Isabel Pereira

Bivariate binomial autoregressive models

This paper introduces new classes of bivariate time series models being useful to fit count data time series with a finite range of counts. Motivation comes mainly from the comparison of schemes for monitoring tourism demand, stock data, production and environmental processes. All models are based on the bivariate binomial distribution of Type II. First, a new family of bivariate integer-valued GARCH models is proposed. Then, a new bivariate thinning operation is introduced and explained in detail. The new thinning operation has a number of advantages including the fact that marginally it behaves as the usual binomial thinning operation and also that allows for both positive and negative cross-correlations. Based upon this new thinning operation, a bivariate extension of the binomial autoregressive model of order one is introduced. Basic probabilistic and statistical properties of the model are discussed. Parameter estimation and forecasting are also covered. The performance of these models is illustrated through an empirical application to a set of rainy days time series collected from 2000 up to 2010 in the German cities of Bremen and Cuxhaven.

Integer-Valued Self-Exciting Threshold Autoregressive Processes

In this article, we introduce a class of self-exciting threshold integer-valued autoregressive models driven by independent Poisson-distributed random variables. Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the least squares-type and likelihood-based ones. Their performance is compared through a simulation study.

Optimal Alarm Systems for Count Processes

In many phenomena described by stochastic processes, the implementation of an alarm system becomes fundamental to predict the occurrence of future events. In this work we develop an alarm system to predict whether a count process will upcross a certain level and give an alarm whenever the upcrossing level is predicted. We consider count models with parameters being functions of covariates of interest and varying on time. This article presents classical and Bayesian methodology for producing optimal alarm systems. Both methodologies are illustrated and their performance compared through a simulation study. The work finishes with an empirical application to a set of data concerning the number of sunspot on the surface of the sun.

Detection of Additive Outliers in Poisson INAR(1) Time Series

Outlying observations are commonly encountered in the analysis of time series. In this paper a Bayesian approach is employed to detect additive outliers in order one Poisson integer-valued autoregressive time series. The methodology is informative and allows the identification of the observations which require further inspection. The procedure is illustrated with simulated and observed data sets.

Bayesian prediction in threshold autoregressive models with exponential white noise

In this paper, we develop a Bayesian analysis of a threshold autoregressive model with exponential noise. An approximate Bayes methodology, which is introduced here, and the Gibbs sampler are used to compute marginal posterior densities for the parameters of the model, including the threshold parameter, and to compute one-step-ahead predictive density functions. The proposed methodogy is illustrated with a simulation study and a real example.

A Periodic Bivariate Integer-Valued Autoregressive Model

In this paper, a bivariate integer-valued autoregressive model with periodic structure is introduced and studied in some detail. The model can be view as a generalization of the one considered in Pedeli and Karlis (Stat. Model. 11:325–349, 2011). Emphasis is placed on models with periodic bivariate Poisson innovations. Basic probabilistic and statistical properties of the model are discussed as well as parameter estimation and forecasting. The proposed model is applied to a bivariate data series concerning the monthly number of fires in neighbor counties, Aveiro and Coimbra, in Portugal.

Surveillance in Discrete Time Series

The analysis of low integer-valued time series is an area of growing interest as time series of counts arising from many different areas have become available in the last three decades. Statistical quality control, computer science, economics and finance, medicine and epidemiology and environmental sciences are just some of the fields that we can mention to point out the wide variety of contexts from which discrete time series have emerged.

Statistical Modelling of Counts with a Simple Integer-Valued Bilinear Process

The aim of this work is the statistical modelling of counts assuming low values and exhibiting sudden and large bursts that occur randomly in time. It is well known that bilinear processes capture these kind of phenomena. In this work the integer-valued bilinear INBL(1,0,1,1) model is discussed and some properties are reviewed. Classical and Bayesian methodologies are considered and compared through simulation studies, namely to obtain estimates of model parameters and to calculate point and interval predictions. Finally, an empirical application to real epidemiological count data is also presented to attest for its practical applicability in data analysis.

Integer-Valued APARCH Processes

The Asymmetric Power ARCH representation for the volatility was introduced by Ding et al. (J Empir Financ 1:83–106, 1993) in order to account for asymmetric responses in the volatility in the analysis of continuous-valued financial time series like, for instance, the log-return series of foreign exchange rates, stock indices, or share prices. As reported by Brannas and Quoreshi (Appl Financ Econ 20:1429–1440, 2010), asymmetric responses in volatility are also observed in time series of counts such as the number of intra-day transactions in stocks. In this work, an asymmetric power autoregressive conditional Poisson model is introduced for the analysis of time series of counts exhibiting asymmetric overdispersion. Basic probabilistic and statistical properties are summarized and parameter estimation is discussed. A simulation study is presented to illustrate the proposed model. Finally, an empirical application to a set of data concerning the daily number of stock transactions is also presented to attest for its practical applicability in data analysis.