A Flexible Univariate Autoregressive Time‐Series Model for Dispersed Count Data
| Autor: | Stephen J. Peng, Kimberly F. Sellers, Ali Arab |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Applied Mathematics 05 social sciences Negative binomial distribution Univariate Poisson distribution 01 natural sciences 010104 statistics & probability symbols.namesake Autoregressive model Overdispersion 0502 economics and business Statistics symbols Statistical dispersion 0101 mathematics Statistics Probability and Uncertainty Time series 050205 econometrics Mathematics Count data |
| Zdroj: | Journal of Time Series Analysis. 41:436-453 |
| ISSN: | 1467-9892 0143-9782 |
| DOI: | 10.1111/jtsa.12516 |
| Popis: | Integer‐valued time series data have an ever‐increasing presence in various applications (e.g., the number of purchases made in response to a marketing strategy, or the number of employees at a business) and need to be analyzed properly. While a Poisson autoregressive (PAR) model would seem like a natural choice to model such data, it is constrained by the equi‐dispersion assumption (i.e., that the variance and the mean equal). Hence, data that are over‐ or under‐dispersed (i.e., have the variance greater or less than the mean respectively) are improperly modeled, resulting in biased estimates and inaccurate forecasts. This work instead develops a flexible integer‐valued autoregressive model for count data that contain over‐ or under‐dispersion. Using the Conway–Maxwell–Poisson (CMP) distribution and related distributions as motivation, we develop a first‐order sum‐of‐CMP's autoregressive (SCMPAR(1)) model that will instead offer a generalizable construct that captures the PAR, and versions of what we refer to as a negative binomial AR model, and binomial AR model respectively as special cases, and serve as an overarching representation connecting these three special cases through the dispersion parameter. We illustrate the SCMPAR model's flexibility and ability to effectively model count time series data containing data dispersion through simulated and real data examples. |
| Databáze: | OpenAIRE |
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