Softplus INGARCH models
Publication date
2022
Document type
Forschungsartikel
Author
Publisher
Statistica Sinica, Institute of Statistical Science, Academia Sinica
Series or journal
Statistica Sinica
ISSN
Periodical volume
32
Periodical issue
2
First page
1099
Last page
1120
Peer-reviewed
✅
Part of the university bibliography
✅
Language
English
Keyword
Count time series
Maximum likelihood estimation
Negative autocorrelation
Softplus link
Description
Numerous models have been proposed for count time series, including the integer-valued autoregressive moving average (ARMA) and integer-valued generalized autoregressive conditional heteroskedasticity (INGARCH) models. However, while both models lead to an ARMA-like autocorrelation function (ACF), the attainable range of ACF values is much more restricted, and negative ACF values are usually not possible. The existing log-linear INGARCH model allows for negative ACF values, but the linear conditional mean and the ARMA-like autocorrelation structure are lost. To resolve this dilemma, a novel family of INGARCH models is proposed that uses the softplus function as a response function. The softplus function is approximately linear, but avoids the drawback of not being differentiable in zero. The stochastic properties of the novel model are derived. The proposed model exhibits an approximately linear structure, confirmed using extensive simulations, which makes its model parameters easier to interpret than those of a log-linear INGARCH model. The asymptotics of the maximum likelihood estimators for the parameters are established, and their finite-sample performance is analyzed using simulations. The usefulness of the proposed model is demonstrated by applying it to three real-data examples.
Version
Published version
Access right on openHSU
Metadata only access