Jeremias Leão

A family of autoregressive conditional duration models applied to financial data

The Birnbaum-Saunders distribution is receiving considerable attention due to its good properties. One of its extensions is the class of scale-mixture Birnbaum-Saunders (SBS) distributions, which shares its good properties, but it also has further properties. The autoregressive conditional duration models are the primary family used for analyzing high-frequency financial data. We propose a methodology based on SBS autoregressive conditional duration models, which includes in-sample inference, goodness-of-fit and out-of-sample forecast techniques. We carry out a Monte Carlo study to evaluate its performance and assess its practical usefulness with real-world data of financial transactions from the New York stock exchange.

The Kumaraswamy Birnbaum–Saunders Distribution

AbstractMotivated by the recent work of Cordeiro and Castro (2011), we study the Kumaraswamy Birnbaum-Saunders (Kw-

Birnbaum-Saunders frailty regression models: Diagnostics and application to medical data: Birnbaum-Saunders frailty regression models

{\mathcal B}{\mathcal S}

Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data: A cure rate model with frailties and its diagnostics

ℬS) distribution. This distribution provides an enormous flexibility in modeling heavy-tailed and skewed data. We derive some mathematical properties of the Kw-

On a new class of skewed Birnbaum–Saunders models

{\mathcal B}{\mathcal S}

A new generalized gamma distribution with applications

ℬS including moments, quantile function, average lifetime function, mean residual lifetime function, and order statistics. In addition, we discuss maximum likelihood estimation of the model parameters.

A new lifetime model with a periodic hazard rate and an application

In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum-Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.

Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data

Cure rate models have been widely studied to analyze time-to-event data with a cured fraction of patients. Our proposal consists of incorporating frailty into a cure rate model, as an alternative to the existing models to describe this type of data, based on the Birnbaum-Saunders distribution. Such a distribution has theoretical arguments to model medical data and has shown empirically to be a good option for their analysis. An advantage of the proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. In addition, the number of competing causes is described by the negative binomial distribution, which absorbs several particular cases. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for this model. We assess local influence on the parameter estimates under different perturbation schemes. Deriving diagnostic tools is needed in all statistical modeling, which is another novel aspect of our proposal. Numerical evaluation of the considered model is performed by Monte Carlo simulations and by an illustration with melanoma data, both of which show its good performance and its potential applications. Particularly, the illustration confirms the importance of statistical diagnostics in the modeling.

The Kumaraswamy BirnbaumSaunders Distribution

Scale mixtures of Birnbaum–Saunders (SBS) distributions are attractive models in lifetime analysis. These models are based on scale mixture of normal (SMN) distributions and provide flexible heavy-tailed distributions. In this article, we propose a skewed version of SBS distributions and we establish some of its probabilistic and inferential properties. We then discuss the maximum likelihood estimation of the model parameters. An illustration of the methodology is provided, using real data.

A new model selection criterion for partial least squares regression

SYNOPTIC ABSTRACT The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. We introduce and study the gamma-Nadarajah–Haghighi model, which can be interpreted as a truncated generalized gamma distribution (Stacy, 1962). It can have a constant, decreasing, increasing, upside-down bathtub or bathtub-shaped hazard rate function depending on the parameter values. We demonstrate that the new density function can be expressed as a mixture of exponentiated Nadarajah–Haghighi densities. Various of its structural properties are derived, including explicit expressions for the moments, quantile and generating functions, skewness, kurtosis, mean deviations, Bonferroni and Lorenz curves, probability weighted moments, and two types of entropy. We also investigate the order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. We illustrate the flexibility of the new distribution by means of two applications to real datasets.