Stochastic properties of multivariate time series equations with emphasis on ARCH
Research output: Contribution to journal › Conference article › Research › peer-review
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.
Original language | English |
---|---|
Journal | IFAC Proceedings Volumes (IFAC-PapersOnline) |
Volume | 36 |
Issue number | 16 |
Pages (from-to) | 227-232 |
Number of pages | 6 |
ISSN | 1474-6670 |
DOIs | |
Publication status | Published - 2003 |
Event | 13th IFAC Symposium on System Identification, SYSID 2003 - Rotterdam, Netherlands Duration: 27 Aug 2003 → 29 Aug 2003 |
Conference
Conference | 13th IFAC Symposium on System Identification, SYSID 2003 |
---|---|
Country | Netherlands |
City | Rotterdam |
Period | 27/08/2003 → 29/08/2003 |
- Asymptotics, Drift Criteria, Geometric Ergodicity, Markov Chain, Multivariate ARCH, Nonlinear processes, Spectral Radius
Research areas
ID: 258714809