Testing Alphas in Conditional Time-Varying Factor Models With High-Dimensional Assets

ABSTRACT

For conditional time-varying factor models with high-dimensional assets, this article proposes a high-dimensional alpha (HDA) test to assess whether there exist abnormal returns on securities (or portfolios) over the theoretical expected returns. To employ this test effectively, a constant coefficient test is also introduced. It examines the validity of constant alphas and factor loadings. Simulation studies and an empirical example are presented to illustrate the finite sample performance and the usefulness of the proposed tests. Using the HDA test, the empirical example demonstrates that the FF three-factor model is better than CAPM in explaining the mean-variance efficiency of both the Chinese and U.S. stock markets. Furthermore, our results suggest that the U.S. stock market is more efficient in terms of mean-variance efficiency than the Chinese stock market. Supplementary materials for this article are available online.     

A Generalized Bayes Rule for Prediction

In the case of prior knowledge about the unknown parameter, the Bayesian predictive density coincides with the Bayes estimator for the true density in the sense of the Kullback-Leibler divergence, but this is no longer true if we consider another loss function. In this paper we present a generalized Bayes rule to obtain Bayes density estimators with respect to any α-divergence, including the Kullback-Leibler divergence and the Hellinger distance. For curved exponential models, we study the asymptotic behaviour of these predictive densities. We show that, whatever prior we use, the generalized Bayes rule improves (in a non-Bayesian sense) the estimative density corresponding to a bias modification of the maximum likelihood estimator. It gives rise to a correspondence between choosing a prior density for the generalized Bayes rule and fixing a bias for the maximum likelihood estimator in the classical setting. A criterion for comparing and selecting prior densities is also given.     

The Whittle Estimator for Strongly Dependent Stationary Gaussian Fields

In this article we generalize results on the asymptotic behaviour of the Whittle estimator for certain stationary Gaussian long range dependent fields. These results have been established in the one-dimensional case under very general conditions. They require controlling the estimation bias and also giving convergence theorems for certain quadratic forms of the observations. In the multidimensional setting, our main interest will be controlling the bias. This can be done for d ≤ 3 using taper functions, and, depending on the shape of the singularity, also introducing certain regularizing functions. In this last case, however, the estimator will no longer be efficient. We also present certain partial results concerning the convergence to a limiting Gaussian distribution of the associated quadratic forms.     

Empirical transform estimation for indexed stochastic models

We present a method for estimating the parameters in indexed stochastic models via a least squares approach based on empirical transforms. Asymptotic approximations are derived for the distribution of the resulting estimators. An explicit expression for the mean-squared error provides a natural way of selecting the transform variable, and a numerical example illustrates the performance of the resulting method. A common finding, which we term 'diagonal optimization', occurs when multiparameter models are fitted by using transforms. Diagonal optimization arises when optimal performance results from equating the elements of the transform vector, and we provide a heuristic explanation of why this occurs.     

Fractal analysis of surface roughness by using spatial data

We develop fractal methodology for data taking the form of surfaces. An advantage of fractal analysis is that it partitions roughness characteristics of a surface into a scale-free component (fractal dimension) and properties that depend purely on scale. Particular emphasis is given to anisotropy where we show that, for many surfaces, the fractal dimension of line transects across a surface must either be constant in every direction or be constant in each direction except one. This virtual direction invariance of fractal dimension provides another canonical feature of fractal analysis, complementing its scale invariance properties and enhancing its attractiveness as a method for summarizing properties of roughness. The dependence of roughness on direction may be explained in terms of scale rather than dimension and can vary with orientation. Scale may be described by a smooth periodic function and may be estimated nonparametrically. Our results and techniques are applied to analyse data on the surfaces of soil and plastic food wrapping. For the soil data, interest centres on the effect of surface roughness on retention of rain-water, and data are recorded as a series of digital images over time. Our analysis captures the way in which both the fractal dimension and the scale change with rainfall, or equivalently with time. The food wrapping data are on a much finer scale than the soil data and are particularly anisotropic. The analysis allows us to determine the manufacturing process which produces the smoothest wrapping, with least tendency for micro-organisms to adhere.     

Higher‐Order Improvements of a Computationally Attractive k‐Step Bootstrap for Extremum Estimators

This paper establishes the higher‐order equivalence of the k‐step bootstrap, introduced recently by Davidson and MacKinnon (1999), and the standard bootstrap. The k‐step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear extremum estimators, such as generalized method of moment and maximum likelihood estimators. The paper also extends results of Hall and Horowitz (1996) to provide new results regarding the higher‐order improvements of the standard bootstrap and the k‐step bootstrap for extremum estimators (compared to procedures based on first‐order asymptotics). The results of the paper apply to Newton‐Raphson (NR), default NR, line‐search NR, and Gauss‐Newton k‐step bootstrap procedures. The results apply to the nonparametric iid bootstrap and nonoverlapping and overlapping block bootstraps. The results cover symmetric and equal‐tailed two‐sided t tests and confidence intervals, one‐sided t tests and confidence intervals, Wald tests and confidence regions, and J tests of over‐identifying restrictions.     

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.     

Improving Ratio Estimators of Second Order Point Process Characteristics

Ripley's K function, the L function and the pair correlation function are important second order characteristics of spatial point processes. These functions are usually estimated by ratio estimators, where the numerators are Horvitz–Thompson edge corrected estimators and the denominators estimate the intensity or its square. It is possible to improve these estimators with respect to bias and estimation variance by means of adapted distance dependent intensity estimators. Further improvement is possible by means of refined estimators of the square of intensity. All this is shown by statistical analysis of simulated Poisson, cluster and hard core processes.     

On a generalization of the test of endogeneity in a two stage least squares estimation

In situations that the predictors are correlated with the error term, we propose a bridge estimator in the two-stage least squares estimation. We apply this estimator to overcome the multicollinearity and sparsity of the explanatory variables, when the endogeneity problem is present.The proposed estimator was applied to modify the Durbin-Wu-Hausman (DWH) test of endogeneity in the presence of multicollinearity. To compare our modified test with the existing DWH for detection of an endogenous problem in multi-collinear data, some numerical assessments are carried out. The numerical results showed that the proposed estimators and the suggested test perform better for the multi-collinear data. Finally, a genetical data set is applied for illustration the our results by estimating the coefficients parameters in the presence of endogeneity and multicollinearity.     

地方政府竞争对环境污染影响效应的实证研究

基于中国1998—2012年省际动态面板数据和通过改进后熵值法计算得到的环境污染综合指数,运用系统广义矩估计(GMM)实证地方政府竞争对环境污染的影响效应。结果表明:地方政府竞争对环境污染呈显著的正向影响,即地方政府竞争显著增加了地区污染排放,降低了区域环境质量。而经济发展水平、资本存量与环境污染均呈倒“U”形关系,经济发展短期会带来环境污染,长远则有助于环境质量的改善;资本存量决定了一个地方的投资能力,投资速度过猛或滞后均会给环境造成影响。认为,应从改革传统政绩考核办法、确立地方政府环境责任制度等方面优化地方政府竞争机制;并进一步加大地方政府环境治理投资力度,着力解决环境污染问题,从而提高环境质量。