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Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This article uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model constructed here permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference are explored. The article first develops the modeling methods, which entail a discrete transformation of a Gaussian process having seasonal dynamics. Properties of this model class are then established and particle filtering likelihood methods of parameter estimation are developed. A simulation study demonstrating the efficacy of the methods is presented and an application to the number of rainy days in successive weeks in Seattle, Washington is given.
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This content will become publicly available on January 1, 2027
Latent Gaussian Dynamic Factor Modeling and Forecasting for Multivariate Count Time Series
ABSTRACT This work considers estimation and forecasting in a multivariate, possibly high‐dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters is based on second‐order properties of the count and underlying Gaussian time series, yielding estimators of the underlying covariance matrices for which standard principal component analysis applies. Theoretical consistency results are established for the proposed estimation, building on certain concentration results for the models of the type considered. They also involve the memory of the latent Gaussian process, quantified through a spectral gap, shown to be suitably bounded as the model dimension increases, which is of independent interest. In addition, novel cross‐validation schemes are suggested for model selection. The forecasting is carried out through a particle‐based sequential Monte Carlo, leveraging Kalman filtering techniques. A simulation study and an application are also considered.
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- Award ID(s):
- 2113662
- PAR ID:
- 10655449
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Journal of Time Series Analysis
- Volume:
- 47
- Issue:
- 1
- ISSN:
- 0143-9782
- Page Range / eLocation ID:
- 43 to 58
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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