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Convolution Copula Econometrics

Authors: Umberto Cherubini, Fabio Gobbi, Sabrina Mulinacci

Publisher: Springer International Publishing

Book Series : SpringerBriefs in Statistics

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This book presents a novel approach to time series econometrics, which studies the behavior of nonlinear stochastic processes. This approach allows for an arbitrary dependence structure in the increments and provides a generalization with respect to the standard linear independent increments assumption of classical time series models. The book offers a solution to the problem of a general semiparametric approach, which is given by a concept called C-convolution (convolution of dependent variables), and the corresponding theory of convolution-based copulas. Intended for econometrics and statistics scholars with a special interest in time series analysis and copula functions (or other nonparametric approaches), the book is also useful for doctoral students with a basic knowledge of copula functions wanting to learn about the latest research developments in the field.

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Table of Contents

Frontmatter

Chapter 1. The Dynamics of Economic Variables

Abstract

In 1957 Pablo Picasso painted a series of interpretations of an old and famous painting by Velázquez of 1656 called Las Meninas, portraying the court of the Infanta Margarita Teresa. He reinterpreted, partitioned, and distorted the image of the painting in many new images.

Umberto Cherubini, Fabio Gobbi, Sabrina Mulinacci

Chapter 2. Estimation of Copula Models

Abstract

In this chapter, we introduce copula functions and their main properties. For a more detailed study, we refer the interested reader to Joe (Multivariate models and dependence concepts, 1997), Nelsen (Introduction to copulas, 2006), and Durante and Sempi (Principles of copula theory, 2015).

Umberto Cherubini, Fabio Gobbi, Sabrina Mulinacci

Chapter 3. Copulas and Estimation of Markov Processes

Abstract

In this section, we briefly introduce a central result due to Darsow, Nguyen, and Olsen (see Darsow et al., Illinois Journal of Mathematics, 36, 600–642, 1992 for the original and complete result) that allows to characterize a Markov process through the dependence structure of the finite dimensional levels independently of their marginal distributions.

Umberto Cherubini, Fabio Gobbi, Sabrina Mulinacci

Chapter 4. Convolution-Based Processes

Abstract

In what follows, we consider a random vector (X, Y) and we study the distribution of \(X+Y\) and the copula associated to the random vector \((X,X+Y)\). Since this represents the basic concept of the book, we include proofs, even if they are also presented in Cherubini et al., (Dynamic copula methods in finance, 2012) (see also Cherubini et al., Journal of Multivariate Analysis, 2011).

Umberto Cherubini, Fabio Gobbi, Sabrina Mulinacci

Chapter 5. Application to Interest Rates

Abstract

There is a large literature investigating the nonlinear dynamics of the short-term rate. It mainly dates back to the last decade of the last century. Most of this literature was about persistence or mean reversion, linearity or nonlinearity, Gaussian or non-Gaussian innovations. Moreover, it is all about extensions and distortions of the linear AR(1) model, that is the subject addressed in this book. It is then the appropriate application to show how our approach works in practice, and maybe to stimulate new research on the subject.

Umberto Cherubini, Fabio Gobbi, Sabrina Mulinacci

Title: Convolution Copula Econometrics
Authors: Umberto Cherubini
Fabio Gobbi
Sabrina Mulinacci
Copyright Year: 2016
Publisher: Springer International Publishing
Electronic ISBN: 978-3-319-48015-2
Print ISBN: 978-3-319-48014-5
DOI: https://doi.org/10.1007/978-3-319-48015-2