Modeling equity market integration using smooth transition analysis:a study of Eastern European stock markets

This paper assesses the extent to which the equity markets of Hungary, Poland the Czech Republic and Russia have become less segmented. Using a variety of tests it is shown there has been a consistent increase in the co-movement of some Eastern European markets and developed markets. Using the variance decompositions from a vector autoregressive representation of returns it is shown that for Poland and Hungary global factors are having an increasing influence on equity returns, suggestive of increased equity market integration. In this paper we model a system of bivariate equity market correlations as a smooth transition logistic trend model in order to establish how rapidly the countries of Eastern Europe are moving away from market segmentation. We find that Hungary is the country which is becoming integrated the most quickly. © 2005 ELsevier Ltd. All rights reserved.

Changes in the comovement of european equity markets

This paper investigates the impact that the removal of exchange controls within major European economies has had on the interdependence of European equity markets. For five years prior to the removal of exchange controls and five years following their removal, we use impulse responses and variance decompositions from vector autoregressions to illustrate that European equity markets have become substantially more integrated after the removal of exchange controls. We undertake further tests that demonstrate that, even if we allow for parallel macroeconomic harmonization, the removal of exchange controls has been a major cause of increased equity market integration within Europe.

Price discovery for Chinese shares cross-listed in multiple markets

In this article we study the relationship between security returns cross-listed on the A share market of China and the H share market at the Stock Exchange of Hong Kong (SEHK). Most of these securities are also cross-listed on other markets. An important feature of this article is that we focus on the multilateral relationships between all cross-listed markets rather than concentrating only on the bi-lateral relationship between A and Hong Kong H shares. Using the impulse response functions and the variance decompositions from a Vector Autoregressive (VAR) process we show that the returns to the A share market are almost exclusively determined by domestic factors. In contrast, we find that the H share market is influenced by both the A share market within China and foreign stock markets elsewhere in the world. Impulse response functions suggest that innovations to the A share market and the Hong Kong H share market are partly transmitted to each other and to stock markets outside China. We show that liquidity has an important role to play in determining the impact that the home market has on cross-listed variance decompositions. © 2012 Copyright Taylor and Francis Group, LLC.

An upper bound on the Bayesian error bars for generalized linear regression

In the Bayesian framework, predictions for a regression problem are expressed in terms of a distribution of output values. The mode of this distribution corresponds to the most probable output, while the uncertainty associated with the predictions can conveniently be expressed in terms of error bars. In this paper we consider the evaluation of error bars in the context of the class of generalized linear regression models. We provide insights into the dependence of the error bars on the location of the data points and we derive an upper bound on the true error bars in terms of the contributions from individual data points which are themselves easily evaluated.

On the relationship between Bayesian error bars and the input data density

We investigate the dependence of Bayesian error bars on the distribution of data in input space. For generalized linear regression models we derive an upper bound on the error bars which shows that, in the neighbourhood of the data points, the error bars are substantially reduced from their prior values. For regions of high data density we also show that the contribution to the output variance due to the uncertainty in the weights can exhibit an approximate inverse proportionality to the probability density. Empirical results support these conclusions.

An introduction to analysis of variance (ANOVA) with special reference to data from clinical experiments in optometry

This article is aimed primarily at eye care practitioners who are undertaking advanced clinical research, and who wish to apply analysis of variance (ANOVA) to their data. ANOVA is a data analysis method of great utility and flexibility. This article describes why and how ANOVA was developed, the basic logic which underlies the method and the assumptions that the method makes for it to be validly applied to data from clinical experiments in optometry. The application of the method to the analysis of a simple data set is then described. In addition, the methods available for making planned comparisons between treatment means and for making post hoc tests are evaluated. The problem of determining the number of replicates or patients required in a given experimental situation is also discussed. Copyright (C) 2000 The College of Optometrists.

The application of analysis of variance (ANOVA) to different experimental designs in optometry

Analysis of variance (ANOVA) is the most efficient method available for the analysis of experimental data. Analysis of variance is a method of considerable complexity and subtlety, with many different variations, each of which applies in a particular experimental context. Hence, it is possible to apply the wrong type of ANOVA to data and, therefore, to draw an erroneous conclusion from an experiment. This article reviews the types of ANOVA most likely to arise in clinical experiments in optometry including the one-way ANOVA ('fixed' and 'random effect' models), two-way ANOVA in randomised blocks, three-way ANOVA, and factorial experimental designs (including the varieties known as 'split-plot' and 'repeated measures'). For each ANOVA, the appropriate experimental design is described, a statistical model is formulated, and the advantages and limitations of each type of design discussed. In addition, the problems of non-conformity to the statistical model and determination of the number of replications are considered. © 2002 The College of Optometrists.

Statnote 23: Non-parametric analysis of variance (ANOVA)

To carry out an analysis of variance, several assumptions are made about the nature of the experimental data which have to be at least approximately true for the tests to be valid. One of the most important of these assumptions is that a measured quantity must be a parametric variable, i.e., a member of a normally distributed population. If the data are not normally distributed, then one method of approach is to transform the data to a different scale so that the new variable is more likely to be normally distributed. An alternative method, however, is to use a non-parametric analysis of variance. There are a limited number of such tests available but two useful tests are described in this Statnote, viz., the Kruskal-Wallis test and Friedmann’s analysis of variance.

The Generalized Malmquist index and capacity utilization change: an application to the Italian manufacturing, 1989-1994

Several indices of plant capacity utilization based on the concept of best practice frontier have been proposed in the literature (Fare et al. 1992; De Borger and Kerstens, 1998). This paper suggests an alternative measure of capacity utilization change based on Generalized Malmquist index, proposed by Grifell-Tatje' and Lovell in 1998. The advantage of this specification is that it allows the measurement of productivity growth ignoring the nature of scale economies. Afterwards, this index is used to measure capacity change of a panel of Italian firms over the period 1989-94 using Data Envelopment Analysis and then its abilities of explaining the short-run movements of output are assessed.

Statnote 10: the two-way analysis of variance

The two-way design has been variously described as a matched-sample F-test, a simple within-subjects ANOVA, a one-way within-groups ANOVA, a simple correlated-groups ANOVA, and a one-factor repeated measures design! This confusion of terminology is likely to lead to problems in correctly identifying this analysis within commercially available software. The essential feature of the design is that each treatment is allocated by randomization to one experimental unit within each group or block. The block may be a plot of land, a single occasion in which the experiment was performed, or a human subject. The ‘blocking’ is designed to remove an aspect of the error variation and increase the ‘power’ of the experiment. If there is no significant source of variation associated with the ‘blocking’ then there is a disadvantage to the two-way design because there is a reduction in the DF of the error term compared with a fully randomised design thus reducing the ‘power’ of the analysis.

Statnote 9: The one-way analysis of variance (random effects model)

There is an alternative model of the 1-way ANOVA called the 'random effects' model or ‘nested’ design in which the objective is not to test specific effects but to estimate the degree of variation of a particular measurement and to compare different sources of variation that influence the measurement in space and/or time. The most important statistics from a random effects model are the components of variance which estimate the variance associated with each of the sources of variation influencing a measurement. The nested design is particularly useful in preliminary experiments designed to estimate different sources of variation and in the planning of appropriate sampling strategies.

Statnote 11: the two-factor analysis of variance

Experiments combining different groups or factors are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the number of replications required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the degrees of freedom (DF) of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than simply the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for each error term of the ANOVA. Finally, in a factorial experiment, it is important to define the design of the experiment in detail because this determines the appropriate type of ANOVA. We will discuss some of the common variations of factorial ANOVA in future statnotes. If there is doubt about which ANOVA to use, the researcher should seek advice from a statistician with experience of research in applied microbiology.

Statnote 12: the split-plot analysis of variance

In some experimental situations, the factors may not be equivalent to each other and replicates cannot be assigned at random to all treatment combinations. A common case, called a ‘split-plot design’, arises when one factor can be considered to be a major factor and the other a minor factor. Investigators need to be able to distinguish a split-plot design from a fully randomized design as it is a common mistake for researchers to analyse a split-plot design as if it were a fully randomised factorial experiment.

Statnote 13: a more complex analysis of variance incorporating a 'repeated measures' factor

Experiments combining different groups or factors and which use ANOVA are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the sample size required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the degrees of freedom (DF) of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for the error term of the ANOVA testing effects of particular interest. Finally, it is important to always consider the design of the experiment because this determines the appropriate ANOVA to use. Hence, it is necessary to be able to identify the different forms of ANOVA appropriate to different experimental designs and to recognise when a design is a split-plot or incorporates a repeated measure. If there is any doubt about which ANOVA to use in a specific circumstance, the researcher should seek advice from a statistician with experience of research in applied microbiology.