Structural Laplace Transform and Compound Autoregressive Models

Abstract

International audienceThis paper presents a new general class of compound autoregressive (Car) models for non-Gaussian time series. The distinctive feature of the class is that Car models are specified by means of the conditional Laplace transforms. This approach allows for simple derivation of the ergodicity conditions and ensures the existence of forecasting distributions in closed form, at any horizon. The last property is of particular interest for applications to finance and economics that investigate the term structure of variables and/or of their nonlinear transforms. The Car class includes a number of time-series models that already exist in the literature, as well as new models introduced in this paper. Their applications are illustrated by examples of portfolio management, term structure and extreme risk analysis

Nonparametric Identification of Positive Eigenfunctions

“…Examples include higher-order vector autoregressive processes (VARs), higher-order nonlinear VARs (Härdle, Tsybakov, and Yang (1998) and references therein), autoregressive Gamma processes , and compound autoregressive processes (Darolles, Gourieroux, and Jasiak, 2006). See, e.g., Monfort and Pegoraro (2007), Bertholon, Monfort, and Pegoraro (2008) and Eraker (2008) for applications of these processes to term structure models.…”

Term Premium Dynamics and the Taylor Rule

“…Nonnegativity is accomplished by modeling z t as an M -dimensional autoregressive gamma process. The properties of a univariate autoregressive gamma process are studied in Gourieroux and Jasiak (2006) and Darolles et al (2006). Le et al (2010) consider the multivariate extension 6 For an earlier analysis of autoregressive gamma term structure models, see Gourieroux et al (2002).…”

Default, Liquidity and Crises: An Econometric Framework

“…We increment l until we can not reject the null hypothesis at the 5% critical value. 45 The means and variances of the VAR residuals can shift across regimes following the specifications presented in 9.3.1. The estimates are obtained by MLE.…”

“…Tractability is notably obtained through an extensive use of Car's -Compound autoregressive processes-properties (see, e.g. Darolles, Gourieroux and Jasiak, 2006 [45]), which leads to quasi-explicit fomulas for bond prices. Both historical and risk-neutral dynamics are explicitely modeled, which is helpful for chosing appropriate specifications under the historical measure, for dealing simultaneously with pricing and forecasting or also for Value-at-Risk calculations.…”