Modelos estruturais na análise de séries temporais de dados ambientais

Dissertação de mestrado em EstatísticaOs modelos em espaço de estados constituem uma classe de modelos muito importante na área de séries temporais devido à sua flexibilidade na análise de fenómenos dinâmicos e da evolução de sistemas que variam, de forma aleatória com significativa variabilidade, ao longo do tempo e têm contribuído significativamente para estender os domínios clássicos da análise de séries temporais. Neste estudo, no contexto de um problema de monitorização da qualidade da água de superfície numa bacia hidrográfica, propõe-se uma abordagem baseada em modelos estruturais de séries temporais com representação em espaço de estados associados ao Filtro de Kalman com o principal objetivo de analisar e avaliar a evolução temporal de séries de variáveis ambientais, identificando tendências ou possíveis mudanças na qualidade da água num contexto dinâmico de controlo. Os dados dizem respeito à bacia hidrográfica do rio Ave, localizada no Noroeste de Portugal, onde a monitorização da qualidade da água se tornou uma prioridade, porque a água tem apresentado um estado de forte degradação desde há muito anos. Para o processo de modelação consideraram-se as séries temporais relativas à variável de qualidade de Oxigénio Dissolvido, medido mensalmente num período de 15 anos (janeiro de 1999 - janeiro de 2014) em 7 estações de amostragem. Assim, são apresentadas de uma forma sucinta as etapas necessárias para o estabelecimento da metodologia a aplicar: os modelos de séries temporais, os modelos em espaço de estados, o Filtro de Kalman, os modelos estruturais e a estimação pela máxima verosimilhança. Os modelos em espaço de estados mostram a versatilidade da incorporação de componentes não observadas (estados), de natureza estocástica, que descrevem a variação da série temporal, tais como a tendência e a sazonalidade, que são atualizadas em tempo real de forma recursiva à medida que novas observações ficam disponíveis e melhorando as previsões ao refletirem a natureza dinâmica do processo em estudo e que têm uma interpretação natural, representando as principais características das séries temporais ambientais sob investigação. Do ponto de vista ambiental, a abordagem proposta permite a obtenção de conclusões pertinentes relativas à avaliação da qualidade da água de superfície e de pontos de mudança destacando assim o valor potencial deste tipo de metodologias e identificando mudanças inesperadas que são importantes no processo de gestão e avaliação da qualidade da água.State space models constitute significantly important class of models in time series analysis due to their flexibility in dynamic phenomena analysis and of variable systems evolution, randomly and with meaningful variability throughout time and have significantly contributed to extending the classic domains of application of statistical time series analysis. In this study, in the context of a surface water quality monitoring problem in a river basin, it is proposed an approach for the structural time series analysis based on the state space models associated to the Kalman filter. The main goal is to analyze and evaluate the temporal evolution of the environmental time series, and to identify trends or possible changes in the water quality within a dynamic monitoring procedure. The data concerns the River Ave's hydrological basin located in the Northwest of Portugal, where monitoring has become a priority in water quality planning and management because its water has been in a state of obvious environmental degradation for many years. As a result, the watershed is now monitored by seven monitoring sites distributed along the River Ave and its main streams. For the modeling process we consider time series relating to the Dissolved Oxygen water variable measured on a monthly basis over a 15-year period (January 1999 January 2014). Thus, are presented succinctly the necessary stages for the establishment of the methodology to apply: the time series models, the state space models, the Kalman filter, the structural models and the maximum likelihood estimation. State space models show the versatility of the incorporation of unobserved components (states), of stochastic nature, that describe the variation of time series, such as trends and seasonality, which are updated in real time in a recursive way, as new observations become available and help to improve the forecasts, by reflecting the dynamic nature of the studied process and that have a natural interpretation, representing the salient features of the environmental time series under investigation. From an environmental point of view, the proposed approach allows to obtain pertinent findings concerning water surface quality interpretation and change point of view, thus highlighting the potential value of this type of analysis, by identifying unexpected changes that are important for the process of management and evaluation of water quality

Time series analysis by state space models applied to a water quality data in Portugal

Time series analysis by state space models provide a very flexible tool for analysing dynamic phenomena and evolving systems, and have significantly contributed to extending the classical domains of application of statistical time series analysis. In this study, in the context of a surface water quality monitoring problem in a river basin, it is proposed an approach for the structural time series analysis based on the state space models associated to the Kalman filter. The main goals are to analyse and evaluate the temporal evolution of the environmental time series, and to identify trends or possible changes in the water quality on a dynamic monitoring procedure. The data concerns the River Ave's hydrological basin located in the Northwest of Portugal, where monitoring has become a priority in water quality planning and management because its water has been in a state of obvious environmental degradation for many years. As a result, the watershed is now monitored by seven monitoring sites distributed along the River Ave and its main streams. For the modeling process we consider the monthly dissolved oxygen concentration dataset between January 1999 and January 2014. The framework of the state space models shows versatility to incorporate unobserved components, such as trends, cycles and seasonals, that have a natural interpretation and represent the salient features of the environmental time series under investigation. From the environmental point of view, the proposed approach allows to obtain pertinent findings concerning water surface quality interpretation and change point, thus highlighting the potential value of this type of analysis, and it is also relevant to identify unanticipated changes that are important in the management process and for the assessment of water quality.A. Manuela Gonc¸alves was supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the FCT-Fundac¸ao para a Ciência e aTecnologia, through the Project PEstOE/MAT/UI0013/2014. Marco Costa was supported by Portuguese funds through the CIDMA-Centre for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology ”FCT-Fundac¸ao para a Ciência e a Tecnologia”, within project UID/MAT/04106/2013

Structural time series modeling: an application to environmental variables

A structural time series model is one which is set up in terms of components which have a direct interpretation. In this paper, the discussion focuses on the dynamic modeling procedure based on the state space approach (associated to the Kalman filter), in the context of surface water quality monitoring, in order to analyze and evaluate the temporal evolution of the environmental variables, and thus identify trends or possible changes in water quality (change point detection). The approach is applied to environmental time series: time series of surface water quality variables in a river basin. The statistical modeling procedure is applied to monthly values of physicochemical variables measured in a network of 8 water monitoring sites over a 15-year period (1999-2014) in the River Ave hydrological basin located in the Northwest region of Portugal.Marco Costa was supported by Portuguese funds through the CIDMA-Centre for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology \FCT-Funda ção para a Ciência e a Tecnologia", within project UID/MAT/04106/2013. A. Manuela Gon calves was supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the \FCT-Funda ção para a Ciência e a Tecnologia", through the Project PEstOE/MAT/UI0013/2014