This article aims at providing a comprehensive survey of recent developments in the field of
integer-valued time series modelling, paying particular attention to models obtained as …

This paper devotes to give a comprehensive review of Z-valued time series models, which
allow negative autocorrelations besides positive autocorrelations. Z-valued versions of …

Real count data time series often show the phenomenon of the underdispersion and
overdispersion. In this paper, we develop two extensions of the first-order integer-valued …

We introduce a class of two-parameter discrete dispersion models, obtained by combining
convolution with a factorial tilting operation, similar to exponential dispersion models which …

Count time series are widely encountered in practice. As with continuous valued data, many
count series have seasonal properties. This article uses a recent advance in stationary count …

In the analysis of real integer‐valued time series data, we often encounter negative values
and negative correlations. For integer‐valued autoregressive time series, there are many …

Over the past few years, interest has increased in models defined on positive and negative
integers. Several application areas lead to data that are differences between positive …

Integer-valued autoregressive (INAR) processes are generally defined by specifying the
thinning operator and either the innovations or the marginal distributions. The major …

We study intraday stochastic volatility for four liquid stocks traded on the New York Stock
Exchange using a new dynamic Skellam model for high-frequency tick-by-tick discrete price …

Overdispersion is a phenomenon commonly observed in count time series. Since Poisson
distribution is equidispersed, the INteger-valued AutoRegressive (INAR) process with …