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。     

Two-stage rank estimation of quantile index models

This paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable. This class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction, thus allowing for very general forms of conditional heteroscedasticity. A two-stage approach is adopted to estimate the relevant parameters. In the first stage the conditional quantile function is estimated nonparametrically by the local polynomial estimator discussed in Chaudhuri (Journal of Multivariate Analysis 39 (1991a) 246–269; Annals of Statistics 19 (1991b) 760–777) and Cavanagh (1996, Preprint). In the second stage, the monotonicity of the quantile function is exploited to estimate the parameters of interest by maximizing a rank-based objective function. The proposed estimator is shown to have desirable asymptotic properties and can then also be used for dimensionality reduction or to estimate the unknown structural function in the context of a transformation model.     

Estimating a class of triangular simultaneous equations models without exclusion restrictions

This paper provides a control function estimator to adjust for endogeneity in the triangular simultaneous equations model where there are no available exclusion restrictions to generate suitable instruments. Our approach is to exploit the dependence of the errors on exogenous variables (e.g. heteroscedasticity) to adjust the conventional control function estimator. The form of the error dependence on the exogenous variables is subject to restrictions, but is not parametrically specified. In addition to providing the estimator and deriving its large-sample properties, we present simulation evidence which indicates the estimator works well.     

The effectiveness of index futures hedging in emerging markets during the crisis period of 2008-2010: Evidence from South Africa

This article provides an assessment of the comparative effectiveness of four econometric methods in estimating the optimal hedge ratio in an emerging equity market, particularly the South African equity and futures markets. The article bases the effectiveness of hedging on volatility reduction and minimization of the coefficient of variation of hedged returns as well as risk-aversion-based utility maximization. The empirical analysis shows that the vector error-correction method and multivariate generalized autoregressive conditional heteroscedasticity methods are most effective over relatively long horizon, weekly and monthly hedging periods.     

Pushing subjects beyond rationality with more alternatives in experimental auctions

The use of experimental economics in valuation of market and nonmarket goods has grown over the past few years. The ability of experimental auctions (EUs) to reveal consumer preferences and their malleability has been praised in previous literature. Because of the high cost of conducting EUs, researchers usually present multiple products to participants, determining how many products to present has no clear guideline. The results of this study show that subjects do not value products the same way across different number of options offered to them. The main indicator is the increasing variance in responses for a benchmark product when more products are available. With an econometric specification allowing for heteroscedasticity as a function of the number of product offerings, the results indicate that the number of goods available for bidding is not to be taken as a trivial task in experimental design for value elicitation.     

异方差和多重共线性的影响——模拟蒙特卡洛

通过蒙特卡洛实验,在计量经济学软件R中实现数据生成过程,当古典线性回归模型基本假定中的同方差假定和无多重共线性假定被违背时,参数的显著性检验是否依然有效。     

HETEROSCEDASTICITY OR PRODUCTION RISK? A SYNTHETIC VIEW

Two veins of literature, namely, production risk literature and stochastic frontier analysis, are examined. Both fields are concerned of output variation; the former due to exogenous shocks, the latter due inefficiency. By covering the literature from both the fields, this review suggests that the concept of heteroscedasticity can be utilized to build a synthesis between these mainly separate branches of literature. However, the synthetic approach brings a challenge how to differentiate between different sources of output variation. This challenge is identified as the main obstacle to meaningfully combine the two approaches.     

Heteroscedasticity diagnostics for <Emphasis Type="Italic">t</Emphasis> linear regression models

The t regression models provide a useful extension of the normal regression models for datasets involving errors with longer-than-normal tails. Homogeneity of variances (if they exist) is a standard assumption in t regression models. However, this assumption is not necessarily appropriate. This paper is devoted to tests for heteroscedasticity in general t linear regression models. The asymptotic properties, including asymptotic Chi-square and approximate powers under local alternatives of the score tests, are studied. Based on the modified profile likelihood (Cox and Reid in J R Stat Soc Ser B 49(1):1–39, 1987), an adjusted score test for heteroscedasticity is developed. The properties of the score test and its adjustment are investigated through Monte Carlo simulations. The test methods are illustrated with land rent data (Weisberg in Applied linear regression. Wiley, New York, 1985). The project supported by NSFC 10671032, China, and a grant (HKBU2030/07P) from the Grant Council of Hong Kong, Hong Kong, China.     

Testing under a special form of heteroscedasticity

In the presence of heteroscedasticity, conventional standard errors (which assume homoscedasticity) can be biased up or down. The most common form of heteroscedasticity leads to conventional standard errors that are too small. In this study, we discuss the conditions under which conventional standard errors are too large. In such settings, standard tests of heteroscedasticity may fail and leave the heteroscedasticity undetected. This is particularly problematic as power gains can be achieved when testing for the causal effect in such settings.     

The ZD-GARCH model: A new way to study heteroscedasticity

This paper proposes a first-order zero-drift GARCH (ZD-GARCH(1, 1)) model to study conditional heteroscedasticity and heteroscedasticity together. Unlike the classical GARCH model, the ZD-GARCH(1, 1) model is always non-stationary regardless of the sign of the Lyapunov exponent ${\gamma }_0$, but interestingly it is stable with its sample path oscillating randomly between zero and infinity over time when ${\gamma }_0=0$. Furthermore, this paper studies the generalized quasi-maximum likelihood estimator (GQMLE) of the ZD-GARCH(1, 1) model, and establishes its strong consistency and asymptotic normality. Based on the GQMLE, an estimator for ${\gamma }_0$, a $t$-test for stability, a unit root test for the absence of the drift term, and a portmanteau test for model checking are all constructed. Simulation studies are carried out to assess the finite sample performance of the proposed estimators and tests. Applications demonstrate that a stable ZD-GARCH(1, 1) model is more appropriate than a non-stationary GARCH(1, 1) model in fitting the KV-A stock returns in Francq and Zakoïan (2012).