Magda Monteiro

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.

Discrimination of water quality monitoring sites in River Vouga using a mixed-effect state space model

The surface water quality monitoring is an important concern of public organizations due to its relevance to the public health. Statistical methods are taken as consistent and essential tools in the monitoring procedures in order to prevent and identify environmental problems. This work presents the study case of the hydrological basin of the river Vouga, in Portugal. The main goal is discriminate the water monitoring sites using the monthly dissolved oxygen concentration dataset between January 2002 and May 2013. This is achieved through the extraction of trend and seasonal components in a linear mixed-effect state space model. The parameters estimation is performed with both maximum likelihood method and distribution-free estimators in a two-step procedure. The application of the Kalman smoother algorithm allows to obtain predictions of the structural components as trend and seasonality. The water monitoring sites are discriminated through the structural components by a hierarchical agglomerative clustering procedure. This procedure identified different homogenous groups relatively to the trend and seasonality components and some characteristics of the hydrological basin are presented in order to support the results.

A mixed-effect state space model to environmental data

This work presents some common issues in the statistical analysis of time series of environmental area. The discussion and the presentation of solutions is raised by the study of a time series of the oxygen concentration variable in a water quality monitoring site in the river Vouga hydrological basin in Portugal. Issues such as trends, seasonality, temporal correlation and detection of change points are addressed.

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.

A note on prediction bias for state space models with estimated parameters

This paper aims to discuss some problems on state space models with estimated parameters. While existing research focus on the prediction mean squared error, this work presents some results on bias propagation into forecast and filter predictions when the mean vector of the state is taking with an estimation bias, namely, non recursive analytical expression for them. In particular, it is discussed the impact of mean bias in invariant state space models.

A Comparison between Single Site Modeling and Multiple Site Modeling Approaches using Kalman Filtering

This work presents a comparative study between two approaches to calibrate radar rainfall in real time. The weather radar provides continuous measurements in real-time which have errors of either meteorological or instrumental nature. Locally, gauge measurements have a greater performance than radar measurements that can be used to improve radar estimates. One way of doing that is via a state space representation associated to the Kalman filter algorithm. In the single-site modeling approach we use the linear calibration model applied in [1] and [3] while the multivariate state-space model proposed in [6] is used in the multiple site approach. This work aims to discuss and compare these two different state space formulations based on the same data set.