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Structural Laplace Transform and Compound Autoregressive Models
Author(s) -
Darolles Serge,
Gourieroux Christian,
Jasiak Joann
Publication year - 2006
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2006.00479.x
Subject(s) - autoregressive model , mathematics , laplace transform , ergodicity , simple (philosophy) , series (stratigraphy) , class (philosophy) , gaussian , econometrics , nonlinear system , mathematical optimization , computer science , artificial intelligence , mathematical analysis , statistics , physics , epistemology , quantum mechanics , biology , paleontology , philosophy
. This 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.