Sequential pattern mining of price interactions

Conferência realizada em Angra do Heroísmo, Açores, de 9-12 de Setembro de 2013The computational analysis of large quantities of data is an important asset for the economic study of interactions among social agents. However, most of available frequent pattern discovery techniques result in a huge number of rules and scalability problems that end up requiring unnecessary subjectivity in data interpretation. This work presents Ramex-Forum, a visualization technique that can highlight important relations often hidden in economic data. A case study using recent asset prices on global economic data confi rm the usefulness of the approach for expressing economic influence cues as poly-trees

Improved Visualization of Frequent Itemset Relationships Using the Minimal Spanning Tree Algorithm

Descriptive data mining techniques offer a way of extracting useful information out of large datasets and presenting it in an interpretable fashion to be used as a basis for future decisions. Since users interpret information most easily through visual means, techniques which produce concise, visually attractive results are usually preferred. We define a method, which converts transactional data into tree-like data structures, which depict important relationships between items contained in this data. The new approach we propose is offering a way to mitigate the loss of information present in previously developed algorithms, which use mined frequent itemsets and construct tree structures. We transfer the problem to the domain of graph theory and through minimal spanning tree construction achieve more informative visualizations. We highlight the new approach with comparison to previous ones by applying it on a real-life datasets – one connected to market basket data and the other from the educational domain

A post Keynesian framework of exchange rate determination

This cumulative dissertation consists of three independent papers on Latin American exchange rates. The three works have in common that volatility and uncertainty play a crucial role for the understanding of exchange rates. The first study, “A post-Keynesian framework of exchange rate determination: a dynamical approach”, presents a mathematical approach to exchange rates dynamics. Following a post-Keynesian approach for exchange rate determination, we develop a model where the dynamics are driven by expectations. The model is capable of producing a rich variety of dynamic behaviors whose complexity is characterized by using the entropy measure. This work also introduces the notion of dynamic regime and shows how it can be used to analyze exchange rates under the post Keynesian framework. This approach contributes to the debate upon these issues, since literature has not provided a comprehensive explanation regarding the volatility of exchange rates in emerging peripheral economies. The second study, “An Application of Minimum Spanning Tress and Hierarchical Tress to the Study of Latin American Exchange Rates”, analyzes a group of nine Latin American currencies with the aim to identify clusters of exchange rates that present similar co-movements. In this work the study of currency relationships is formulated as a network problem where each currency is represented as a node, and the relationship between each pair of currencies as a link. The paper combines two method: Symbolic Time Series Analysis (STSA) and a clustering method based on the Minimal Spanning Tree (MST) from which we obtain a Hierarchical Tree (HT). Symbolic Time Series Analysis consists of the transformation of a given time series into a symbolic sequence with the aim of identifying patterns in the set of data. The Minimal Spanning Tree condenses the core information on the global structure of the network, and its main advantage is that it greatly simplifies comparisons by dramatically reducing the number of elements that must be compared. We identify two main clusters in the currency network, as well as specific currencies that function as transmission channels between clusters. Using data regarding the degree of financial liberalization, as well as the distinction between inflation targeting (IT) and non-IT countries, the analysis suggests that the obtained taxonomy is economically relevant. In the third study, “Entropy evolution of Latin American exchange rates”, we analyze the entropy evolution of nine Latin American currencies before and after the financial crisis of 2008. We utilize the concept of entropy to analyze the evolution of the exchange rates in terms of the ‘randomness of the third kind’. This randomness is produced by the continuing interaction between open-systems; as they interact, they exchange information and modify their levels of randomness. The main contribution of this chapter is threefold: First, we identify cycles in the evolution of entropy. Particularly, we observe the presence of entropic bubbles. Second, we address the question of differences in exchange rate regimes. We introduce an entropic ranking and classify currencies. Thereby we show that low entropy is associated with fix regimes, and high entropy with floating regimes. Finally, we introduce a statistical randomness test based on the entropy measure. The results reject randomness in all cases, which implies that pure flotation regimes are not present.Die vorliegende, kumulative Dissertation besteht aus drei eigenständigen Arbeiten über lateinamerikanische Wechselkurse. Diese drei haben gemeinsam, dass Volatilität und Unsicherheit als entscheidende Faktoren für das Verständnis, wie Wechselkurse funktionieren, identifiziert wurden. Das erste Kapitel, „A post-Keynesian framework of exchange rate determination: a dynamical approach“, beschreibt einen mathematische Herangehensweise zur Wechselkursdynamik. Ausgehend von einem postkeynesianischen Ansatz zur Wechselkursbestimmung, entwickeln wir ein Modell, bei dem die Dynamik von den Erwartungen bestimmt wird. Das Modell ist in der Lage eine Vielzahl von dynamischen Verhaltensweisen zu erzeugen, deren Komplexität durch die Verwendung des Entropiemaßes charakterisiert wird. Diese Arbeit führt auch in den Begriff des dynamischen Regimes ein und zeigt, wie er zur Analyse von Wechselkursen im postkeynesianischen Rahmen verwendet werden kann. Dieser Ansatz trägt zur Debatte über diese Fragen bei, da die Literatur keine umfassende Erklärung für die Volatilität der Wechselkurse in Schwellenländern der Peripherie liefert. Die zweite Studie, „ An Application of Minimum Spanning Tress and Hierarchical Tress to the Study of Latin American Exchange Rates“, analysiert eine Gruppe von neun lateinamerikanischen Währungen mit dem Ziel, Cluster von Wechselkursen mit ähnlichen Co-Bewegungen zu identifizieren. In dieser Arbeit wird die Untersuchung von Währungsbeziehungen als Netzwerkproblem formuliert, wobei jede Währung als Knoten, und die Beziehung zwischen jedem Währungspaar als Verbindung dargestellt wird. Der Artikel kombiniert zwei Methoden: die symbolische Zeitreihenanalyse (STSA) und eine Clustering-Methode, die auf dem Minimal Spanning Tree (MST) basiert. Daraus erhalten wir einen hierarchischen Baum (HT). Die symbolische Zeitreihenanalyse besteht in der Umwandlung einer bestimmten Zeitreihe in eine symbolische Folge mit dem Ziel, Muster in der Datenmenge zu identifizieren. Der Minimal Spanning Tree verdichtet die Kerninformationen über die globale Struktur des Netzwerks und hat den Hauptvorteil, dass Vergleiche erheblich vereinfacht werden, indem die Anzahl der zu vergleichenden Elemente drastisch reduziert wird. Wir identifizieren zwei Hauptcluster im Währungsnetzwerk, sowie bestimmte Währungen, die als Übertragungskanäle zwischen Clustern fungieren. Unter Verwendung von Daten zum Grad der Finanzliberalisierung, sowie zur Unterscheidung zwischen Inflation Targeting (IT) und Nicht-IT-Ländern, lässt die Analyse darauf schließen, dass die ermittelte Taxonomie wirtschaftlich relevant ist. In der dritten Studie, „Entropy evolution of Latin American exchange rates“, analysieren wir die Entropieentwicklung von neun lateinamerikanischen Währungen vor und nach der Finanzkrise von 2008. Wir verwenden das Konzept der Entropie, um die Entwicklung der Wechselkurse im Hinblick auf die Zufälligkeit der dritten Art zu analysieren. Diese Zufälligkeit entsteht durch die ständige Interaktion zwischen offenen Systemen; während der Interaktion tauschen sie Informationen aus und ändern ihre Zufälligkeitsebenen. Der Hauptbeitrag dieses Kapitels teilt sich in drei Teile auf. Zunächst identifizieren wir Zyklen in der Entwicklung der Entropie. Hierbei beobachten wir insbesondere das Vorhandensein von entropischen Blasen. Zweitens befassen wir uns mit der Frage der Unterschiede in den Wechselkursregelungen. Hierzu führen wir ein entropisches Ranking ein und klassifizieren Währungen. Wir zeigen, dass niedrige Entropie mit festen Regimen verbunden ist und hohe Entropie mit Flotationsregimen. Schließlich führen wir einen statistischen Zufallstest ein, der auf dem Entropiemaß basiert. Die Ergebnisse lehnen in allen Fällen die Zufälligkeit ab, was impliziert, dass keine reinen Flotationsregime vorhanden sind

Ramex-Forum: a tool for displaying and analysing complex sequential patterns of financial products

Financial data provides a valuable up‐to‐date knowledge of the world economy. However, it is presented in extremely large data volumes, in diverse formats, and is constantly being updated at a high speed. The Ramex‐Forum algorithm is oriented to guide financial experts in finding new and relevant information.We present a sensitivity analysis and newvisualizations using an improved version of the Ramex‐Forum algorithm. The proposed algorithm is applied to two case studies – the petroleum production chain and the European financial institutions risk analysis. Different combinations of parameters and new ways to visualize data are used. Results highlight the importance of Ramex‐Forum for analysing relevant relationships in price variations in financial markets.info:eu-repo/semantics/publishedVersio

Theory and Calibration of Swap Market Models

This paper introduces a general framework for market models, named Market Model Approach, through the concept of admissible sets of for-ward swap rates spanning a given tenor structure. We relate this concept to results in graph theory by showing that a set is admissible if and only if the associated graph is a tree. This connection enables us to enumerate all admissible models for a given tenor structure. Three main classes are identified within this framework, and correspond to the co-terminal, co-initial, and co-sliding model. We prove that the LIBOR market model is the only admissible model of a co-sliding type. By focusing on the co-terminal model in a lognormal setting, we develop and compare several approximating analytical formulae for caplets, while swaptions can be priced by a simple Black-type formula. A novel calibration technique is introduced to allow simultaneous calibration to caplet and swaption prices. Empirical calibration of the co-terminal model is shown to be faster, more robust and more efficient than the same procedure applied to the LIBOR market model. We then argue that the co-terminal approach is the simplest and most convenient market model for pricing and hedging a large variety of exotic interest-rate derivatives.Swap Market Model, Cap, Swaption, Calibration, Graph Theory

Irving Fisher and Index Number Theory

There are four main approaches to bilateral index number theory: the fixed basket, stochastic, test and economic approaches. The paper reviews the contributions of Irving Fisher to these approaches to index number theory which are still in use today. The paper also reviews Fisher’s contributions to multilateral index number theory. The main themes of the paper are developed in the context of a review of the early history of index number theory: a history that conveys a wealth of information and insight into the making and use of index numbers today.Price indexes, quantity indexes, bilateral price indexes, multilateral price indexes, the Fisher ideal index, the test approach to index number theory