However, such estimation approaches are not yet routinely available and therefore not ready for general use (Davis et al. Kuk and Cheng ( 1997) considered the MC Newton Raphson method. To estimate the parameters of parameter-driven models, Chan and Ledolter ( 1995) employed a Monte Carlo EM algorithm. The main issue lies in the calculation requirement of very high dimensional integrals when using maximum likelihood estimation techniques, such that estimation methods based on Monte-Carlo (MC) integration are typically considered. However, parameter estimations in parameter-driven models require considerable computational effort. In observation-driven models, the mean of the conditional distribution of the current observation \(y_\) to be dependent on this latent process and can deal with auto-correlation as well as over-dispersion in the model. ( 1981): observation-driven models and parameter-driven models. To allow for dependence between time series data, two classes of models have been proposed in Cox et al. 2015) and regression based models (Fokianos 2012 Tjøstheim 2016). Generally, integer-valued time series models can be classified into two categories: “thinning” operator based models (Scotto et al. 2016 Weiß 2018, and references therein for reviews). The performance of the proposed method is evaluated via a simulation study and empirical applications.ĭespite a long history in the literature analyzing continuous time series variables, it is only in the recent years or so that much attention has been given to time series variables that are integer-valued (see Winkelmann 2008 Fahrmeir et al. Due to the high computational demand, we resort to adaptive Markov chain Monte Carlo sampling schemes for parameter estimations and inferences. Moreover, we adopt Bayesian inference for better quantifying the uncertainty of unknown parameters. This paper develops a log-linear version of the BNB-INGARCH model, which accommodates both negative and positive serial correlations. However, such proposed process allows for positive correlation only. The state of the art research on this topic is presented by Gorgi (J R Stat Soc Ser B (Stat Methodol) 82:1325–1347, 2020) very recently, which introduced a linear Beta-negative binomial integer-valued generalized autoregressive conditional heteroscedastic (BNB-INGARCH) model. However, current literature on modelling integer-valued time series data with heavy-tailedness is less considered. The literature coping with continuous-valued time series with extreme observations is well explored. When dealing with time series with outlying and atypical data, a commonly used approach is to develop models based on heavy-tailed distributions.
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