The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
MIXING AND MOMENT PROPERTIES OF VARIOUS GARCH AND STOCHASTIC VOLATILITY MODELS
Abstract
This paper first provides some useful results on a generalized random coefficient autoregressive model and a generalized hidden Markov model. These results simultaneously imply strict stationarity, existence of higher order moments, geometric ergodicity, and β-mixing with exponential decay rates, which are important properties for statistical inference. As applications, we then provide easy-to-verify sufficient conditions to ensure β-mixing and finite higher order moments for various linear and nonlinear GARCH(1,1), linear and power GARCH(p,q), stochastic volatility, and autoregressive conditional duration models. For many of these models, our sufficient conditions for existence of second moments and exponential β-mixing are also necessary. For several GARCH(1,1) models, our sufficient conditions for existence of higher order moments again coincide with the necessary ones in He and Terasvirta (1999, Journal of Econometrics 92, 173–192).
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Cites
Generalized autoregressive conditional heteroskedasticity
Bollerslev, T. (1986) · Journal of Econometrics · doi:10.1016/0304-4076(86)90063-1 · Cited by 22,254
Engle, R. F. (1982) · Econometrica · doi:10.2307/1912773 · Cited by 20,795
Conditional Heteroskedasticity in Asset Returns: A New Approach
Nelson, D. B. (1991) · Econometrica · doi:10.2307/2938260 · Cited by 10,236
On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks
GLOSTEN, L. R., JAGANNATHAN, R., & RUNKLE, D. E. (1993) · The Journal of Finance · doi:10.1111/j.1540-6261.1993.tb05128.x · Cited by 9,008
Measuring and Testing the Impact of News on Volatility
ENGLE, R. F., & NG, V. K. (1993) · The Journal of Finance · doi:10.1111/j.1540-6261.1993.tb05127.x · Cited by 3,611
Why Does Stock Market Volatility Change Over Time?
SCHWERT, G. W. (1989) · The Journal of Finance · doi:10.1111/j.1540-6261.1989.tb02647.x · Cited by 3,427
A long memory property of stock market returns and a new model
Ding, Z., Granger, C. W. J., & Engle, R. F. (1993) · Journal of Empirical Finance · doi:10.1016/0927-5398(93)90006-d · Cited by 3,250
Matrix Differential Calculus with Applications in Statistics and Econometrics.
Magnus, J. R., & Neudecker, H. (1988) · Biometrics · doi:10.2307/2531754 · Cited by 2,699
Threshold heteroskedastic models
Zakoian, J.-M. (1994) · Journal of Economic Dynamics and Control · doi:10.1016/0165-1889(94)90039-6 · Cited by 2,281
Non-linear Time Series: A Dynamical System Approach
Tong, H. (1990) · doi:10.1093/oso/9780198522249.001.0001 · Cited by 1,854
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From Predictive to Prescriptive Analytics
Bertsimas, D., & Kallus, N. (2020) · Management Science · doi:10.1287/mnsc.2018.3253 · Cited by 784
Estimation of multivariate models for time series of possibly different lengths
Patton, A. J. (2006) · Journal of Applied Econometrics · doi:10.1002/jae.865 · Cited by 421
Copula–Based Models for Financial Time Series
Patton, A. J. (2009) · Handbook of Financial Time Series · doi:10.1007/978-3-540-71297-8_34 · Cited by 360
Modelling Nonlinear Economic Time Series
Teräsvirta, T., Tjøstheim, D., & Granger, C. W. J. (2010) · doi:10.1093/acprof:oso/9780199587148.001.0001 · Cited by 352
Copula Methods for Forecasting Multivariate Time Series
Patton, A. (2013) · Handbook of Economic Forecasting · doi:10.1016/b978-0-444-62731-5.00016-6 · Cited by 320
Metadata
- Authors
- Carrasco, M., & Chen, X.
- Venue
- Econometric Theory
- Publisher
- Cambridge University Press (CUP)
- Published
- 2002-02
- Volume
- 18
- Issue
- 1
- Pages
- 17-39
- ISSN
- 0266-4666 (ISSN-L)
- 1469-4360
- OpenAlex
- W2056075622
- Cited by
- 566
- References
- 19
- FWCI
- 28.96
- Type
- journal article
- Language
- en
- Open access
- closed
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- Carrasco, M., & Chen, X. (2002). MIXING AND MOMENT PROPERTIES OF VARIOUS GARCH AND STOCHASTIC VOLATILITY MODELS. Econometric Theory. https://doi.org/10.1017/s0266466602181023
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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.
