The Continuous Wavelet Transform: A Primer

Wavelet analysis is becoming more popular in the Economics discipline. Until recently, most works have made use of tools associated with the Discrete Wavelet Transform. However, after 2005, there has been a growing body of work in Economics and Finance that makes use of the Continuous Wavelet Transform tools. In this article, we give a self-contained summary on the most relevant theoretical results associated with the Continuous Wavelet Transform, the Cross-Wavelet Transform, the Wavelet Coherency and the Wavelet Phase-Difference. We describe how the transforms are usually implemented in practice and provide some examples. We also introduce the Economists to a new class of analytic wavelets, the Generalized Morse Wavelets, which have some desirable properties and provide an alternative to the Morlet Wavelet. Finally, we provide a user friendly toolbox which will allow any researcher to replicate our results and to use it in his/her own research.Economic cycles; ContinuousWavelet Transform, Cross-Wavelet Transform, Wavelet Coherency, Wavelet Phase-Difference; The Great Moderation.

Codimension Two Determinantal Varieties with Isolated Singularities

We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in C^4, we obtain a L\^e-Greuel formula expressing the Milnor number of the surface in terms of the second polar multiplicity and the Milnor number of a generic section. We also relate the Milnor number with Ebeling and Gusein-Zade index of the 1- form given by the differential of a generic linear projection defined on the surface. To illustrate the results, in the last section we compute the Milnor number of some normal forms from A. Fr\"uhbis-Kr\"uger and A. Neumer [2] list of simple determinantal surface singularities

On a generic symmetry defect hypersurface

We show that symmetry defect hypersurfaces for two generic members of the irreducible algebraic family of n-dimensional smooth irreducible subvarieties in general position in C²ⁿ are homeomorphic and they have homeomorphic sets of singular points. In particular symmetry defect curves for two generic curves in C² of the same degree have the same numer of singular points

Identification of Monetary Policy Shocks in the Brazilian Market for Bank Reserves

We estimate an identified VAR (SVAR) with contemporaneous restrictions derived from a model of the market for bank reserves, which allows us to disentangle monetary policy shocks from demand shocks for reserves in Brazil. The main results are: i) the Central Bank of Brazil acts in order to smooth the bank reserve market interest rate (Selic); ii) the spread between the Selic rate and the discount rate provides information to estimate the demand curve for borrowed reserves; iii) overidentifying restrictions show that we cannot reject, for any period or model, the interest rate operational target hypothesis, even during the fixed exchange rate regime; iv) the impulse response functions show that shocks to the demand for reserves and to borrowed reserves generate statistically significant responses in real output and the inflation rate; v) all models display the liquidity effect and a small inflation rate puzzle.

On a singular variety associated to a polynomial mapping from \C^n to \C^{n-1}

We construct a singular variety ${\mathcal{V}}_G$ associated to a polynomial mapping G : \C^{n} \to \C^{n - 1} where $n \geq 2$. We prove that in the case G : \C^{3} \to \C^{2}, if $G$ is a local submersion but is not a fibration, then the homology and the intersection homology with total perversity (with compact supports or closed supports) in dimension two of the variety ${\mathcal{V}}_G$ is not trivial. In the case of a local submersion G : \C^{n} \to \C^{n - 1} where $n \geq 4$, the result is still true with an additional condition

Marginalized narratives

This issue of CITAR (Journal of Arts Science and Technology) is especially devoted to what we designated as Marginalized Narratives. It is a special issue that collects studies published upon the 5th Colloquium on Narrative, Medium and Cognition, held at the University of Algarve in November 2018, and which was focused on that topic. In line with what the colloquium proposed, the works now published share a broad understanding of the concept of narrative.info:eu-repo/semantics/publishedVersio