The DOI matches its Crossref record; 20 of the 20 references it cites were found in a registry or an index.
Generalized Autoregressive Moving Average Models
Abstract
A class of generalized autoregressive moving average (GARMA) models is developed that extends the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. The dependent variable is assumed to have a conditional exponential family distribution given the past history of the process. The model estimation is carried out using an iteratively reweighted least squares algorithm. Properties of the model, including stationarity and marginal moments, are either derived explicitly or investigated using Monte Carlo simulation. The relationship of the GARMA model to other models is shown, including the autoregressive models of Zeger and Qaqish, the moving average models of Li, and the reparameterized generalized autoregressive conditional heteroscedastic GARCH model (providing the formula for its fourth marginal moment not previously derived). The model is demonstrated by the application of the GARMA model with a negative binomial conditional distribution to a well-known time series dataset of poliomyelitis counts.
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Rigby, R. A., & Stasinopoulos, D. M. (2005) · Journal of the Royal Statistical Society Series C: Applied Statistics · doi:10.1111/j.1467-9876.2005.00510.x · Cited by 3,228
Self-citationIncidence trends of type 1 and type 2 diabetes among youths, 2002–2012
Mayer-Davis, E. J., Lawrence, J. M., Dabelea, D., Divers, J., Isom, S., Dolan, L., Imperatore, G., Linder, B., Marcovina, S., Pettitt, D. J., et al. (2017) · New England Journal of Medicine · doi:10.1056/nejmoa1610187 · Cited by 1,476
Wagenknecht, L. E., Lawrence, J. M., Isom, S., Jensen, E. T., Dabelea, D., Liese, A. D., Dolan, L. M., Shah, A. S., Bellatorre, A., Sauder, K., et al. (2023) · The Lancet Diabetes & Endocrinology · doi:10.1016/s2213-8587(23)00025-6 · Cited by 264
Predictive Analytics for Complex IoT Data Streams
Akbar, A., Khan, A., Carrez, F., & Moessner, K. (2017) · IEEE Internet of Things Journal · doi:10.1109/jiot.2017.2712672 · Cited by 136
Clustering of Temporal and Visual Data: Recent Advancements
Mudgal, P. (2026) · Data · doi:10.3390/data11010007 · Cited by 2
Metadata
- Authors
- Benjamin, M. A., Rigby, R. A., & Stasinopoulos, D. M.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2003-03
- Volume
- 98
- Issue
- 461
- Pages
- 214-223
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1965792011
- Cited by
- 403
- References
- 20
- FWCI
- 4.73
- Type
- journal article
- Language
- en
- Open access
- closed
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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.
