Choosing a base for the BLUS vector

A mechanism is proposed for identifying the 'optimal' base for the BLUS residual vector, which involves discarding from estimation the potentially disruptive high leverage observations of the regressor matrix.     

Constructing smooth tests without estimating the eigenpairs of the limiting process

Based on the well known Karhunen–Loève expansion, it can be shown that many omnibus tests lack power against “high frequency” alternatives. The smooth tests of  Neyman (1937) may be employed to circumvent this power deficiency problem. Yet, such tests may be difficult to compute in many applications. In this paper, we propose a more operational approach to constructing smooth tests. This approach hinges on a Fourier representation of the postulated empirical process with known Fourier coefficients, and the proposed test is based on the normalized principal components associated with the covariance matrix of finitely many Fourier coefficients. The proposed test thus needs only standard principal component analysis that can be carried out using most econometric packages. We establish the asymptotic properties of the proposed test and consider two data-driven methods for determining the number of Fourier coefficients in the test statistic. Our simulations show that the proposed tests compare favorably with the conventional smooth tests in finite samples.     

Local Asymptotic Power of Breitung's Test*

In this article, we derive the local asymptotic power function of the unit root test proposed by Breitung [Journal of Econometrics (2002) Vol. 108, pp. 343–363]. Breitung's test is a non‐parametric test and is free of nuisance parameters. We compare the local power curve of the Breitungs’ test with that of the Dickey–Fuller test. This comparison is in fact a quantification of the loss of power that one has to accept when applying a non‐parametric test.     

Stationary bootstrapping for common mean change detection in cross-sectionally dependent panels

Stationary bootstrapping is applied to a CUSUM test for common mean break detection in cross-sectionally correlated panel data. Asymptotic null distribution of the bootstrapped test is derived, which is the same as that of the original CUSUM test depending on cross-sectional correlation parameter. A bootstrap test using the CUSUM test with bootstrap critical values is proposed and its asymptotic validity is proved. Finite sample Monte-Carlo simulation shows that the proposed test has reasonable size while other existing tests have severe size distortion under cross-section correlation. The simulation also shows good power performance of the proposed test against non-cancelling mean changes. The simulation also shows that the theoretically justified stationary bootstrapping CUSUM test has comparable size and power relative to other, theoretically unjustified, moving block or tapered block bootstrapping CUSUM tests.     

A study of several new and existing tests for heteroscedasticity in the general linear model1

Several optimum non-parametric tests for heteroscedasticity are proposed and studied along with the tests introduced in the literature in terms of power and robustness properties. It is found that all tests are reasonably robust to the Ordinary Least Squares (OLS) residual estimates, number and character of the regressors. Only a few are robust to both the distributional and independence assumptions about the errors. The power of tests can be improved with the OLS residual estimates, the increased sample size and the variability of the regressors. It can be substantially reduced if the observations are not normally distributed, and may increase or decrease if the errors are dependent. Each test is optimum to detect a specific form of heteroscedasticity and a serious power loss may occur if the underlying heteroscedasticity assumption in the data generation deviates from it.     

A moment-based test for extreme-value dependence

This paper proposes a new rank-based test of extreme-value dependence. The procedure is based on the first three moments of the bivariate probability integral transform of the underlying copula. It is seen that the test statistic is asymptotically normal and its finite- and large-sample variance are calculated explicitly. Consistent plug-in estimators for the variance are proposed, and a fast algorithm for their computation is given. Although it is shown via counterexamples that no test based on the probability integral transform can be consistent, the proposed procedure achieves good power against common alternatives, both in finite samples and asymptotically.     

Inference on the cointegration rank in fractionally integrated processes

For univariate time series we suggest a new variant of efficient score tests against fractional alternatives. This test has three important merits. First, by means of simulations we observe that it is superior in terms of size and power in some situations of practical interest. Second, it is easily understood and implemented as a slight modification of the Dickey–Fuller test, although our score test has a limiting normal distribution. Third and most important, our test generalizes to multivariate cointegration tests just as the Dickey–Fuller test does. Thus it allows to determine the cointegration rank of fractionally integrated time series. It does so by solving a generalized eigenvalue problem of the type proposed by Johansen (J. Econ. Dyn. Control 12 (1988) 231). However, the limiting distribution of the corresponding trace statistic is χ², where the degrees of freedom depend only on the cointegration rank under the null hypothesis. The usefulness of the asymptotic theory for finite samples is established in a Monte Carlo experiment.     

自相关检验方法的检验功效研究

研究目标:探究DW检验和LM检验的检验功效及其渐近性。研究方法:运用蒙特卡罗模拟实验方法结合相关影响因素对两种检验方法进行分析与比较。影响因素包括样本容量、解释变量的随机性及自相关性、随机误差项的自相关程度以及分布形态。研究发现:DW和LM检验功效与样本容量和随机误差项的自相关程度正相关,与解释变量的自相关程度负相关;解释变量的随机性对DW和LM检验功效无显著影响;误差项的几种常见分布形态的变化对DW和LM检验功效的影响可以忽略;在误差项存在一阶自相关的情况下,DW检验效果优于LM检验效果。研究创新:以DW检验和LM检验的假设条件为出发点,探究比较不同条件下自相关检验方法的检验功效。研究价值:在实证研究背景下为有效地选择自相关检验方法提供借鉴参考。     

A Panel CUSUM Test of the Null of Cointegration*

This paper proposes a simple residual‐based panel CUSUM test of the null hypothesis of cointegration. The test has a limiting normal distribution that is free of nuisance parameters, it is robust to heteroskedasticity and it allows for mixtures of cointegrated and spurious alternatives. Our Monte Carlo results suggest that the test has small‐size distortions and reasonable power. In our empirical application to international R&D spillovers, we present evidence suggesting that total factor productivity is heterogeneously cointegrated with foreign and domestic R&D capital stocks.     

Enabling or “real” power and influence in leadership

On the theme of personal development, this conceptual article aims to provoke thought about power and influence in leadership by means of a short excursion into character depictions in J.R.R. Tolkien's The Lord of the Rings ( 1966 ). It is said of mythopoeic literature, the genre of Tolkien's work, that the very simplicity of the lens “pares away distractions,” “opens the way to unexpected connections, … [and] draws attention to alternative modes of being and thinking” (Greene, 1994 , p. 457). Taking the liberty of perceived applicability of Tolkien's literary genius to motifs on leadership, this article provokes thinking on what constitutes “real” power and influence in leadership. It is contended that demonstrating real power and influence in leadership lies not in coercive tactics of wielding power over others but in withholding usurping power to work with and enable others to achieve worthwhile ends. Three suggested markers of enabling or real power and influence in leadership are explored. Each one contains an element of paradox. The proposed markers suggest, in turn, that enabling or real power and influence does not usurp but serves, that it sublimates self‐interest for the interests of others and the intended goal, and that it positions for growth for the self and others and fosters true engagement in leadership. The article offers some empirical evidence as to the efficacy of the proposed markers for effective leadership and suggests a further research strategy to test the proposed markers empirically.     

A consistent nonparametric test for nonlinear causality—Specification in time series regression

Since the pioneering work by Granger (1969), many authors have proposed tests of causality between economic time series. Most of them are concerned only with “linear causality in mean”, or if a series linearly affects the (conditional) mean of the other series. It is no doubt of primary interest, but dependence between series may be nonlinear, and/or not only through the conditional mean. Indeed conditional heteroskedastic models are widely studied recently. The purpose of this paper is to propose a nonparametric test for possibly nonlinear causality. Taking into account that dependence in higher order moments are becoming an important issue especially in financial time series, we also consider a test for causality up to the Kth conditional moment. Statistically, we can also view this test as a nonparametric omitted variable test in time series regression. A desirable property of the test is that it has nontrivial power against T^1/2-local alternatives, where T is the sample size. Also, we can form a test statistic accordingly if we have some knowledge on the alternative hypothesis. Furthermore, we show that the test statistic includes most of the omitted variable test statistics as special cases asymptotically. The null asymptotic distribution is not normal, but we can easily calculate the critical regions by simulation. Monte Carlo experiments show that the proposed test has good size and power properties.     

非参数统计视角下的异方差检验设计及其应用

以数据生成过程为导向,探讨了异方差来源的基本类型;依据非参数统计的基本思想,设计了切实可行的Mood方差检验方法与平方秩检验方法,并针对异方差来源类型,分析了相应的检验思路。蒙特卡罗模拟表明,Mood方差检验方法在异方差检验方面具有很高的检验效力;平方秩检验方法在异常经济现象情形下检验效力较低,而在其他情形下检验效力很高。同时,进一步阐释了纠正异方差的基本逻辑。     

An alternative model for the analysis of variance with random effects

The standard model for the analysis of variance with random effects implies, for the case of two independent variables, that single effects must be tested not against the error, but against the interaction mean squares. This causes, in comparison with the fixed effects AV, a considerable loss of test power, particularly for the 2 × 2 table. An alternative modelling of the interaction effect is proposed which completely avoids the loss of power.     

Relative Efficiency of the Fuzzy p-Value Approach to Hypothesis Testing

In missing data problems, it is often the case that there is a natural test statistic for testing a statistical hypothesis had all the data been observed. A fuzzy  p -value approach to hypothesis testing has recently been proposed which is implemented by imputing the missing values in the "complete data" test statistic by values simulated from the conditional null distribution given the observed data. We argue that imputing data in this way will inevitably lead to loss in power. For the case of scalar parameter, we show that the asymptotic efficiency of the score test based on the imputed "complete data" relative to the score test based on the observed data is given by the ratio of the observed data information to the complete data information. Three examples involving probit regression, normal random effects model, and unidentified paired data are used for illustration. For testing linkage disequilibrium based on pooled genotype data, simulation results show that the imputed Neyman Pearson and Fisher exact tests are less powerful than a Wald-type test based on the observed data maximum likelihood estimator. In conclusion, we caution against the routine use of the fuzzy  p -value approach in latent variable or missing data problems and suggest some viable alternatives.     

Bootstrap testing for the null of no cointegration in a threshold vector error correction model

We develop a test for the linear no cointegration null hypothesis in a threshold vector error correction model. We adopt a sup-Wald type test and derive its null asymptotic distribution. A residual-based bootstrap is proposed, and the first-order consistency of the bootstrap is established. A set of Monte Carlo simulations shows that the bootstrap corrects size distortion of asymptotic distribution in finite samples, and that its power against the threshold cointegration alternative is significantly greater than that of conventional cointegration tests. Our method is illustrated with used car price indexes.     

Simulation‐based Finite Sample Linearity Test against Smooth Transition Models*

In this paper, we use Monte Carlo (MC) testing techniques for testing linearity against smooth transition models. The MC approach allows us to introduce a new test that differs in two respects from the tests existing in the literature. First, the test is exact in the sense that the probability of rejecting the null when it is true is always less than or equal to the nominal size of the test. Secondly, the test is not based on an auxiliary regression obtained by replacing the model under the alternative by approximations based on a Taylor expansion. We also apply MC testing methods for size correcting the test proposed by Luukkonen, Saikkonen and Teräsvirta (Biometrika, Vol. 75, 1988, p. 491). The results show that the power loss implied by the auxiliary regression‐based test is non‐existent compared with a supremum‐based test but is more substantial when compared with the three other tests under consideration.     

平滑转移误差修正模型的转移函数选取问题研究

针对非线性平滑转移误差修正模型转移函数选取中存在的统计量极限分布非标准、检验统计量功效较低的问题,本文在推导非线性平滑转移协整检验统计量极限分布的基础上构造了如下转移函数选取步骤。首先,计算F_NST统计量,进行非线性平滑转移协整检验;其次,计算t_EST和t_LST统计量及相依概率P_est和P_lst;最后,比较P_est和P_lst大小并与临界值相比,得出结论。蒙特卡洛仿真模拟结果显示,转移函数选取中各统计量具有良好的功效和势,且转移函数选取中各统计量的功效明显优于其他统计量的功效。实证分析表明我国利率期限结构具有明显的非线性对称调整效应,非线性平滑转移误差修正模型中转移函数应该选取指数函数。     

Raised conditional level of significance for the 2 × 2-table when testing the equality of two probabilities

In this paper it is to be shown that F isher's non-randomizing exact test for 2 × 2-tables, which is a conditional test, can by simple means be changed into an unconditional test using raised levels of significance; not seldom, especially for not too large samples, the level of significance can be doubled. This leads in many cases to a considerable increase of power of the test. A table with raised levels has been prepared up to sample sizes of 50 and a rule of thumb, which can be used if this table is not available, has been developEd.     

Wavelet analysis of change-points in a non-parametric regression with heteroscedastic variance

In this paper we develop wavelet methods for detecting and estimating jumps and cusps in the mean function of a non-parametric regression model. An important characteristic of the model considered here is that it allows for conditional heteroscedastic variance, a feature frequently encountered with economic and financial data. Wavelet analysis of change-points in this model has been considered in a limited way in a recent study by Chen et al. (2008) with a focus on jumps only. One problem with the aforementioned paper is that the test statistic developed there has an extreme value null limit distribution. The results of other studies have shown that the rate of convergence to the extreme value distribution is usually very slow, and critical values derived from this distribution tend to be much larger than the true ones. Here, we develop a new test and show that the test statistic has a convenient null limit N(0,1) distribution. This feature gives the proposed approach an appealing advantage over the existing approach. Another attractive feature of our results is that the asymptotic theory developed here holds for both jumps and cusps. Implementation of the proposed method for multiple jumps and cusps is also examined. The results from a simulation study show that the new test has excellent power and the estimators developed also yield very accurate estimates of the positions of the discontinuities.     

The analysis of ranked data in blocked factorial experiments

A non-parametric method for the analysis of blocked factorial experiments, based on ranking within blocks, is proposed and shown to be equivalent to partitioning Friedman's test statistic into a set of contrasts reflecting polynomial components of the main effects and interaction. A slightly modified version of the procedure is suggested to partially overcome the problem of loss of power to detect one component when the model includes other components. This alternative procedure is shown to be equivalent to applying a standard normal theory analysis of variance to the ranks. The null distributions and power comparisons are investigated using simulation methods, and it is shown that the non-parametric methods are almost as powerful as the analysis of variance. Received: February 1999