Journal of Advanced Statistics

7

Authors: Kalovwe Sebastian Kaweto, Mwaniki Ivivi Joseph

This paper seeks to model daily, weekly and monthly stock indices returns using GARCH (1,1) model which is expected to reproduce most of the stylized facts of financial time series data which, in most cases, are found in different types of market. In addition, the distributional behavior of returns as the data changes from daily through to monthly returns is investigated by performing the JB and K-S tests. The results indicate evidence of volatility clustering, leverage effects, Gaussianity and leptokurtic distribution in the stock returns. A key observation is that the monthly returns of the three indices follow a Gaussian distribution (i.e. as the data changes from daily through to monthly returns it follows a normal distribution).

10

Authors: Cleto Corposanto, Beba Molinari

This paper aims to explore the new opportunities offered by the web 2.0, with particular emphasis on the level of intrusiveness concerning web surveys and their different methods of administration. Particular attention will be drawn to the Apps and the way they intervene in the research design to give the researchers the opportunity to learn about the preferences and the consultations which are mostly relevant to the users, thanks to the analysis carried out by data mining and web survey.

15

Authors: Jin-Ting Zhang, Bu Zhou, Jia Guo, Xuefeng Liu

A two-way multivariate analysis of variance (MANOVA) aims to compare the effects of several levels of two factors in a factorial experiment with two-way layout. It is widely used in experimental sciences, e.g., biology, psychology, physics, among others. When the cell covariance matrices are the same, it can be solved using the well-known Wilks likelihood ratio, Lawley-Hotelling trace, Bartlett-Nanda-Pillai trace and Roy’s largest root tests ([1]). However, when the homogeneous assumption is violated, these tests may become seriously biased. To overcome this problem, several authors have proposed and studied different approximation solutions. In this paper, we propose and study a Modified Bartlett (MB) test using a Wald-type statistic and the modified Bartlett correction ([2]) for heteroscedastic two-way MANOVA problems. The MB test can be easily implemented using the usual χ 2 -distribution with known degrees of freedom. We show that it admits several invariant properties. Simulation studies show that the MB test generally outperforms the classical LawleyHotelling trace (LHT) test and a modified LHT test of [3] under various parameter configurations in terms of size controlling and power. A real data example illustrates our method and the effect of heteroscedasticity.