A non-parametric spatial independence test using symbolic entropy

In the present paper, we construct a new, simple, consistent and powerful test for spatial independence, called the SG test, by using the new concept of symbolic entropy as a measure of spatial dependence. The standard asymptotic distribution of the test is an affine transformation of the symbolic entropy under the null hypothesis. The test statistic, with the proposed symbolization procedure, and its standard limit distribution have appealing theoretical properties that guarantee the general applicability of the test. An important aspect is that the test does not require specification of the W matrix and is free of a priori assumptions. We include a Monte Carlo study of our test, in comparison with the well-known Moran's I, the SBDS (de Graaff et al., 2001) and τ test (Brett and Pinkse, 1997) that are two non-parametric tests, to better appreciate the properties and the behaviour of the new test. Apart from being competitive compared to other tests, results underline the outstanding power of the new test for non-linear dependent spatial processes.     

A non-parametric test for independence based on symbolic dynamics

In the present paper we propose a powerful, yet simple, non-parametric test for independence based on symbolic dynamic analysis. The absence of dependences in the unknown underlying data generating process is studied via symbolic dynamics. This is possible due to the ordering property of real numbers on an interval. Interestingly, the test is closely related to entropy concepts. Apart from being correctly sized, the new test is powerful for realistic finite data sets, and it is easy to use as one does not need to select any free parameter, which sharply contrasts with other tests of independence. In addition, the test is robust in the presence of noise which is one of the most typical cases when dealing with economic time series.     

Testing Integration of Macroeconomic Time Series in Transitional Socialist Economies. A Modification of Perron Test

The presence of structural breaks reduces the power of integration tests. A number of methods were suggested to improve the statistical properties of integration tests in the presence of structural breaks. The most known are Perron tests, which allow to test for the level of integration of time series with one structural break. Perron tests allow for two types of structural breaks: additive outlier an innovative outlier. These tests are, however, not very useful in testing the level of integration of macroeconomic time series in countries in transition from centrally-planned to market economy. In such case one should expect two structural breaks to affect the time series: one at the beginning and one at the end of the transformation process. Test that allows for two additive outlier type structural breaks in time series is developed in this paper. This test has superior power as compared to standard Dickey-Fuller and Perron tests. This paper provides asymptotic distribution as well as finite sample properties of proposed test. Therefore practitioners receive a reliable tool for analyzing macroeconomic processes in transitional economies. This revised version was published online in July 2006 with corrections to the Cover Date.     

Random walk or chaos: A formal test on the Lyapunov exponent

A formal test on the Lyapunov exponent is developed to distinguish a random walk model from a chaotic system, which is based on the Nadaraya–Watson kernel estimator of the Lyapunov exponent. The asymptotic null distribution of our test statistic is free of nuisance parameter, and simply given by the range of standard Brownian motion on the unit interval. The test is consistent against the chaotic alternatives. A simulation study shows that the test performs reasonably well in finite samples. We apply our test to some of the standard macro and financial time series, finding no significant empirical evidence of chaos.     

Het matchen in de psychologie

Matching in Psychology
In experimental psychology the matching method seems to be one of the most promising methods. This paper deals with the matching of a series of t elements against a series of t other elements. The stated null hypothesis is: for a fixed order of one of the series each permutation of the second series has the same probability.
As a test criterion in the case of one matching is defined: the number r of matches, e.g. the number of "right pairs"; for n matchings: .
As the distribution of for t=3 cannot be found in literature, a table of is given for n=I(I)30: see table I. The way of calculating and verifying is discussed.
For the problem of t=3 and n 31 the degree of approximation by the normal distribution and by the Pearson's Type III distributions is examined. With the application of a correction for continuity the former gives for n=30 a reasonable approximation, the latter a very good approximation: see table 2.     

Causality and the independence phenomenon: The case of the demand for money

We examine the demand for money using causality results with data from two alternative policy regimes. For Spanish series of money and prices we obtain the same result of independence that Feige and others found with U.S. data. The result of the test for the German hyperinflation period reveals bidirectional causality. It is shown that the somehow striking results of widespread independence among economic time series do not disprove but rather confirm the existence of a true underlying causal relationship. Causality results, and independence in particular, give us testable restriction for the structural form. In the case of models for expectations in the rate of inflation, these restrictions allow us to revalidate the stability of the demand for money as postulated by the Quantity Theory.     

A consistent nonparametric test of affiliation in auction models

We propose a new nonparametric test of affiliation, a strong form of positive dependence with independence as a special, knife-edge, case. The test is consistent against all departures from the null of affiliation, and its null distribution is standard normal. Like most nonparametric tests, a sample-size dependent input parameter is needed. We provide an informal procedure for choosing the input parameter and evaluate the test’s performance using a simulation study. Our test can be used to test the fundamental assumptions of the auctions literature. We implement our test empirically using the Outer Continental Shelf (OCS) auction data.     

A general dependence test and applications

We describe a test, based on the correlation integral, for the independence of a variable and a vector that can be used with serially dependent data. Monte Carlo simulations suggest that the test has good power to detect dependence in several models, performing nearly as well or better than the BDS test in univariate time series and complementing the BDS test in distributed lag models. Finally, we apply our test in conjunction with the BDS test to examine models of US unemployment rates. © 1998 John Wiley & Sons, Ltd.     

Index

We study two Durbin-Watson type tests for serial correlation of errors inregression models when observations are missing. We derive them by applying standard methods used in time series and linear models to deal with missing observations. The first test may be viewed as a regular Durbin-Watson test in the context of an extended model. We discuss appropriate adjustments that allow one to use all available bounds tables. We show that the test is locally most powerful invariant against the same alternative error distribution as the Durbin-Watson test. The second test is based on a modified Durbin-Watson statistic suggested by King (1981a) and is locally most powerful invariant against a first-order autoregressive process.     

A new approach to distribution free tests in contingency tables

We suggest an extremely wide class of asymptotically distribution free goodness of fit tests for testing independence in two-way contingency tables, or equivalently, independence of two discrete random variables. The nature of these tests is that the test statistics can be viewed as definite functions of the transformation of \(\widehat{T}_n = (\widehat{T}_{ij})=\Big (\frac{\nu _{ij}- n\hat{a}_i\hat{b}_j}{\sqrt{n\hat{a}_i\hat{b}_j}}\Big )\) where \(\nu _{ij}\) are frequencies and \(\hat{a}_i, \hat{b}_j\) are estimated marginal distributions. Our method is also applicable for testing independence of two discrete random vectors. We make some comparisons on statistical powers of the new tests with the conventional chi-square test and suggest some cases in which this class is significantly more powerful.     

Tests of independence in a bivariate exponential distribution

The problem of testing independence in a two component series system is considered. The joint distribution of component lifetimes is modeled by the Pickands bivariate exponential distribution, which includes the widely used Marshall and Olkins distribution and the Gumbels type II distribution. The case of identical components is first addressed. Uniformly most powerful unbiased test (UMPU) and likelihood ratio test are obtained. It is shown that inspite of a nuisance parameter, the UMPU test is unconditional and this test turns out to be the same as the likelihood ratio test. The case of nonidentical components is also addressed and both UMPU and likelihood ratio tests are obtained. A UMPU test is obtained to test the identical nature of the components and extensions to the type II censoring scheme and multiple component systems are also discussed. Some modifications to account for the difference in parameters under test and use conditions are also discussed.     

Testing multivariate distributions in GARCH models

In this paper, we consider testing distributional assumptions in multivariate GARCH models based on empirical processes. Using the fact that joint distribution carries the same amount of information as the marginal together with conditional distributions, we first transform the multivariate data into univariate independent data based on the marginal and conditional cumulative distribution functions. We then apply the Khmaladze's martingale transformation (K-transformation) to the empirical process in the presence of estimated parameters. The K-transformation eliminates the effect of parameter estimation, allowing a distribution-free test statistic to be constructed. We show that the K-transformation takes a very simple form for testing multivariate normal and multivariate t-distributions. The procedure is applied to a multivariate financial time series data set.     

Distribution-free tests of mean vectors and covariance matrices for multivariate paired data

We study a permutation procedure to test the equality of mean vectors, homogeneity of covariance matrices, or simultaneous equality of both mean vectors and covariance matrices in multivariate paired data. We propose to use two test statistics for the equality of mean vectors and the homogeneity of covariance matrices, respectively, and combine them to test the simultaneous equality of both mean vectors and covariance matrices. Since the combined test has composite null hypothesis, we control its type I error probability and theoretically prove the asymptotic unbiasedness and consistency of the combined test. The new procedure requires no structural assumption on the covariances. No distributional assumption is imposed on the data, except that the permutation test for mean vector equality assumes symmetric joint distribution of the paired data. We illustrate the good performance of the proposed approach with comparison to competing methods via simulations. We apply the proposed method to testing the symmetry of tooth size in a dental study and to finding differentially expressed gene sets with dependent structures in a microarray study of prostate cancer.     

Combining Significance of Correlated Statistics with Application to Panel Data*

The inverse normal method, which is used to combine P‐values from a series of statistical tests, requires independence of single test statistics in order to obtain asymptotic normality of the joint test statistic. The paper discusses the modification by Hartung (1999, Biometrical Journal, Vol. 41, pp. 849–855) , which is designed to allow for a certain correlation matrix of the transformed P‐values. First, the modified inverse normal method is shown here to be valid with more general correlation matrices. Secondly, a necessary and sufficient condition for (asymptotic) normality is provided, using the copula approach. Thirdly, applications to panels of cross‐correlated time series, stationary as well as integrated, are considered. The behaviour of the modified inverse normal method is quantified by means of Monte Carlo experiments.     

Detecting overdispersion in INARCH(1) processes

A statistical test for the degree of overdispersion of count data time series based on the empirical version of the (Poisson) index of dispersion is considered. The test design relies on asymptotic properties of this index of dispersion, which in turn have been analyzed for time series stemming from a compound Poisson (Poisson‐stopped sum) INAR(1) model. This approach is extended to the popular Poisson INARCH(1) model, which exhibits unconditional overdispersion but has an (equidispersed) conditional Poisson distribution. The asymptotic distribution of the index of dispersion if applied to time series stemming from such a model is derived. These results allow us to investigate the ability of the dispersion test to discriminate between Poisson INAR(1) and INARCH(1) models. Furthermore, the question is considered if the index of dispersion could be used to test the null of a Poisson INARCH(1) model against the alternative of an INARCH(1) model with additional conditional overdispersion.     

Diagnostic Tests of Cross‐section Independence for Limited Dependent Variable Panel Data Models*

This article considers the problem of testing for cross‐section independence in limited dependent variable panel data models. It derives a Lagrangian multiplier (LM) test and shows that in terms of generalized residuals of Gourieroux et al. (1987) it reduces to the LM test of Breusch and Pagan (1980) . Because of the tendency of the LM test to over‐reject in panels with large N (cross‐section dimension), we also consider the application of the cross‐section dependence test (CD) proposed by Pesaran (2004) . In Monte Carlo experiments it emerges that for most combinations of N and T the CD test is correctly sized, whereas the validity of the LM test requires T (time series dimension) to be quite large relative to N. We illustrate the cross‐sectional independence tests with an application to a probit panel data model of roll‐call votes in the US Congress and find that the votes display a significant degree of cross‐section dependence.     

Unit root tests in panel data: asymptotic and finite-sample properties

We consider pooling cross-section time series data for testing the unit root hypothesis. The degree of persistence in individual regression error, the intercept and trend coefficient are allowed to vary freely across individuals. As both the cross-section and time series dimensions of the panel grow large, the pooled t-statistic has a limiting normal distribution that depends on the regression specification but is free from nuisance parameters. Monte Carlo simulations indicate that the asymptotic results provide a good approximation to the test statistics in panels of moderate size, and that the power of the panel-based unit root test is dramatically higher, compared to performing a separate unit root test for each individual time series.     

The multiple filter test for change point detection in time series

A framework for the detection of change points in the expectation in sequences of random variables is presented. Specifically, we investigate time series with general distributional assumptions that may show an unknown number of change points in the expectation occurring on multiple time scales and that may also contain change points in other parameters. To that end we propose a multiple filter test (MFT) that tests the null hypothesis of constant expectation and, in case of rejection of the null hypothesis, an algorithm that estimates the change points.The MFT has three important benefits. First, it allows for general distributional assumptions in the underlying model, assuming piecewise sequences of i.i.d. random variables, where also relaxations with regard to identical distribution or independence are possible. Second, it uses a MOSUM type statistic and an asymptotic setting in which the MOSUM process converges weakly to a functional of a Brownian motion which is then used to simulate the rejection threshold of the statistical test. This approach enables a simultaneous application of multiple MOSUM processes which improves the detection of change points that occur on different time scales. Third, we also show that the method is practically robust against changes in other distributional parameters such as the variance or higher order moments which might occur with or even without a change in expectation. A function implementing the described test and change point estimation is available in the R package MFT.     

转型升级期中小企业面临的问题与应对策略

发展新兴产业、加快自主创新、推进中小企业产业转型是实现转型发展的战略选择。现阶段我国中小企业已进入转型升级提升水平的新时期,但宏观经济运行中仍然存在很多不稳定不确定因素,长期困扰中小企业发展的深层次矛盾依然存在,促进中小企业发展要有新思路、新策略。应实行差异化发展战略,发挥独特优势在市场竞争中谋取一席之地;大力推进中小企业品牌建设,提升中小企业品牌综合竞争力;激活中小企业财务战略,提升可持续发展能力和创造长久价值的能力;拓展中小企业供应链融资服务,在服务模式上寻求新突破;从健全机制、配套政策、落实担保入手,促进中小企业集合债券健康发展。     

Testing conditional independence via empirical likelihood

We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis and a sequence of Pitman local alternatives. We also show that the tests possess an asymptotic optimality property in terms of average power. Simulations suggest that the tests are well behaved in finite samples. Applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear Granger causality test fails to detect.