QMLE of periodic integer-valued time series models

A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases

“…For the very small sample size n = 50, the estimates of the parameter λ were not so much accurate. Therefore, we have also considered an empirical simulation study using the methods proposed in [22] and [29], which make use of the conditional Poisson distribution. Our simulations indicated that the methods performed quite similarly which corroborates the use of the proposed estimation method even when dealing with a time series with small sample size in a real application.…”

“…The interest of using INAR processes in count time series and their extensions, from theoretical and applied point of views, is still a growing subject in the literature with a large field of applications. For example, recently, Bentarzi and Aries [29] introduced the periodic integer-valued ARMA(p, q) model, denoted by PINARMA S (p, q), and established the consistency and the asymptotic normality of the quasi maximum likelihood estimator. This model is also considered here, in the application section, for comparison purpose.…”

“…S (p, q) Poisson model discussed in[29], and the periodic integervalued generalized autoregressive conditional heteroskedastic, PINGARCH S(1,1) …”