The article featured today is from the Canadian Journal of Statistics with the full article now available to read here.

 

Integer-valued time series naturally occur in many contexts, including actuarial science, social science, epidemiology, finance, economics, etc. In the analysis of data in above mentioned situations, the data often encounter negative values and negative correlations. Many parametric time series models are applicable to this situation, but some of them are relatively restrictive.Besides, with little background information of the real data, which parametric model to choose is controversial. For this reason, a nonparametric time series model seems to be more suit-able in this case. It comes as a surprise that little attention has been paid to nonparametric counting time series, even in the simple integer-valued autoregressive settings. To deal with this common circumstances, a rounded semiparametric autoregressive model with a log-concave innovation is proposed, which can deal with Z-valued time series with arbitrary signs of autoregressive coefficients, and more information can be provided than parametric models, such as the confidence interval of the innovation distribution. With the log-concave shape restriction,the innovation class is sufficiently large that it encompasses most potential distributions and no initial distribution of the innovation is required in the estimation procedure. For the above reasons, the proposed model is flexible and practical in real data analysis.