Wild-bootstrapped variance-ratio test for autocorrelation in the presence of heteroskedasticity

The Breusch–Godfrey LM test is one of the most popular tests for autocorrelation. However, it has been shown that the LM test may be erroneous when there exist heteroskedastic errors in a regression model. Recently, remedies have been proposed by Godfrey and Tremayne [9] and Shim et al. [21]. This paper suggests three wild-bootstrapped variance-ratio (WB-VR) tests for autocorrelation in the presence of heteroskedasticity. We show through a Monte Carlo simulation that our WB-VR tests have better small sample properties and are robust to the structure of heteroskedasticity.     

A residual-based test for autocorrelation in quantile regression models

Quantile regression (QR) models have been increasingly employed in many applied areas in economics. At the early stage, applications in the QR literature have usually used cross-sectional data, but the recent development has seen an increase in the use of QR in both time-series and panel data sets. However, testing for possible autocorrelation, especially in the context of time-series models, has received little attention. As a rule of thumb, one might attempt to apply the usual Breusch–Godfrey LM test to the residuals of a baseline QR. In this paper, we demonstrate analytically and by Monte Carlo simulations that such an application of the LM test can result in potentially large size distortions, especially in either low or high quantiles. We then propose a correct test (named the QF test) for autocorrelation in QR models, which does not suffer from size distortion. Monte Carlo simulations demonstrate that the proposed test performs fairly well in finite samples, across either different quantiles or different underlying error distributions.     

Lagrange multiplier unit root test in the presence of a break in the innovation variance

We show that the Lagrange multiplier (LM) unit root test exhibits size distortions when a break in the innovation variance exists but is ignored. We develop a modified LM unit root test that is based on a generalized least-squares transformation of the original series. The asymptotic null distribution of the new modified LM unit root test is derived. Finite-sample simulation evidence shows that the modified LM unit root test maintains its size and has reasonable power against the trend stationary alternative.     

A test for the parametric form of the variance function in a partial linear regression model

We consider the problem of testing for a parametric form of the variance function in a partial linear regression model. A new test is derived, which can detect local alternatives converging to the null hypothesis at a rate n^-1/2$n^{-1/2}$ and is based on a stochastic process of the integrated variance function. We establish weak convergence to a Gaussian process under the null hypothesis, fixed and local alternatives. In the special case of testing for homoscedasticity the limiting process is a scaled Brownian bridge. We also compare the finite sample properties with a test based on an L²$L^2$-distance, which was recently proposed by You and Chen [2005. Testing heteroscedasticity in partially linear regression models. Statist. Probab. Lett. 73, 61–70].     

Doubly robust point and variance estimation in the presence of imputed survey data

Imputation is often used in surveys to treat item nonresponse. It is well known that treating the imputed values as observed values may lead to substantial underestimation of the variance of the point estimators. To overcome the problem, a number of variance estimation methods have been proposed in the literature, including resampling methods such as the jackknife and the bootstrap. In this paper, we consider the problem of doubly robust inference in the presence of imputed survey data. In the doubly robust literature, point estimation has been the main focus. In this paper, using the reverse framework for variance estimation, we derive doubly robust linearization variance estimators in the case of deterministic and random regression imputation within imputation classes. Also, we study the properties of several jackknife variance estimators under both negligible and nonnegligible sampling fractions. A limited simulation study investigates the performance of various variance estimators in terms of relative bias and relative stability. Finally, the asymptotic normality of imputed estimators is established for stratified multistage designs under both deterministic and random regression imputation. The Canadian Journal of Statistics 40: 259–281; 2012 © 2012 Statistical Society of Canada     

Inferences of variance function - a parametric robust way

Tsou (2003a) proposed a parametric procedure for making robust inference for mean regression parameters in the context of generalized linear models. This robust procedure is extended to model variance heterogeneity. The normal working model is adjusted to become asymptotically robust for inference about regression parameters of the variance function for practically all continuous response variables. The connection between the novel robust variance regression model and the estimating equations approach is also provided.     

Bootstrap test for a structural break under possible heteroscedasticity

In this article, we consider the Wald test statistic for testing equality between the sets of regression coefficients in two linear regression models when the disturbance variances may possibly be unequal. This test can be also used as a test for a structural break. However, it is well known that the test based on the Wald test statistic suffers from severe size distortion in small sample when the disturbance variances of the two regression models are unequal. Our simulation results show that substantial improvements are made when the bootstrap methods are applied.     

Testing the disturbance variance after a pre-test for a linear hypothesis on coefficients in a linear regression

In this paper, we examine the sampling performance of a two-stage test which consists of a pre-test for a linear hypothesis on regression coeffiecients followed by a main-test for a disturbance variance in a linear regression. It is shown that the actual size of the two-stage test can be well-controlled around the normal size if the suggested sizes presented in this paper are used in the pre-test. It is also shown that the two-stage test when the suggested sizes are used in the preferable to the usual test for the disturbance variable which incorporates no pre-test in terms of the power.     

Modified tests for change points in variance in the possible presence of mean breaks

This paper considers the detection problem of variance changes for the time series involving abrupt and/or smooth breaks in mean. Often, in these situations, the tests of choice are based on cumulative sum of squares statistics. We show that the test statistics are not robust in the presence of broken mean and their sizes suffer severe distortions. The adjusted residual-based method is then proposed to eliminate these deficiencies and makes a significant improvement. Finally, simulation results confirm the validity of these modified test statistics, and an empirical data analysis using some stock price series from the Shanghai Stock Exchange is reported.     

A Cauchy estimator test for autocorrelation

This article presents a new test for serial correlation in an observed stationary time series. Rather than using the traditional portmanteau tests based on the sample autocorrelation function, we propose a test based on the Cauchy estimator of correlation. A goodness-of-fit statistic for fitted autoregressive moving average models is also derived and the asymptotic distribution of this statistic is quantified. The test can be employed using either this asymptotic distribution or by using Monte-Carlo quantiles. The small sample behaviour is studied via simulation and the Monte-Carlo-based test seems to be more precise. The method is demonstrated on monthly asset returns for Facebook, Incorporated.     

On the power of the durbin-watson test under high autocorrelation

In the linear regression model without an intercept, it is known that the limiting power of the Durbin-Watson test (as correlation among errors increases) equals either one or zero, depending on the underlying regressor matrix. This paper considers the limiting power in the model with an intercept, and proves that it will never equal one or zero.     

A test for the variance residual life

In this paper we develop a test based on the empirical distribution function for the alternative representing 'decreasing variance residual life1 property. The test is consistent with asymptotically normal test statistic and is shown to perform well in the Pitman's asymptotic relative efficiency sense.     

基于傅里叶变换的含确定性趋势结构突变的协整回归模型和不等方差检验

一般来说,数据结构突变点的位置是未知的或突变点的存在性无法准确预知。Enders和Lee（2009,2011）[1][2]证明低频的傅里叶变换（Fourier transformation）就能较精确地处理单位根检验中的数据结构突变（异质结构突变）问题。本文在协整模型框架下,使用傅里叶变换处理协整模型确定性趋势项下的结构突变,考察了协整模型参数的收敛速度,并重新推导了不等方差检验。傅里叶近似项参数的收敛速度为： 。使用蒙特卡洛模拟表明：在缺乏结构突变的先验知识的情况下,使用低频的傅里叶变换能较好地处理协整回归中的确定性趋势的结构突变的问题,显著提高协整向量的估计效率。使用改进后的方法,重新研究了中国股市和国际股市联动关系的密切程度,实证结果更为强烈地支持：中国投资者投资于澳大利亚市场分散风险的收益显著弱于投资其他国际市场。     

A robust test for the homogeneity of scales

Many robust tests for the equality of variances have been proposed recently. Brown and Forsythe (1974) and Layard (1973) review some of the well-known procedures and compare them by simulation methods. Brown and Forsythe’s alternative formulation of Levene’s test statistic is found to be quite robust under certain nonnormal distributions. The performance of the methods, however, suffers in the presence of heavy tailed distributions such as the Cauchy distribution.

In this paper, we propose and study a simple robust test. The results obtained from the Monte Carlo study compare favorably with those of the existing procedures.     

Asymptotic properties of kruskal-wallis test and friedman test in the analysis of variance models with random effects

In this paper, asymptotic properties of the Kruskal-Wallis test in the one-way analysis of variance model and that of the Friedman test in the two-way classification model are investigated under alternatives when the treatment effects are random. It is shown that the asymptotic distribution of each statistic is the same as a mixture of central chi-squared variables. Asymptotic comparisons of the tests with respect to their parametric competitors are also performed     

A test for the presence of conditional heteroskedasticity within arch-m framework

This paper is concerned with testing the presence of ARCH within the ARCH-M model as the alternative hypothesis. Standard testing procedures are inapplicable since a nuisance parameter is unidentified under the null hypothesis. Nonetheless, the diagnostic tests for the presence of the conditional variance is very important since any misspecification in the conditional variance equation leads to inconsistent estimates of the conditional mean parameters. BTo resolve the problem of unidentified nuisance parameter, 'Ne apply Davies' approach, and investigate its finite sample performance through a Monte Carlo study.     

The rank von neumann test as a test for autocorrelation in regression models

The rank Von Neumann test, which performs extremely well as a test for serial correlation in raw data, is here compared with the Durbin-Watson and Geary tests as a test for autocorrelation in regression residuals. The test convincingly outperforms the Geary test but it is less robust than the Durbin-Watson test     

A test for the presence of conditional heteroskedasticity within arch-m framework

This paper is concerned with testing the presence of ARCH within the ARCH-M model as the alternative hypothesis. Standard testing procedures are inapplicable since a nuisance parameter is unidentified under the null hypothesis. Nonetheless, the diagnostic tests for the presence of the conditional variance is very important since any misspecification in the conditional variance equation leads to inconsistent estimates of the conditional mean parameters. BTo resolve the problem of unidentified nuisance parameter, ‘Ne apply Davies’ approach, and investigate its finite sample performance through a Monte Carlo study.     

Limit theory for moderate deviations from a unit root with a break in variance

Consider the model y_t = ρ_ny_{t ? 1} + u_t, t = 1, …, n with ρ_n = 1 + c/k_n and u_t = σ₁?_tI{t ? k₀} + σ₂?_tI{t > k₀}, where c is a non-zero constant, σ₁ and σ₂ are two positive constants, I{ · } denotes the indicator function, k_n is a sequence of positive constants increasing to ∞ such that k_n = o(n), and {?_t, t ? 1} is a sequence of i.i.d. random variables with mean zero and variance one. We derive the limiting distributions of the least squares estimator of ρ_n and the t-ratio of ρ_n for the above model in this paper. Some pivotal limit theorems are also obtained. Moreover, Monte Carlo experiments are conducted to examine the estimators under finite sample situations. Our theoretical results are supported by Monte Carlo experiments.