|
|||||
|
|
Poisson QMLE of Count Time Series Models |
|
| Authors: | Ali Ahmad Christian Francq |
| Affiliation: | 1. Université Lille 3, Villeneuve d'Ascq Cedex, France;2. CREST, France |
| Abstract: | Regularity conditions are given for the consistency of the Poisson quasi‐maximum likelihood estimator of the conditional mean parameter of a count time series model. The asymptotic distribution of the estimator is studied when the parameter belongs to the interior of the parameter space and when it lies at the boundary. Tests for the significance of the parameters and for constant conditional mean are deduced. Applications to specific integer‐valued autoregressive (INAR) and integer‐valued generalized autoregressive conditional heteroscedasticity (INGARCH) models are considered. Numerical illustrations, Monte Carlo simulations and real data series are provided. |
| Keywords: | Boundary of the parameter space consistency and asymptotic normality integer‐valued AR and GARCH models non‐normal asymptotic distribution Poisson quasi‐maximum likelihood estimator time series of counts |
