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Markov Regression Models for Time Series: A Quasi-Likelihood Approach
Abstract
This paper discusses a quasi-likelihood (QL) approach to regression analysis with time series data. We consider a class of Markov models, referred to by Cox (1981, Scandinavian Journal of Statistics 8, 93-115) as "observation-driven" models in which the conditional means and variances given the past are explicit functions of past outcomes. The class includes autoregressive and Markov chain models for continuous and categorical observations as well as models for counts (e.g., Poisson) and continuous outcomes with constant coefficient of variation (e.g., gamma). We focus on Poisson and gamma data for illustration. Analogous to QL for independent observations, large-sample properties of the regression coefficients depend only on correct specification of the first conditional moment.
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Citations
Cites
Engle, R. F. (1982) · Econometrica · doi:10.2307/1912773 · Cited by 20,795
Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method
WEDDERBURN, R. W. M. (1974) · Biometrika · doi:10.1093/biomet/61.3.439 · Cited by 2,122
Cited by
Generalized Autoregressive Moving Average Models
Benjamin, M. A., Rigby, R. A., & Stasinopoulos, D. M. (2003) · Journal of the American Statistical Association · doi:10.1198/016214503388619238 · Cited by 403
Model Selection for Extended Quasi-Likelihood Models in Small Samples
Hurvich, C. M., & Tsai, C.-L. (1995) · Biometrics · doi:10.2307/2533006 · Cited by 305
Relationship between sleep and mood in patients with rapid-cycling bipolar disorder
Leibenluft, E., Albert, P. S., Rosenthal, N. E., & Wehr, T. A. (1996) · Psychiatry Research · doi:10.1016/0165-1781(96)02854-5 · Cited by 178
Enscore, R. E., Biggerstaff, B. J., Brown, T. L., Fulgham, R. E., Reynolds, P. J., Engelthaler, D. M., Levy, C. E., Parmenter, R. R., Montenieri, J. A., Cheek, J. E., et al. (2002) · The American journal of tropical medicine and hygiene · doi:10.4269/ajtmh.2002.66.186 · Cited by 166
Johansson, M. A., Reich, N. G., Hota, A., Brownstein, J. S., & Santillana, M. (2016) · Scientific Reports · doi:10.1038/srep33707 · Cited by 120
Metadata
- Authors
- Zeger, S. L., & Qaqish, B.
- Venue
- Biometrics
- Publisher
- JSTOR
- Published
- 1988-12
- Volume
- 44
- Issue
- 4
- Pages
- 1019
- ISSN
- 0006-341X (ISSN-L)
- OpenAlex
- W2009632219
- Cited by
- 431
- References
- 2
- FWCI
- 4.82
- Type
- journal article
- Language
- en
- Open access
- closed
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- Zeger, S. L., & Qaqish, B. (1988). Markov Regression Models for Time Series: A Quasi-Likelihood Approach. Biometrics. https://doi.org/10.2307/2531732
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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.
