Rui Menezes

Long Memory and Volatility Clustering: is the empirical evidence consistent across stock markets?

Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynamics. Another interesting manner to study the volatility phenomenon is by using measures based on the concept of entropy. In this paper we investigate the long memory and volatility clustering for the SP 500, NASDAQ 100 and Stoxx 50 indexes in order to compare the US and European Markets. Additionally, we compare the results from conditionally heteroscedastic models with those from the entropy measures. In the latter, we examine Shannon entropy, Renyi entropy and Tsallis entropy. The results corroborate the previous evidence of nonlinear dynamics in the time series considered.

An econophysics approach to analyse uncertainty in financial markets:an application to the Portuguese stock market

Abstract.In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing interrelationship between physics and financial theory. In this field the analysis of uncertainty, which is crucial in financial analysis, can be made using measures of physics statistics and information theory, namely the Shannon entropy. One advantage of this approach is that the entropy is a more general measure than the variance, since it accounts for higher order moments of a probability distribution function. An empirical application was made using data collected from the Portuguese Stock Market.

On the integrated behaviour of non-stationary volatility in stock markets

This paper analyses the behaviour of volatility for several international stock market indexes, namely the SP 500 (USA), the Nikkei (Japan), the PSI 20 (Portugal), the CAC 40 (France), the DAX 30 (Germany), the FTSE 100 (UK), the IBEX 35 (Spain) and the MIB 30 (Italy), in the context of non-stationarity. Our empirical results point to the evidence of the existence of integrated behaviour among several of those stock market indexes of different dimensions. It seems, therefore, that the behaviour of these markets tends to some uniformity, which can be interpreted as the existence of a similar behaviour facing to shocks that may affect the worldwide economy. Whether this is a cause or a consequence of market globalization is an issue that may be stressed in future work.

Self-similarity principle: the reduced description of randomness

A new general fitting method based on the Self-Similar (SS) organization of random sequences is presented. The proposed analytical function helps to fit the response of many complex systems when their recorded data form a self-similar curve. The verified SS principle opens new possibilities for the fitting of economical, meteorological and other complex data when the mathematical model is absent but the reduced description in terms of some universal set of the fitting parameters is necessary. This fitting function is verified on economical (price of a commodity versus time) and weather (the Earth’s mean temperature surface data versus time) and for these nontrivial cases it becomes possible to receive a very good fit of initial data set. The general conditions of application of this fitting method describing the response of many complex systems and the forecast possibilities are discussed.

Asymmetric conditional volatility in international stock markets

Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare the results for the Portuguese Stock Market Index PSI 20 with six other Stock Market Indices, namely the SP 500, FTSE 100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TARCH and EGARCH. We also test for asymmetry after controlling for the effect of macroeconomic factors on stock market returns using TAR and M-TAR specifications within a VAR framework. Our results show that the conditional variance is an asymmetric function of past innovations raising proportionately more during market declines, a phenomenon known as the leverage effect. However, when we control for the effect of changes in macroeconomic variables, we find no significant evidence of asymmetric behaviour of the stock market returns. There are some signs that the Portuguese Stock Market tends to show somewhat less market efficiency than other markets since the effect of the shocks appear to take a longer time to dissipate.

Entropy: A new measure of stock market volatility?

When uncertainty dominates understanding stock market volatility is vital. There are a number of reasons for that. On one hand, substantial changes in volatility of financial market returns are capable of having significant negative effects on risk averse investors. In addition, such changes can also impact on consumption patterns, corporate capital investment decisions and macroeconomic variables. Arguably, volatility is one of the most important concepts in the whole finance theory. In the traditional approach this phenomenon has been addressed based on the concept of standard-deviation (or variance) from which all the famous ARCH type models – Autoregressive Conditional Heteroskedasticity Models– depart. In this context, volatility is often used to describe dispersion from an expected value, price or model. The variability of traded prices from their sample mean is only an example. Although as a measure of uncertainty and risk standard-deviation is very popular since it is simple and easy to calculate it has long been recognized that it is not fully satisfactory. The main reason for that lies in the fact that it is severely affected by extreme values. This may suggest that this is not a closed issue. Bearing on the above we might conclude that many other questions might arise while addressing this subject. One of outstanding importance, from which more sophisticated analysis can be carried out, is how to evaluate volatility, after all? If the standard-deviation has some drawbacks shall we still rely on it? Shall we look for an alternative measure? In searching for this shall we consider the insight of other domains of knowledge? In this paper we specifically address if the concept of entropy, originally developed in physics by Clausius in the XIX century, which can constitute an effective alternative. Basically, what we try to understand is, which are the potentialities of entropy compared to the standard deviation. But why entropy? The answer lies on the fact that there is already some research on the domain of Econophysics, which points out that as a measure of disorder, distance from equilibrium or even ignorance, entropy might present some advantages. However another question arises: since there is several measures of entropy which one since there are several measures of entropy, which one shall be used? As a starting point we discuss the potentialities of Shannon entropy and Tsallis entropy. The main difference between them is that both Renyi and Tsallis are adequate for anomalous systems while Shannon has revealed optimal for equilibrium systems.

Avaliação do processo de ensino: uma abordagem multivariada

A pratica da qualidade na gestao universitaria se faz com o comprometimento de toda comunidade escolar. Assim, atraves da avaliacao do processo de ensino, o presente trabalho objetivou identificar, na opiniao do discente, os pontos fracos e fortes do processo de ensino, por meio da analise multivariada. Assim sendo, para este estudo, foram considerados questionarios que abrangeram as categorias de variaveis: 1) auto-avaliacao do aluno, 2) avaliacao da importância dos conteudos para o curso e o desempenho pedagogico do professor, 3) avaliacao docente pelo discente e 4) avaliacao discente pelo docente. Os dados obtidos no final de 2003 compuseram a primeira amostra que apresentou uma participacao de 54% dos alunos do curso de administracao em comercio exterior. Os dados referentes ao processo de avaliacao realizado ao final de 2005 corresponderam a uma participacao de 87% dos alunos matriculados nos cursos de graduacao da Instituicao de Ensino Superior IES. As informacoes foram processadas utilizando-se a tecnica estatistica de analise fatorial com rotacao varimax normalizada. Da analise fatorial, resultaram fatores, com consistencia interna satisfatoria que definiram as dimensoes: 1) situacoes de estimulo por parte do professor para o aluno buscar conhecimento com uma explicacao de 50%, 2) com 21% de explicacao os alunos referiram-se as relacoes entre conteudos e objetivos do curso e suas aplicacoes praticas como satisfatorias, 3) situacoes metodologicas apropriadas para o processo de ensino e aprendizagem com 11% de explicacao e como ponto fraco no processo de ensino, 4) a interdisciplinaridade nao foi percebida pelo aluno com a real importância e 5) a frequencia a biblioteca e o habito da leitura devem ser bem mais motivados como tambem a participacao em eventos, a pesquisa e extensao. Os resultados mostraram, por meio de consistencia interna dos fatores, a validez do construto que da suporte ao processo de ensino desta IES. Desse modo, essa forma de analise favorece uma melhor observacao dos gestores nas percepcoes que os alunos tem sobre o processo de ensino em determinada situacao, possibilitando, assim direcionar investimentos em busca da qualidade.

An alternative method for the evaluation of a multivariate productive process in the presence of volatility

Technological development and production processes require that the statistical process control uses alternative techniques for the evaluation of a productive process. This paper proposes an alternative procedure to the monitoring of a multivariate productive process using residuals obtained from principal component scores modeled by the general class of AutoRegressive Integrated Moving Average (ARIMA) and the Generalized AutoRegressive Conditional Heteroskedasticity — (GARCH) processes. Non-correlated and independent residuals are sought to be obtained and investigated by means of X-bar and Exponentially Weighted Moving Average (EWMA) charts as a way to capture large and small variations in the productive process. The level of volatility persistence in the productive process is intended to be determined when an external action occurs. The principal component analysis deals with the correlation among the variables and provides the dimensionality reduction. The ARIMA-GARCH model estimates jointly the mean and volatility of the principal components selected, providing independent residuals that are analyzed by means of control charts. Thus, a multivariate process can be assessed by univariate techniques, with the advantage of taking into account both the mean and the volatility behavior of the process. Therefore, we emphasize that an alternative procedure is presented to evaluate a process with multivariate features.

Forecasting the portuguese stock market time series by using artificial neural networks

In this paper, we show that neural networks can be used to uncover the non-linearity that exists in the financial data. First, we follow a traditional approach by analysing the deterministic/stochastic characteristics of the Portuguese stock market data and some typical features are studied, like the Hurst exponents, among others. We also simulate a BDS test to investigate nonlinearities and the results are as expected: the financial time series do not exhibit linear dependence. Secondly, we trained four types of neural networks for the stock markets and used the models to make forecasts. The artificial neural networks were obtained using a three-layer feed-forward topology and the back-propagation learning algorithm. The quite large number of parameters that must be selected to develop a neural network forecasting model involves some trial and as a consequence the error is not small enough. In order to improve this we use a nonlinear optimization algorithm to minimize the error. Finally, the output of the 4 models is quite similar, leading to a qualitative forecast that we compare with the results of the application of k-nearest-neighbor for the same time series.

Fairness evaluation method of resource allocation based on BPSO multidimensional perspective

In order to improve the effectiveness of fairness evaluation algorithm for public health resources, a kind of fairness evaluation method for public health resources based on BPSO dimension reduction under multi-perspective was proposed in the thesis. Firstly, data sources and research methods for fairness evaluation of public health resources was introduced; computational steps of Lorenz index were given; then, in order to reduce the complexity of data processing, particle swarm optimization was used to implement dimension reduction processing for software failure data; character string (0 or 1) of binary system was used to show particle position so as to realize simplification of data processing. Finally, effectiveness of methods mentioned in the thesis is verified in the positive analysis of fairness evaluation for regional distribution of health resources in Shaoguan city, Guangdong province.