<p>Diss. (sammanfattning) Stockholm : Handelshögskolan, 2006 [6], xiii, [1] s.: sammanfattning, s. 1-259, [5] s.: 4 uppsatser. Spikblad saknas</p>

The main topic of the paper is on-line filtering for non-Gaussian dynamic (state space) models by approximate computation of the first two posterior moments using efficient numerical integration. Based on approximating the prior of the state vector by a normal density, we prove that the posterior moments of the state vector are related to the posterior moments of the linear predictor in a simple way. For the linear predictor Gauss-Hermite integration is carried out with automatic reparametrization based on an approximate posterior mode filter. We illustrate how further topics in applied state space modelling such as estimating hyperparameters, computing model likelihoods and predictive residuals, are managed by integration-based Kalman-filtering. The methodology derived in the paper is applied to on-line monitoring of ecological time series and filtering for small count data. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

<p>Dynamic models, also termed state space models, comprise an extremely rich model class for time series analysis. This dissertation focuses on building state space models for a variety of contexts and computationally efficient methods for Bayesian inference for simultaneous estimation of latent states and unknown fixed parameters.</p><p>Chapter 1 introduces state space models and methods of inference in these models. Chapter 2 describes a novel method for jointly sampling the entire latent state vector in a nonlinear Gaussian state space model using a computationally efficient adaptive mixture modeling procedure. This method is embedded in an overall Markov chain Monte Carlo algorithm for estimating fixed parameters as well as states. In Chapter 3 the method of the previous chapter is implemented in a few illustrative</p><p>nonlinear models and compared to standard existing methods. This chapter also looks at the effect of the number of mixture components as well as length of the time series on the efficiency of the method. I then turn to an biological application in Chapter 4. I discuss modeling choices as well as derivation of the state space model to be used in this application. Parameter and state estimation are analyzed in these models for both simulated and real data. Chapter 5 extends the methodology introduced in Chapter 2 from nonlinear Gaussian models to general state space models. The method is then applied to a financial</p><p>stochastic volatility model on US $ - British £ exchange rates. Bayesian inference in the previous chapter is accomplished through Markov chain Monte Carlo which is suitable for batch analyses, but computationally limiting in sequential analysis. Chapter 6 introduces sequential Monte Carlo. It discusses two methods currently available for simultaneous sequential estimation of latent states and fixed parameters and then introduces a novel algorithm that reduces the key, limiting degeneracy issue while being usable in a wide model class. Chapter 7 implements the novel algorithm in a disease surveillance context modeling influenza epidemics. Finally, Chapter 8 suggests areas for future work in both modeling and Bayesian inference. Several appendices provide detailed technical support material as well as relevant related work.</p> / Dissertation

The topic of the paper is filtering for non-Gaussian dynamic (state space) models by approximate computation of posterior moments using numerical integration. A Gauss-Hermite procedure is implemented based on the approximate posterior mode estimator and curvature recently proposed in 121. This integration-based filtering method will be illustrated by a dynamic trend model for non-Gaussian time series. Comparision of the proposed method with other approximations ([15], [2]) is carried out by simulation experiments for time series from Poisson, exponential and Gamma distributions. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Η διαρκώς αυξανόμενη διαθεσιμότητα ηλεκτρονικών πηγών πληροφόρησης έχει δημιουργήσει νέα δεδομένα και απαιτήσεις στην περιοχή της Ανάκτησης Πληροφορίας. Υπάρχει αδιάκοπη ανάγκη για βελτίωση των υπαρχόντων και σχεδίαση νέων αλγορίθμων, που να επιτυγχάνουν υψηλή απόδοση και αξιοπιστία. Ένα επιπλέον ζητούμενο είναι η κατασκευή λογισμικού περιβάλλοντος που θα διευκολύνει τη χρήση υπαρχόντων αλγορίθμων, την εισαγωγή νέων, το συνδυασμό τους και τη συγκριτική αξιολόγησή τους. Στην παρούσα διδακτορική διατριβή, εστιάζουμε σε μεθόδους ανάκτησης πληροφορίας (με έμφαση στην ανάκτηση κειμένου), που έχουν στον πυρήνα τους τεχνολογίες Γραμμικής Άλγεβρας και πιο συγκεκριμένα σε τεχνικές που αξιοποιούν τα φασματικά χαρακτηριστικά των μητρώων όρων-κειμένων. Υπενθυμίζουμε ότι περίοπτη θέση στην περιοχή της Ανάκτησης Πληροφορίας, όσον αφορά τις τεχνικές της γραμμικής άλγεβρας, κατέχουν οι ιδιάζουσες τιμές και τα ιδιάζοντα διανύσματα των μητρώων. Περιγράφουμε επίσης το σχεδιασμό και την κατασκευή ενός ολοκληρωμένου περιβάλλοντος που διευκολύνει τους χρήστες στην ανάπτυξη, χρήση και αξιολόγηση των αλγορίθμων που στηρίζεται στο εξαιρετικά διαδεδομένο περιβάλλον της MATLAB. Αρχικά, εξετάζουμε τα βασικά προβλήματα στην Ανάκτηση Πληροφορίας, που είναι η ομαδοποίηση, η εξαγωγή σχετικών κειμένων και η κατηγοριοποίηση. Στην πρώτη κατηγορία προβλημάτων, στόχος μας είναι η βελτίωση παραδοσιακών αλγορίθμων όπως οι k-means και PDDP. Στο πλαίσιο αυτό προτείνουμε ένα σύνολο υβριδικών τεχνικών που βασίζονται στους δύο αυτούς αλγορίθμους και αντιμετωπίζουν προβλήματα που σχετίζονται με αυτούς. Ειδικότερα, πετυχαίνουν τη βελτίωση της απόδοσής τους ως προς την ποιότητα των παρεχόμενων αποτελεσμάτων ή ως προς την ταχύτητά τους. Σε σύγκριση με τον k-means, επιτυγχάνουν την αφαίρεση του στοιχείου της τυχαιότητας που τον χαρακτηρίζει, λόγω της γνωστής ευαισθησίας του στις αρχικές συνθήκες. Επιπλέον, προτείνουμε ένα ενιαίο σύνολο αποδοτικών "μεθόδων πυρήνα" (kernel methods) που μπορούν να χρησιμοποιηθούν στην περίπτωση που τα δεδομένα του προβλήματος έχουν μη γραμμικά χαρακτηριστικά. Οι παραπάνω υβριδικές μέθοδοι εφαρμόζονται και στο πρόβλημα της μπλοκ διαγωνιοποίησης στοχαστικών μητρώων που μοντελοποιούν για παράδειγμα χημικές διεργασίες, μέσω μαρκοβιανών αλυσίδων. Τα αρχικά αποτελέσματα που έχουμε, υποδεικνύουν ότι η προσέγγιση αυτή μπορεί να βελτιώσει σημαντικά υπάρχουσες μεθόδους, παρέχοντας ταυτόχρονα προσεγγίσεις του πλήθους των μπλοκ που αντιστοιχούν σε σταθερές καταστάσεις της μαρκοβιανής αλυσίδας. Τέλος, προτείνουμε μια διαφορετική προσέγγιση με τον αλγόριθμο ομαδοποίησης Oriented k-windows ο οποίος, όπως και ο PDDP, χρησιμοποιεί ιδιάζοντα διανύσματα (ισοδύναμα, κύριους άξονες - PCA) με σκοπό την εξαγωγή πληροφορίας αναφορικά με τον κυρίαρχο προσανατολισμό των ομάδων στον Ευκλείδειο χώρο. Στη συνέχεια, παρουσιάζουμε αλγορίθμους ανάκτησης σχετικών κειμένων και αλγορίθμους κατηγοριοποίησης που βασίζονται στη "Λανθάνουσα Σημασιολογική Δεικτοδότηση" (LSI). Πιο συγκεκριμένα, παρουσιάζουμε ένα αλγοριθμικό πλαίσιο που στηρίζεται σε μια "μεθοδολογία αντιπροσώπων", με την οποία προσπαθούμε να προσεγγίσουμε σημασιολογικά μια συλλογή, εξάγοντας υποχώρους του χώρου στηλών του μητρώου όρων-κειμένων που προσεγγίζουν τον βέλτιστο υποχώρο της διάσπασης ιδιαζουσών τιμών. Η μεθοδολογία μας χρησιμοποιεί αλγορίθμους ομαδοποίησης, όπως οι υβριδικές μέθοδοι που αναφέραμε, με σκοπό τη διάσπαση του προβλήματος σε ένα σύνολο όσο γίνεται περισσότερο ανεξάρτητων προβλημάτων που μπορούν να λυθούν περισσότερο αποδοτικά. Μέσα από μια εκτεταμένη πειραματική μελέτη, δείχνουμε ότι η συγκεκριμένη μεθοδολογία μπορεί να βελτιώσει άλλες διαδεδομένες προσεγγίσεις (LSI, LLSF κ.λπ.). Επίσης, επεκτείνουμε και εφαρμόζουμε τη "μεθοδολογία αντιπροσώπων" σε μεθόδους πυρήνα, καθώς επίσης και στο πρόβλημα υπολογισμού μη αρνητικών παραγοντοποίησεων μητρώων (NMF). Δείχνουμε ότι η χρήση της μεθοδολογίας επιφέρει σημαντική μείωση του κόστους σε μνήμη και υπολογισμούς των μεθόδων πυρήνα και βελτίωση της ποιότητας των αποτελεσμάτων της NMF. Η διατριβή στάθηκε αφορμή για την ανάπτυξη ενός ολοκληρωμένου λογισμικού περιβάλλοντος. Πιο συγκεκριμένα, οι νέες μέθοδοι που αναφέραμε, καθώς και άλλες διαδεδομένες τεχνικές έχουν υλοποιηθεί και ενταχθεί στο περιβάλλον Text to Matrix Generator (TMG). Το TMG στηρίζεται κατά κύριο λόγο στη MATLAB ενώ μικρότερα τμήματά του έχουν γραφτεί σε Perl. Το TMG αποτελείται από έξι τμήματα, ενώ είναι εύκολα επεκτάσιμο. Τα τμήματα αυτά παρέχουν μια ευρεία συλλογή μεθόδων ανάκτησης πληροφορίας που αποτελείται από μεθόδους (i) κατασκευής και ανανέωσης μητρώων όρων-κειμένων, (ii) υπολογισμού προσεγγίσεων μειωμένης διάστασης και (iii) μη αρνητικών παραγοντοποιήσεων, (iv) ανάκτησης σχετικών κειμένων, (v) ομαδοποίησης και (vi) κατηγοριοποίησης. Για όλα τα παραπάνω, το εργαλείο παρέχει κατάλληλα προσαρμοσμένες γραφικές διεπαφές που διευκολύνουν το χρήστη. Εναλλακτικά, οι λειτουργίες του μπορούν να κληθούν απευθείας από τη γραμμή εντολών. Το TMG διευκολύνει την ταχεία προτοτυποποίηση αλγορίθμων και διατίθεται ελεύθερα μέσω ιστοσελίδας (http://scgroup.hpclab.ceid.upatras.gr/scgroup/Projects/TMG/). Από αναζητήσεις τεκμηριώνεται ότι έχει υποστηρίξει πολλούς επιστήμονες παγκοσμίως τόσο σε ερευνητικό όσο και σε εκπαιδευτικό επίπεδο. Περιγράφουμε επίσης τις πρόσφατες εργασίες μας για την ανάδειξη του TMG ως υπηρεσίας στον Παγκόσμιο Ιστό. Ειδικότερα, αναπτύσσεται λογισμικό για την απομακρυσμένη χρήση του TMG μέσω ειδικού API και τίθενται οι βάσεις για μελλοντική έρευνα που θα αφορά στην βελτιωμένη επίδοση και στην αποδοτική χρήση του συστήματος. / The amount of digital data is rapidly growing and continuously motivates research innovation in Information Retrieval. Much of the data is text, so there is an ever present need to push the field of Text Mining forward by designing and implementing novel, effective algorithms that attain high performance and reliability. It is also desirable to develop software environments that facilitate not only access to existing methods, but also enable the rapid prototyping, performance evaluation and incorporation of new algorithms for Text Mining. In this research we focus on algorithms that use Linear Algebra and Matrix Analysis tools as computational kernels. We use the term spectral to highlight the fact that our methods rely on the spectral characteristics of the underlying term-document matrices that encode the texts under study. We consolidate our new and existing algorithms in a software environment, called TMG, that we built on top of MATLAB and Perl. First, we consider the basic text mining tasks, namely clustering, ad-hoc retrieval and text classication. In clustering, we focus on a well-known spectral method, called PDDP (Principal Direction Divisive Partitioning) and investigate hybrid methods that combine PDDP and standard workhorses such as k-means. In particular, the proposed methods improve the performance of the aforementioned algorithms, regarding the quality of the attained clustering and/or their speed. Compared with k-means, our algorithms eliminate the non-determinism originating from k-means' initialization phase. We also propose a framework for kernel methods, that can be used in case the data exhibit non-linearities. Our spectral clustering algorithms are applied in sparse matrix reordering, specifically in the block diagonalization of row stochastic matrices. In addition to helping in the intepretation of a recent method for identifying metastable states of Markov chains, they also provide the means to improve their performance. Initial results, demonstrate that the proposed methodology can improve significantly over existing techniques, deriving approximations of the number of blocks corresponding to dinstict stable states of the underlying Markov chain. We also show how to use spectral methods to improve the performance of a density-based clustering approach, called Oriented k-windows. In particular, the algorithm uses information derived from the Principal Component Analysis (PCA), in order to guide a windowing technique, namely k-windows, that could give insights about the data orientation. The next part of the thesis deals with ad-hoc retrieval and classification methods, based on Latent Semantic Indexing (LSI). We propose an algorithmic framework based on a "representatives methodology", in order to approximate a collection semantically, by extracting subspaces of the column space of the term-document matrix, that approximate the optimal subspace derived by the SVD. Our methodology uses clustering techniques, like the aforementioned hybrid methods, in a preprocessing stage. Our objective is to split the problem into a set of independent subproblems that could be solved more efficiently. Results from extensive experimentation indicate that our methodology can improve a state-of-the-art method like LSI. We also apply the representatives methodology to kernel methods and Nonnegative Matrix Factorization (NMF). Extensive numerical experiments indicate that this methodology improves the computational cost and memory requirements of kernel methods and also increases the quality of the nonnegative approximations. We have incorporated all the proposed methods in a software environment, called Text to Matrix Generator (TMG). The first release of TMG was before this Ph.D. was even started. but has since undergone several upgrades and rewrites. TMG currently consists of six easily extensible modules. These modules provide methods for (i) constructing and updating term-document matrices, (ii) computing low rank approximations and (iii) non negative factorizations, and (iv) ad-hoc retrieval, (v) clustering and (vi) classification. TMG is accessible in two primary modes, graphical and command line and is freely downloadable from its webpage (http://scgroup.hpclab.ceid.upatras.gr/scgroup/Projects/TMG/). As our usage logs indicate, TMG is being used worldwide for research and educational uses. We also describe a brief overview of open problems and ongoing work. We describe our first version of "remote TMG", that views TMG as a Web resource and provides remote access mode to it by means of a special API.

This thesis explores the methodology of state, and in particular, parameter estimation for time series datasets. Various approaches are investigated that are suitable for nonlinear models and non-Gaussian observations using state space models. The methodologies are applied to a dataset consisting of the historical lynx and hare populations, typically modeled by the Lotka- Volterra equations. With this model and the observed dataset, particle filtering and parameter estimation methods are implemented as a way to better predict the state of the system. Methods for parameter estimation considered include: maximum likelihood estimation, state augmented particle filtering, multiple iterative filtering and particle Markov chain Monte Carlo (PMCMC) methods. The specific advantages and disadvantages for each technique are discussed. However, in most cases, PMCMC is the preferred parameter estimation solution. It has the advantage over other approaches in that it can well approximate any posterior distribution from which inference can be made. / Master's thesis

Background: Respiratory illnesses can have a substantial impact on population health and burden hospitals in terms of patient load. Advance warnings of the spread of such illness could inform public health interventions and help hospitals manage patient services. Previous research showed that calls for respiratory complaints to Telehealth Ontario are correlated up to two weeks in advance with emergency department visits for respiratory illness at the provincial level. Objectives: This thesis examined whether Telehealth Ontario calls for respiratory complaints could be used to accurately forecast the daily and weekly number of emergency department visits for respiratory illness at the health unit level for each of the 36 health units in Ontario up to 14 days in advance in the context of a real-time syndromic surveillance system. The forecasting abilities of three different time series modeling techniques were compared. Methods: The thesis used hospital emergency department visit data from the National Ambulatory Care Reporting System database and Telehealth Ontario call data and from June 1, 2004 to March 31, 2006. Parallel Cascade Identification (PCI), Fast Orthogonal Search (FOS), and Numerical Methods for Subspace State Space System Identification (N4SID) algorithms were used to create prediction models for the daily number of emergency department visits using Telehealth call counts and holiday/weekends as predictors. Prediction models were constructed using the first year of the study data and their accuracy was measured over the second year of data. Factors associated with prediction accuracy were examined. Results: Forecast error varied widely across health units. Prediction error increased with lead time and lower call-to-visits ratio. Compared with N4SID, PCI and FOS had significantly lower forecast error. Forecasts of the weekly aggregate number of visits showed little evidence of ability to accurately flag corresponding actual increases. However, when visits were aggregated over a four day period, increases could be flagged more accurately than chance in six of the 36 health units accounting for approximately half of the Ontario population. Conclusions: This thesis suggests that Telehealth Ontario data collected by a real-time syndromic surveillance system could play a role in forecasting health services demand for respiratory illness. / Thesis (Master, Community Health & Epidemiology) -- Queen's University, 2009-08-11 16:20:44.553

O presente estudo analisa a evolução, o comportamento e a natureza cíclica do crédito brasileiro no período compreendido entre janeiro de 2003 e dezembro de 2013. Mais especificamente, verifica se a postura da condução da oferta de crédito público, de fato, destoou daquela apresentada pelo crédito privado, especialmente após o advento da crise financeira de 2007/2008. Para tanto, se vale de uma revisão das literaturas nacional e internacional e realiza um resgate histórico dos principais bancos públicos do Brasil – etapa que se dá concomitantemente à análise da evolução do desempenho dos mesmos nos últimos tempos. Com isso, além de se mostrar a performance recente destas instituições, demonstra-se também que, a despeito da redução da participação das instituições bancárias públicas na década de 1990, estas foram decisivas para a melhor reação da economia brasileira frente aos efeitos adversos da crise de 2007/2008 – o que fornece mais indícios da validade do problema de pesquisa e traz, por conseguinte, mais força à hipótese de trabalho. Na sequência, são discutidos alguns aspectos metodológicos no intuito de identificar qual a modelagem econométrica seria a mais adequada para descobrir como os bancos públicos e privados se comportaram no período abordado e, mais especificamente, como eles reagiram após o advento da crise financeira dos subprimes – procurou-se também, uma abordagem que, especificamente, ajudasse a desvendar a natureza cíclica dos créditos privado e público. Nesse sentido, optou-se pela modelagem econométrica denominada de Modelos Estruturais de Espaço de Estados, também conhecida como Modelos de Componentes não-observáveis. Através desta metodologia, foi possível verificar, de maneira endógena, se existiram e quando ocorreram outliers e quebras estruturais nas séries de dados referentes à evolução do crédito brasileiro no período. Os resultados obtidos vieram a corroborar a hipótese de trabalho, mostrando a existência de uma relação negativa e estatisticamente significante entre as variáveis representativas do produto interno bruto e as do crédito público e do crédito total. Dessa maneira, chegou-se à conclusão de que, realmente, o crédito público mostrou características contra-cíclicas no período de 2003 a 2013, especialmente após o ano de 2008 – fato que é reforçado pela ocorrência de quebras de nível positivas neste ano. / This study analyses the evolution, behavior and cyclical nature of the Brazilian credit supply in the period from January 2003 to December 2013. Specifically, it checks if the posture of public credit supply’s conduction has differed, indeed, from the one presented by the private credit, particularly after the financial crisis of 2007-08. For this purpose, this paper reviews national and international literature and performs a historical examination of the main Brazilian state-owned banks – which is presented concomitantly to the analysis of their lately performance’s evolution. Therewith, besides showing these institutions’ recent performance, it also demonstrates that, in spite of the reduction in the state-owned banks participation in the 1990s, these were decisive to the better reaction of the Brazilian economy in the face of the adverse effects of the 2007-08 crisis – which provides further evidence of the research question validity and brings, therefore, strenght to the working hypothesis. In the next step, some methodological aspects are discussed aiming to identify which would be the most appropriate econometric modelling to find out how the public and private banks behaved in this period, and specifically, to discover how they reacted after the subprime financial crisis – in this point, a research was made in order to identify an approach that, particularly, helped to reveal the cyclical nature of private and public credits. It was decided to use an econometric approach called Space-State Modelling, also known as Unobservable Component Models. Through this methodology, it was possible to check, in an endogenous way, if there were – and when they occurred – outliers and structural breaks in the data series referring to the Brazilian credit evolution in the period. The results came to support the working hypothesis, showing the existence of a negative and statistically significant relationship between the variables representing the gross domestic product and the ones representing public credit and the total credit. Thus, it was concluded that the public credit, indeed, showed counter-cyclical characteristics in the period between 2003 and 2013, especially after 2008 – a fact that is reinforced by the occurrence of positive level breaks in this year.

Considerando a importância de uma medida de alta frequência para o PIB do Rio Grande do Sul, o principal indicador de atividade econômica do estado, este trabalho foi dividido em três objetivos. O primeiro foi a estimação de uma série com frequência mensal para o PIB real do Rio Grande do Sul entre janeiro de 2002 e março de 2017, dado que o mesmo só é contabilizado em frequência trimestral. Para tanto, foi utilizado um modelo em espaço de estados que permite a estimação e nowcast do PIB mensal, utilizando séries coincidentes como fonte de informação para a interpolação dos dados trimestrais do PIB, em linha com Bernanke, Gertler e Watson (1997), Mönch e Uhlig (2005) e Issler e Notini (2016). O segundo objetivo foi comparar a série estimada com um indicador de atividade calculado pelo Banco Central do Brasil para o estado, o Índice de Atividade Econômica Regional (IBCR-RS), tanto em termos metodológicos como na capacidade em antecipar as variações do PIB trimestral antes de sua divulgação (nowcasting). O terceiro objetivo foi estabelecer a cronologia dos ciclos de expansão e recessão da economia gaúcha com o uso do algoritmo de Bry e Boschan (1971). Após a etapa de seleção das séries coincidentes e da estimação de diversos modelos de interpolação, foi escolhido para gerar a série mensal do PIB o modelo que utiliza somente a produção industrial como variável auxiliar, tendo este apresentado o melhor ajuste. A comparação do PIB mensal interpolado com o IBCR-RS mostrou que, além da vantagem computacional a favor do método proposto neste trabalho, a imposição da disciplina de que as variações do PIB mensal estimado devem ser exatamente iguais às do PIB trimestral faz com que a dinâmica de curto e longo prazo das variáveis sejam idênticas, o que não ocorre com o IBCR-RS. A cronologia dos pontos de inflexão da atividade econômica apontou três períodos recessivos na economia gaúcha desde janeiro de 2002: jun/2003 a abr/2005 (23 meses e queda acumulada de 8,79%); abr/2011 a abr/2012 (13 meses e queda acumulada de 9,47%); e jun/2013 a nov/2016 (42 meses e queda acumulada de 10,41%), sendo o encerramento deste último apontado somente com a inclusão dos resultados estimados pelo modelo para o segundo trimestre de 2017. Finalmente, os resultados do exercício de nowcasting do PIB mostraram desempenho superior do método proposto frente ao IBCR-RS em termos de antecipação do resultado do PIB de um trimestre a frente, tomando como base as medidas de MAE (erro absoluto médio, em inglês) e MSE (erro quadrático médio, em inglês), comumente usadas nesse intuito. / Giving the importance of a high frequency measure for Rio Grande do Sul’s GDP, the main indicator of economic activity of the state, this work was divided into three objectives. The first one was the estimation of monthly frequency series for Rio Grande do Sul’s real GDP between January/2002 and March/2017, since it is only accounted in quarterly basis. Therefore, we used a State-Space model that enables to estimate and nowcast the monthly GDP, using coincident series as a source of information for the interpolation of quarterly GDP data, in line with Bernanke, Gertler e Watson (1997), Mönch e Uhlig (2005) and Issler e Notini (2016). The second objective was to compare the estimated series with an activity indicator calculated by the Central Bank of Brazil for the state, the Regional Economic Activity Index (IBCR-RS), both in methodological terms and in the capability to anticipate the quarterly GDP release (nowcasting). The third objective was to establish the chronology of the cycles of expansion and recession of the economy of Rio Grande do Sul using the algorithm of Bry e Boschan (1971). After the selection of the coincident series and the estimation of several interpolation models, the chosen model to generate the monthly GDP series uses only the industrial production as an auxiliary variable, and this one presented the best fit. The comparison of the monthly GDP interpolated with the IBCR-RS showed that, in addition to the computational advantage in favor of the method proposed in this work, the imposition of the discipline that the estimated monthly GDP changes must be exactly the same as the quarterly GDP makes the short-term and long-term dynamics of the variables are identical, which is not the case with IBCR-RS. The chronology of the turning points of the economic activity pointed to three recessive periods in the economy of Rio Grande do Sul since January 2002: June/2003 to April/2005 (23 months and accumulated drop of 8.79%); April/2011 to April/2012 (13 months and accumulated fall of 9.47%); and June/2013 to November/2016 (42 months and 10.41% accumulated decrease), with the latter one closing only with the inclusion of the results estimated by the model for the second quarter of 2017. Finally, results for GDP’s nowcasting showed superior performance of the proposed method compared to the IBCR-RS in terms of anticipating quarter-to-quarter GDP results, based on the measures of MAE (absolute mean error) and MSE (mean square error), commonly used for this purpose.

Considerando a importância de uma medida de alta frequência para o PIB do Rio Grande do Sul, o principal indicador de atividade econômica do estado, este trabalho foi dividido em três objetivos. O primeiro foi a estimação de uma série com frequência mensal para o PIB real do Rio Grande do Sul entre janeiro de 2002 e março de 2017, dado que o mesmo só é contabilizado em frequência trimestral. Para tanto, foi utilizado um modelo em espaço de estados que permite a estimação e nowcast do PIB mensal, utilizando séries coincidentes como fonte de informação para a interpolação dos dados trimestrais do PIB, em linha com Bernanke, Gertler e Watson (1997), Mönch e Uhlig (2005) e Issler e Notini (2016). O segundo objetivo foi comparar a série estimada com um indicador de atividade calculado pelo Banco Central do Brasil para o estado, o Índice de Atividade Econômica Regional (IBCR-RS), tanto em termos metodológicos como na capacidade em antecipar as variações do PIB trimestral antes de sua divulgação (nowcasting). O terceiro objetivo foi estabelecer a cronologia dos ciclos de expansão e recessão da economia gaúcha com o uso do algoritmo de Bry e Boschan (1971). Após a etapa de seleção das séries coincidentes e da estimação de diversos modelos de interpolação, foi escolhido para gerar a série mensal do PIB o modelo que utiliza somente a produção industrial como variável auxiliar, tendo este apresentado o melhor ajuste. A comparação do PIB mensal interpolado com o IBCR-RS mostrou que, além da vantagem computacional a favor do método proposto neste trabalho, a imposição da disciplina de que as variações do PIB mensal estimado devem ser exatamente iguais às do PIB trimestral faz com que a dinâmica de curto e longo prazo das variáveis sejam idênticas, o que não ocorre com o IBCR-RS. A cronologia dos pontos de inflexão da atividade econômica apontou três períodos recessivos na economia gaúcha desde janeiro de 2002: jun/2003 a abr/2005 (23 meses e queda acumulada de 8,79%); abr/2011 a abr/2012 (13 meses e queda acumulada de 9,47%); e jun/2013 a nov/2016 (42 meses e queda acumulada de 10,41%), sendo o encerramento deste último apontado somente com a inclusão dos resultados estimados pelo modelo para o segundo trimestre de 2017. Finalmente, os resultados do exercício de nowcasting do PIB mostraram desempenho superior do método proposto frente ao IBCR-RS em termos de antecipação do resultado do PIB de um trimestre a frente, tomando como base as medidas de MAE (erro absoluto médio, em inglês) e MSE (erro quadrático médio, em inglês), comumente usadas nesse intuito. / Giving the importance of a high frequency measure for Rio Grande do Sul’s GDP, the main indicator of economic activity of the state, this work was divided into three objectives. The first one was the estimation of monthly frequency series for Rio Grande do Sul’s real GDP between January/2002 and March/2017, since it is only accounted in quarterly basis. Therefore, we used a State-Space model that enables to estimate and nowcast the monthly GDP, using coincident series as a source of information for the interpolation of quarterly GDP data, in line with Bernanke, Gertler e Watson (1997), Mönch e Uhlig (2005) and Issler e Notini (2016). The second objective was to compare the estimated series with an activity indicator calculated by the Central Bank of Brazil for the state, the Regional Economic Activity Index (IBCR-RS), both in methodological terms and in the capability to anticipate the quarterly GDP release (nowcasting). The third objective was to establish the chronology of the cycles of expansion and recession of the economy of Rio Grande do Sul using the algorithm of Bry e Boschan (1971). After the selection of the coincident series and the estimation of several interpolation models, the chosen model to generate the monthly GDP series uses only the industrial production as an auxiliary variable, and this one presented the best fit. The comparison of the monthly GDP interpolated with the IBCR-RS showed that, in addition to the computational advantage in favor of the method proposed in this work, the imposition of the discipline that the estimated monthly GDP changes must be exactly the same as the quarterly GDP makes the short-term and long-term dynamics of the variables are identical, which is not the case with IBCR-RS. The chronology of the turning points of the economic activity pointed to three recessive periods in the economy of Rio Grande do Sul since January 2002: June/2003 to April/2005 (23 months and accumulated drop of 8.79%); April/2011 to April/2012 (13 months and accumulated fall of 9.47%); and June/2013 to November/2016 (42 months and 10.41% accumulated decrease), with the latter one closing only with the inclusion of the results estimated by the model for the second quarter of 2017. Finally, results for GDP’s nowcasting showed superior performance of the proposed method compared to the IBCR-RS in terms of anticipating quarter-to-quarter GDP results, based on the measures of MAE (absolute mean error) and MSE (mean square error), commonly used for this purpose.