The Jacobian of the exponential function

We derive closed-form expressions for the Jacobian of the matrix exponential function for both diagonalizable and defective matrices. The results are applied to two cases of interest in macroeconometrics: a continuous-time macro model and the parametrization of rotation matrices governing impulse response functions in structural vector autoregressions.

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Year of publication:	2020
Authors:	Magnus, Jan R. ; Pijls, Henk G.J. ; Sentana, Enrique
Publisher:	Amsterdam and Rotterdam : Tinbergen Institute
Subject:	Matrix differential calculus \| Orthogonal matrix \| Continuous-time Markov chain \| Ornstein-Uhlenbeck process

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Series:	Tinbergen Institute Discussion Paper ; TI 2020-035/III
Type of publication:	Book / Working Paper
Type of publication (narrower categories):	Working Paper
Language:	English
Other identifiers:	1702117642 [GVK] hdl:10419/220072 [Handle] RePEc:tin:wpaper:20200035 [RePEc]
Classification:	C65 - Miscellaneous Mathematical Tools ; C32 - Time-Series Models ; C63 - Computational Techniques
Source:	EconStor

Persistent link: https://www.econbiz.de/10012233997