TY - GEN

T1 - Stochastic properties of multivariate time series equations with emphasis on ARCH

AU - Rahbek, Anders

PY - 2003

Y1 - 2003

N2 - Markov chain theory is applied to the nonlinear modelling of conditional variance with focus on the in financial econometrics widely applied class of multivariate autoregressive conditional heteroscedastic (ARCH) processes. The multivariate socalled BEKK-ARCH of Engle and Kroner (1995) as well as other multivariate ARCH processes in the literature are discussed. The results show that an essential regularity condition for the existence of moments is that the largest modulus of the eigenvalues or equivalently, that the spectral radius of a certain matrix Φ parametrizing the conditional heteroscedasticity in the ARCH process is smaller than one. Due to the fact that multivariate systems are considered it is demonstrated that an important step in the derivations is based on changing the measure of size of the matrix Φ from norm to spectral radius.

AB - Markov chain theory is applied to the nonlinear modelling of conditional variance with focus on the in financial econometrics widely applied class of multivariate autoregressive conditional heteroscedastic (ARCH) processes. The multivariate socalled BEKK-ARCH of Engle and Kroner (1995) as well as other multivariate ARCH processes in the literature are discussed. The results show that an essential regularity condition for the existence of moments is that the largest modulus of the eigenvalues or equivalently, that the spectral radius of a certain matrix Φ parametrizing the conditional heteroscedasticity in the ARCH process is smaller than one. Due to the fact that multivariate systems are considered it is demonstrated that an important step in the derivations is based on changing the measure of size of the matrix Φ from norm to spectral radius.

KW - Asymptotics

KW - Drift Criteria

KW - Geometric Ergodicity

KW - Markov Chain

KW - Multivariate ARCH

KW - Nonlinear processes

KW - Spectral Radius

UR - http://www.scopus.com/inward/record.url?scp=84894225565&partnerID=8YFLogxK

U2 - 10.1016/S1474-6670(17)34767-5

DO - 10.1016/S1474-6670(17)34767-5

M3 - Conference article

AN - SCOPUS:84894225565

VL - 36

SP - 227

EP - 232

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 16

T2 - 13th IFAC Symposium on System Identification, SYSID 2003

Y2 - 27 August 2003 through 29 August 2003

ER -