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1.
During the last three decades, integer‐valued autoregressive process of order p [or INAR(p)] based on different operators have been proposed as a natural, intuitive and maybe efficient model for integer‐valued time‐series data. However, this literature is surprisingly mute on the usefulness of the standard AR(p) process, which is otherwise meant for continuous‐valued time‐series data. In this paper, we attempt to explore the usefulness of the standard AR(p) model for obtaining coherent forecasting from integer‐valued time series. First, some advantages of this standard Box–Jenkins's type AR(p) process are discussed. We then carry out our some simulation experiments, which show the adequacy of the proposed method over the available alternatives. Our simulation results indicate that even when samples are generated from INAR(p) process, Box–Jenkins's model performs as good as the INAR(p) processes especially with respect to mean forecast. Two real data sets have been employed to study the expediency of the standard AR(p) model for integer‐valued time‐series data. 相似文献
2.
To test the null hypothesis of a Poisson marginal distribution, test statistics based on the Stein–Chen identity are proposed. For a wide class of Poisson count time series, the asymptotic distribution of different types of Stein–Chen statistics is derived, also if multiple statistics are jointly applied. The performance of the tests is analyzed with simulations, as well as the question which Stein–Chen functions should be used for which alternative. Illustrative data examples are presented, and possible extensions of the novel Stein–Chen approach are discussed as well. 相似文献
3.
《Statistica Neerlandica》2018,72(2):90-108
Variable selection and error structure determination of a partially linear model with time series errors are important issues. In this paper, we investigate the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation penalty for a partially linear model with a divergent number of covariates and finite order autoregressive time series errors. Both consistency and asymptotic normality of the proposed penalized estimators are derived. The oracle property of the resultant estimators is proved. Simulation studies are carried out to assess the finite‐sample performance of the proposed procedure. A real data analysis is made to illustrate the usefulness of the proposed procedure as well. 相似文献
4.
Forecast error is not only caused by the randomness of the data-generating process but also by the uncertainty due to estimated model parameters. We investigate these different sources of forecast error for a popular type of count process, the Poisson first-order integer-valued autoregressive (INAR(1)) process. However, many of our analytical derivations also hold for the more general family of conditional linear AR(1) (CLAR(1)) processes. In addition, results from a simulation study are presented, to verify and complement our asymptotic approximations. 相似文献
5.
We give some comments on the paper by Mendes and Yigit where some misleading statements on rank tests have been given. Also, we give some additional important references on the same topic, which are not cited in this paper. By extending the simulations presented in the Mendes and Yigit paper to larger and unequal sample sizes, we demonstrate that the main conclusions are misleading. 相似文献