A note on the distribution of mean square error of forecasting

Simulation has been a very important and widely used method in the study of misspecification or order determination in time series analysis. Mean square error of forecasting (MSEF) has been a major criterion for comparing the performance of different models. In simulation studies, standard deviations of MSEF's are calculated from the computed values of the MSEF's, In this note, the distribution of MSEF from simulation studies is established. Exact variance of the MSEF can be obtained from the prespecified values of the model selected for simulation. This variance should be a more appropriate criterion for evaluating the performance between models.     

Overnight and Daytime Stock-Return Dynamites on the London Stock Exchange: The Impacts of “Big Bang” and the 1987 Stock-Market Crash

We explore the time series properties of stock returns on the London Stock Exchange around the 1986 market restructuring (Big Bang) and the 1987 stock-market crash using a modified generalized autoregressive conditional heteroscedasticity model. Using this general dynamic model, which allows (a) intradaily returns to have different impacts and persistence on stock-return volatility, (b) return effects on volatility to be asymmetric, and (c) intradaily returns to follow conditional distributions with different fourth moments, we uncover important changes in return dynamics and conditional fourth moments following Big Bang and the 1987 crash not reported before.     

Procedures for Selecting Good Exponential Populations

Suppose exponential populations π _i with parameters (μ_i , σ_i ) (i = 1,2,…,k) are given. This article discusses how to select “good” populations in the sense of [Lam (1986 Lam, K. 1986. A new procedure for selecting good populations. Biometrika, 73(1): 201–206. [Crossref], [Web of Science ®] , [Google Scholar]). A new procedure for selecting good populations. Biometrika 73(1):201–206]. Depending on whether the σ _i 's are known or unknown, several one-stage and a two-stage procedure of selection are proposed. The two-stage procedure can be replaced by a one-stage procedure if the second-stage sample is proved intangible. An attracting feature of these procedures is that they need no new statistical tables to implement.     

Dynamic Identification of Dynamic Stochastic General Equilibrium Models

This paper studies dynamic identification of parameters of a dynamic stochastic general equilibrium model from the first and second moments of the data. Classical results for dynamic simultaneous equations do not apply because the state space solution of the model does not constitute a standard reduced form. Full rank of the Jacobian matrix of derivatives of the solution parameters with respect to the parameters of interest is necessary but not sufficient for identification. We use restrictions implied by observational equivalence to obtain two sets of rank and order conditions: one for stochastically singular models and another for nonsingular models. Measurement errors, mean, long‐run, and a priori restrictions can be accommodated. An example is considered to illustrate the results.     

爱和艺术的可见性与不可见性——论歌德的《亲和力》和本雅明对“无性美学”的批判

在<亲和力>这部歌德的晚期作品中,诗人探求的是"情爱美学",重在"无性美学"的理念.他试图从性的欲望中逃脱出来,寻求一种"无性的圣洁".情爱和性欲作为决定婚姻选择的亲和力,成为引导命运的一种力量.在现实世界中,歌德的"情爱"无法逃脱"爱欲"的支配,注定是失败者.在虚构的世界中, 歌德试图与这一"命运"进行抗争.本文尝试从歌德<亲和力>的创作以及本雅明对歇德的文学批评入手,通过对作品"实在内涵"的分析,探求其"真实内涵",即作品中"不可见"的一面.     

Test for the existence of finite moments via bootstrap

This paper develops a bootstrap hypothesis test for the existence of finite moments of a random variable, which is nonparametric and applicable to both independent and dependent data. The test is based on a property in bootstrap asymptotic theory, in which the m out of n bootstrap sample mean is asymptotically normal when the variance of the observations is finite. Consistency of the test is established. Monte Carlo simulations are conducted to illustrate the finite sample performance and compare it with alternative methods available in the literature. Applications to financial data are performed for illustration.     

Some nonparametric precedence-type tests based on progressively censored samples and evaluation of power

In this paper, we consider the problem of testing the equality of two distributions when both samples are progressively Type-II censored. We discuss the following two statistics: one based on the Wilcoxon-type rank-sum precedence test, and the second based on the Kaplan–Meier estimator of the cumulative distribution function. The exact null distributions of these test statistics are derived and are then used to generate critical values and the corresponding exact levels of significance for different combinations of sample sizes and progressive censoring schemes. We also discuss their non-null distributions under Lehmann alternatives. A power study of the proposed tests is carried out under Lehmann alternatives as well as under location-shift alternatives through Monte Carlo simulations. Through this power study, it is shown that the Wilcoxon-type rank-sum precedence test performs the best.     

Welfare Attitudes of Singaporeans – Ambiguity in Shifting Socio‐political Dynamics

This article presents findings from a survey of 440 Singaporeans on their attitudes towards welfare and welfare recipients. Attitudes were generally favourable, but sentiments towards higher taxes to help the poor were ambivalent. Controlled for demographic characteristics, ‘poverty sympathizers’ and affiliates of opposition political parties held the most liberal views, but were not more willing to pay higher taxes. Instead, poor respondents on the one hand and highly educated respondents on the other hand were more willing to pay higher taxes. Knowledge accumulation and beliefs about causes of poverty were strong predictors of attitudes. Effects of personal values and self‐interest were less evident. Couched against the backdrop of an economy that has experienced rapid transformation and one of the widest income inequality in the developed world, the article discusses the critical juncture of social response and policy choices that Singapore finds itself.     

Robust inference for bivariate point processes

In the analysis of recurrent events where the primary interest lies in studying covariate effects on the expected number of events occurring over a period of time, it is appealing to base models on the cumulative mean function (CMF) of the processes (Lawless & Nadeau 1995). In many chronic diseases, however, more than one type of event is manifested. Here we develop a robust inference procedure for joint regression models for the CMFs arising from a bivariate point process. Consistent parameter estimates with robust variance estimates are obtained via unbiased estimating functions for the CMFs. In most situations, the covariance structure of the bivariate point processes is difficult to specify correctly, but when it is known, an optimal estimating function for the CMFs can be obtained. As a convenient model for more general settings, we suggest the use of the estimating functions arising from bivariate mixed Poisson processes. Simulation studies demonstrate that the estimators based on this working model are practically unbiased with robust variance estimates. Furthermore, hypothesis tests may be based on the generalized Wald or generalized score tests. Data from a trial of patients with bronchial asthma are analyzed to illustrate the estimation and inference procedures.