte Carlo method for exact goodness‐of‐fit testing for the Ising model that avoids computing a Markov basis and also leads to a better connectivity of the Markov chain and hence to a faster convergence. We show how this method can be applied to analyze the spatial organization of receptors on the cell membrane.     

Exact Estimation of Demand Functions under Block-Rate Pricing

This article proposes an exact estimation of demand functions under block-rate pricing by focusing on increasing block-rate pricing. This is the first study that explicitly considers the separability condition which has been ignored in previous literature. Under this pricing structure, the price changes when consumption exceeds a certain threshold and the consumer faces a utility maximization problem subject to a piecewise-linear budget constraint. Solving this maximization problem leads to a statistical model in which model parameters are strongly restricted by the separability condition. In this article, by taking a hierarchical Bayesian approach, we implement a Markov chain Monte Carlo simulation to properly estimate the demand function. We find, however, that the convergence of the distribution of simulated samples to the posterior distribution is slow, requiring an additional scale transformation step for parameters to the Gibbs sampler. These proposed methods are then applied to estimate the Japanese residential water demand function.     

Maximum Likelihood Unit Root Testing in the Presence of GARCH: A New Test with Increased Power

The literature on testing the unit root hypothesis in the presence of GARCH errors is extended. A new test based upon the combination of local-to-unity detrending and joint maximum likelihood estimation of the autoregressive parameter and GARCH process is presented. The finite sample distribution of the test is derived under alternative decisions regarding the deterministic terms employed. Using Monte Carlo simulation, the newly proposed ML t-test is shown to exhibit increased power of relative to rival tests. Finally, the empirical relevance of the simulation results is illustrated via an application to real GDP for the UK.     

Testing for linearity in Markov switching models: a bootstrap approach

Testing for linearity in the context of Markov switching models is complicated because standard regularity conditions for likelihood based inference are violated. In particular, under the null hypothesis of linearity, some parameters are not identified and scores are identically zero. Thus, the asymptotic distribution of the relevant test statistic does not possess the standard χ ²-distribution. A bootstrap resampling scheme to approximate the distribution of the relevant test statistic under the null of linearity is proposed. The procedure is relatively easy to program and computation requirements are reasonable. The performance of the bootstrap-based test is investigated by means of Monte Carlo simulations. Results show that this test works well and outperforms the Hansen test and the Carrasco et al. test.     

Testing linearity against nonlinear moving average models

Lagrange multiplier (LM) test statistics are derived for testing a linear moving average model against an asymmetric moving average model and an LM type test against an additive smooth transition moving average model. The latter model is introduced in the paper. The small sample performance of the proposed tests are evaluated in a Monte Carlo study and compared to Wald and likelihood ratio statistics. The size properties of the Lagrange multiplier test are better than those of other tests.