We characterize the interrelation of CO2 prices with energy prices (gas and electricity), and with economic activity. Previous studies have relied on time-domain techniques, such as Vector Auto-Regressions. In this study, we use multivariate wavelet analysis, which operates in the time-frequency domain. Wavelet analysis provides convenient tools to distinguish relations at particular frequencies and at particul...
We use wavelet analysis to study the impact of the Euro adoption on the oil price macroeconomy relation in the Euroland. We uncover evidence that the oil-macroeconomy relation changed in the past decades. We show that after the Euro adoption some countries became more similar with respect to how their macroeconomies react to oil shocks. However, we also conclude that the adoption of the common currency did not ...
Economists are already familiar with the Discrete Wavelet Transform. However, a body of work using the Continuous Wavelet Transform has also been growing. We provide a self-contained summary on continuous wavelet tools, such as the Continuous Wavelet Transform, the Cross-Wavelet, the Wavelet Coherency and the Phase-Difference. Furthermore, we generalize the concept of simple coherency to Partial Wavelet Coheren...
We use wavelet analysis to study business cycle synchronization across the EU-15 and the Euro-12 countries. Based on the wavelet transform, we propose a metric to measure and test for business cycles synchronization. Several conclusions emerge. France and Germany form the core of the Euro land, being the most synchronized countries with the rest of Europe. Portugal, Greece, Ireland and Finland do not show stati...
We use (cross) wavelet analysis to decompose the time–frequency effects of oil price changes on the macroeconomy. We argue that the relation between oil prices and industrial production is not clear-cut. There are periods and frequencies where the causality runs from one variable to the other and vice-versa, justifying some instability in the empirical evidence about the macroeconomic effects of oil price shock...
Spectral analysis and ARMA models have been the most common weapons of choice for the detection of cycles in political time-series. Controversies about cycles, however, tend to revolve about an issue that both techniques are badly equipped to address: the possibility of irregular cycles without fixed periodicity throughout the entire time-series. This has led to two main consequences. On the one hand, proponent...
The use of wavelet analysis is very common in a large variety of disciplines, such as signal and image processing, quantum mechanics, geophysics, medicine, biology, etc. In economics, however, wavelets are still a mysterious, but colorful, tool for time-series analysis. The pioneering work of Ramsey and Lampart [26] is unknown to the majority of economists. Among the exceptions to this rule, one can point to [4...
Slides das aulas de Processamento de Sinal e Ôndulas do Mestrado em Matemática e Computação da UM.
Texto de apoio para as disciplinas de Álgebra Linear e Geometria Analítica (Lic. Optometria e Ciências da Visão) e Álgebra Linear B (Lic. Eng. Materiais). ; Sistemas Lineares. Matrizes. Determinantes. Espaços Vectoriais. Transformações Lineares. Valores e Vectores Próprios. Soluções dos Exercícios.
We use wavelet analysis to study cycle synchronization across the EU-15 and the Euro-12 countries. Based on the wavelet transform, we propose a metric to measure and test for business cycles synchronization. Several conclusions emerge. France and Germany form the core of the Euro land, being the most synchronized countries with the rest of Europe. Portugal, Greece, Ireland and Finland do not show statistically ...
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