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

Kumaraswamy autoregressive moving average models for double bounded environmental data

In this paper we introduce the Kumaraswamy autoregressive moving average models (KARMA), which is a dynamic class of models for time series taking values in the double bounded interval $(a,b)$ following the Kumaraswamy distribution. The Kumaraswamy family of distribution is widely applied in many areas, especially hydrology and related fields. Classical examples are time series representing rates and proportions observed over time. In the proposed KARMA model, the median is modeled by a dynamic structure containing autoregressive and moving average terms, time-varying regressors, unknown parameters and a link function. We introduce the new class of models and discuss conditional maximum likelihood estimation, hypothesis testing inference, diagnostic analysis and forecasting. In particular, we provide closed-form expressions for the conditional score vector and conditional Fisher information matrix. An application to environmental real data is presented and discussed.Comment: 25 pages, 4 tables, 4 figure

A Dynamic Model for Double Bounded Time Series With Chaotic Driven Conditional Averages

In this work we introduce a class of dynamic models for time series taking values on the unit interval. The proposed model follows a generalized linear model approach where the random component, conditioned on the past information, follows a beta distribution, while the conditional mean specification may include covariates and also an extra additive term given by the iteration of a map that can present chaotic behavior. The resulting model is very flexible and its systematic component can accommodate short and long range dependence, periodic behavior, laminar phases, etc. We derive easily verifiable conditions for the stationarity of the proposed model, as well as conditions for the law of large numbers and a Birkhoff-type theorem to hold. A Monte Carlo simulation study is performed to assess the finite sample behavior of the partial maximum likelihood approach for parameter estimation in the proposed model. Finally, an application to the proportion of stored hydroelectrical energy in Southern Brazil is presented

On the behavior of the DFA and DCCA in trend-stationary processes

In this work, we develop the asymptotic theory of the Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) for trend-stationary stochastic processes without any assumption on the specific form of the underlying distribution. All results are presented and derived under the general framework of potentially overlapping boxes for the polynomial fit. We prove the stationarity of the DFA and DCCA, viewed as stochastic processes, obtain closed forms for moments up to second order, including the covariance structure for DFA and DCCA and a miscellany of law of large number related results. Our results generalize and improve several results presented in the literature. To verify the behavior of our theoretical results in small samples, we present a Monte Carlo simulation study and an empirical application to econometric time series

Copulas, Chaotic Processes and Time Series: a Survey

In this work we summarize some of recent and classical results on the role played by copulas in the analysis of chaotic processes and univariate time series. We review some aspects of the copulas related to chaotic process, its properties and applications. We also present a review on classical and modern approaches to understand the relationship among random variables in Markov processes as well as short and long memory time series as well as ergodic properties of copula-based Markov processes

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

Unit-Weibull Autoregressive Moving Average Models

In this work we introduce the class of unit-Weibull Autoregressive Moving Average models for continuous random variables taking values in $(0,1)$. The proposed model is an observation driven one, for which, conditionally on a set of covariates and the process' history, the random component is assumed to follow a unit-Weibull distribution parameterized through its $\rho$th quantile. The systematic component prescribes an ARMA-like structure to model the conditional $\rho$th quantile by means of a link. Parameter estimation in the proposed model is performed using partial maximum likelihood, for which we provide closed formulas for the score vector and partial information matrix. We also discuss some inferential tools, such as the construction of confidence intervals, hypotheses testing, model selection, and forecasting. A Monte Carlo simulation study is conducted to assess the finite sample performance of the proposed partial maximum likelihood approach. Finally, we examine the prediction power by contrasting our method with others in the literature using the Manufacturing Capacity Utilization from the US

Granger causality and time series regression for modelling the migratory dynamics of influenza into Brazil

cknowledgments.Aline F. Grande and Guilherme Pumi gratefully acknowledge the support of CNPq and FAPERGS. Gabriela B. Cybis gratefully acknowledges the support of the Serrapilheira Institute (grant number Serra-G1709-18939). The authors are also grateful to Rafaela Gomes de Jesus for helping with the genetic diversity data assembly.In this work we study the problem of modelling and forecasting the dynamics of the influenza virus in Brazil at a given month, from data on reported cases and genetic diversity collected from previous months, in other locations. Granger causality is employed as a tool to assess possible predictive relationships between covariates. For modelling and forecasting purposes, a time series regression approach is applied considering lagged information regarding reported cases and genetic diversity in other regions. Three different models are analysed, including stepwise time series regression and LASSO