Nazaré Mendes-Lopes

A Decision Procedure for Bilinear Time Series Based on the Asymptotic Separation

This paper presents a non-classical decision procedure for a bilinear model with a general error process. This procedure allows us to decide, in a consistent way, between two hypotheses on the model. By establishing the asymptotic separation of the sequences of probability laws defined by each hypothesis, we obtain the consistence of this decision method. Some studies about the rate of convergence are presented and an exponential decay is obtained. A simulation study is done to illustrate the behaviour of the power and level functions in small and moderate samples when this procedure is used as a test.

Zero-inflated compound Poisson distributions in integer-valued GARCH models

In this paper we introduce a wide class of integer-valued stochastic processes that allows to take into consideration, simultaneously, relevant characteristics observed in count data namely zero inflation, overdispersion and conditional heteroscedasticity. This class includes, in particular, the compound Poisson, the zero-inflated Poisson and the zero-inflated negative binomial INGARCH models, recently proposed in literature. The main probabilistic analysis of this class of processes is here developed. Precisely, first- and second-order stationarity conditions are derived, the autocorrelation function is deduced and the strict stationarity is established in a large subclass. We also analyse in a particular model the existence of higher-order moments and deduce the explicit form for the first four cumulants, as well as its skewness and kurtosis.

On the Finite Dimensional Laws of Threshold GARCH Processes

In this chapter we establish bounds for the finite dimensional laws of a threshold GARCH process, X, with generating process Z. In this class of models the conditional standard deviation has different reactions according to the sign of past values of the process. So, we firstly find lower and upper bounds for the law of \(\left ({X}_{1}^{+},-{X}_{1}^{+},\ldots,{X}_{n}^{+},-{X}_{n}^{+}\right )\), in certain regions of \({\mathbb{R}}^{2n}\), and use them to find bounds of the law of \(\left ({X}_{1},\ldots,{X}_{n}\right )\). Some of these bounds only depend on the parameters of the model and on the distribution function of the independent generating process, Z. An application of these bounds to control charts for time series is presented.

Zero-truncated compound Poisson integer-valued GARCH models for time series

ABSTRACT Starting from the compound Poisson INGARCH models, we introduce in this paper a new family of integer-valued models suitable to describe count data without zeros that we name zero-truncated CP-INGARCH processes. For such class of models, a probabilistic study concerning moments existence, stationarity and ergodicity is developed. The conditional quasi-maximum likelihood method is introduced to consistently estimate the parameters of a wide zero-truncated compound Poisson subclass of models. The conditional maximum likelihood method is also used to estimate the parameters of ZTCP-INGARCH processes associated with well-specified conditional laws. A simulation study that compares some of those estimators and illustrates their finite distance behaviour as well as a real-data application conclude the paper.

On the Distribution Estimation of Power Threshold Garch Processes

The aim of this paper is to estimate the probability distribution of power TGARCH processes by establishing bounds for their nite dimensional laws. These bounds only depend on the parameters of the model and on the distribu- tion function of its independent generating process. The application of this study to some particular models allows us to conjecture that this procedure is an ade- quate alternative to the corresponding estimation using the empirical distribution functions, particularly useful in the development of control charts for this kind of models.