The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Stationarity and Persistence in the GARCH(1,1) Model
Abstract
This paper establishes necessary and sufficient conditions for the stationarity and ergodicity of the GARCH(l.l) process. As a special case, it is shown that the IGARCH(1,1) process with no drift converges almost surely to zero, while IGARCH(1,1) with a positive drift is strictly stationary and ergodic. We examine the persistence of shocks to conditional variance in the GARCH(l.l) model, and show that whether these shocks "persist" or not depends crucially on the definition of persistence. We also develop necessary and sufficient conditions for the finiteness of absolute moments of any (including fractional) order.
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Citations
Cites
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433
Engle, R. F. (1982) · Econometrica · doi:10.2307/1912773 · Cited by 20,795
Cited by
A forecast comparison of volatility models: does anything beat a GARCH(1,1)?
Hansen, P. R., & Lunde, A. (2005) · Journal of Applied Econometrics · doi:10.1002/jae.800 · Cited by 1,773
Modeling and pricing long memory in stock market volatility
Bollerslev, T., & Ole Mikkelsen, H. (1996) · Journal of Econometrics · doi:10.1016/0304-4076(95)01736-4 · Cited by 1,208
Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility
ANDERSEN, T. G. (1996) · The Journal of Finance · doi:10.1111/j.1540-6261.1996.tb05206.x · Cited by 1,020
ARCH models as diffusion approximations
Nelson, D. B. (1990) · Journal of Econometrics · doi:10.1016/0304-4076(90)90092-8 · Cited by 938
Self-citationThe econometrics of financial markets
Pagan, A. (1996) · Journal of Empirical Finance · doi:10.1016/0927-5398(95)00020-8 · Cited by 873
Metadata
- Authors
- Nelson, D. B.
- Venue
- Econometric Theory
- Publisher
- Cambridge University Press (CUP)
- Published
- 1990-09
- Volume
- 6
- Issue
- 3
- Pages
- 318-334
- ISSN
- 0266-4666 (ISSN-L)
- 1469-4360
- OpenAlex
- W2077115352
- Cited by
- 1,093
- References
- 2
- FWCI
- 21.07
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
