arXiv subjects

Guilherme Pumi

Publications and source records attributed to Guilherme Pumi.

22 records · Page 2Linked to original sources

arXiv2018

Beta Autoregressive Fractionally Integrated Moving Average Models

In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval $(0,1)$. The proposed model accommodates a set of regressors and a long-range dependent time series structure. We derive the partial likelihood estimator for the parameters of the proposed model, obtain the associated score vector and Fisher information matrix. We also prove the consistency and asymptotic normality of the estimator under mild conditions. Hypotheses testing, diagnostic tools and forecasting are also proposed. A Monte Carlo simulation is considered to evaluate the finite sample performance of the partial likelihood estimators and to study some of the proposed tests. An empirical application is also presented and discussed.

stat.ME↗

arXiv2013

A Semiparametric Estimator for Long-Range Dependent Multivariate Processes

In this paper we propose a generalization of a class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter for long-range dependent multivariate time series. We generalize a known GSE-type estimator by introducing some modifications at the objective function level regarding the process' spectral density matrix estimator. We study large sample properties of the estimator without assuming Gaussianity as well as hypothesis testing. The class of models considered here satisfies simple conditions on the spectral density function, restricted to a small neighborhood of the zero frequency. This includes, but is not limited to, the class of VARFIMA models. A simulation study to assess the finite sample properties of the proposed estimator is presented and supports its competitiveness. We also present an empirical application to an exchange rate data.

math.ST↗

arXiv2013

A Generalization of a Gaussian Semiparametric Estimator on Multivariate Long-Range Dependent Processes

In this paper we propose and study a general class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter in the context of long-range dependent multivariate time series. We establish large sample properties of the estimator without assuming Gaussianity. The class of models considered here satisfies simple conditions on the spectral density function, restricted to a small neighborhood of the zero frequency and includes important class of VARFIMA processes. We also present a simulation study to assess the finite sample properties of the proposed estimator based on a smoothed version of the GSE which supports its competitiveness.

math.ST↗

arXiv2012

Copulas Related to Manneville-Pomeau Processes

In this work we derive the copulas related to Manneville-Pomeau processes. We examine both bidimensional and multidimensional cases and derive some properties for the related copulas. Computational issues, approximations and random variate generation problems are addressed and simple numerical experiments to test the approximations developed are also performed. In particular, we propose an approximation to the copulas derived which we show to converge uniformly to the true copula. To illustrate the usefulness of the theory, we derive a fast procedure to estimate the underlying parameter in Manneville-Pomeau processes.

math.ST↗