Exploratory semiparametric analysis of two-dimensional diffusions in finance

We examine bivariate extensions of Aït-Sahalia’s approach to the estimation of univariate diffusions. Our message is that extending his idea to a bivariate setting is not straightforward. In higher dimensions, as opposed to the univariate case, the elements of the Itô and Fokker-Planck representations do not coincide; and, even imposing sensible assumptions on the marginal drifts and volatilities is not sufficient to obtain direct generalisations. We develop exploratory estimation and testing procedures, by parametrizing the drifts of both component processes and setting restrictions on the terms of either the Itô or the Fokker-Planck covariance matrices. This may lead to highly nonlinear ordinary differential equations, where the definition of boundary conditions is crucial. For the methods developed, the Fokker-Planck representation seems more tractable than the Itô’s. Questions for further research include the design of regularity conditions on the time series dependence in the data, the kernels actually used and the bandwidths, to obtain asymptotic properties for the estimators proposed. A particular case seems promising: “causal bivariate models” in which only one of the diffusions contributes to the volatility of the other. Hedging strategies which estimate separately the univariate diffusions at stake may thus be improved.

Testing covariance stationarity

In this paper, we show that the widely used stationarity tests such as the KPSS test have power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) In the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) In the presence a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) The proposed test has the same size as traditional stationarity tests under the null hypothesis of stationarity. An application to daily observations of return on US Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in subsamples.

Testing covariance stationarity

In this paper, we show that the widely used stationarity tests such as the KPSS test has power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) In the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) In the presence a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) The proposed test has the same size as traditional stationarity tests under the null hypothesis of covariance stationarity. An application to daily observations of return on US Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in sub-samples.

A class of improved heteroskedasticity-consistent covariance matrix estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White (1980), also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto, Ferrari & Cordeiro (2000) have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that also commonly used by practitioners. These include the HC1, HC2 and HC3 estimators, which have proven to have superior small-sample behavior relative to White’s estimator. This paper defines a general bias-correction mechamism that can be applied not only to White’s estimator, but to variants of this estimator as well, such as HC1, HC2 and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.

Otimização de carteiras regularizadas empregando informações de grupos de ativos para o mercado brasileiro

Este trabalho se dedica a analisar o desempenho de modelos de otimização de carteiras regularizadas, empregando ativos financeiros do mercado brasileiro. Em particular, regularizamos as carteiras através do uso de restrições sobre a norma dos pesos dos ativos, assim como DeMiguel et al. (2009). Adicionalmente, também analisamos o desempenho de carteiras que levam em consideração informações sobre a estrutura de grupos de ativos com características semelhantes, conforme proposto por Fernandes, Rocha e Souza (2011). Enquanto a matriz de covariância empregada nas análises é a estimada através dos dados amostrais, os retornos esperados são obtidos através da otimização reversa da carteira de equilíbrio de mercado proposta por Black e Litterman (1992). A análise empírica fora da amostra para o período entre janeiro de 2010 e outubro de 2014 sinaliza-nos que, em linha com estudos anteriores, a penalização das normas dos pesos pode levar (dependendo da norma escolhida e da intensidade da restrição) a melhores performances em termos de Sharpe e retorno médio, em relação a carteiras obtidas via o modelo tradicional de Markowitz. Além disso, a inclusão de informações sobre os grupos de ativos também pode trazer benefícios ao cálculo de portfolios ótimos, tanto em relação aos métodos tradicionais quanto em relação aos casos sem uso da estrutura de grupos.

Labor earnings dynamics in post-stabilization Brazil

This paper analyzes both the levels and evolution of wage inequality in the Brazilian formal labor market using administrative data from the Brazilian Ministry of Labor (RAIS) from 1994 to 2009. After the covariance structure of the log of real weekly wages is estimated and the variance of the log of real weekly wages is decomposed into its permanent and transitory components, we verify that nearly 60% of the inequality within age and education groups is explained by the permanent component, i.e., by time-invariant individual productive characteristics. During this period, wage inequality decreased by 29%. In the rst years immediately after the macroeconomic stabilization (1994