Related papers: Statistical Inference for Generalized Integer Auto…
In this paper, we discuss integer-valued autoregressive time series (INAR), Hawkes point processes, and their interrelationship. Besides presenting structural analogies, we derive a convergence theorem. More specifically, we generalize the…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
For modeling the serial dependence in time series of counts, various approaches have been proposed in the literature. In particular, models based on a recursive, autoregressive-type structure such as the well-known integer-valued…
We introduce a two-parameter expectation thinning operator based on a linear fractional probability generating function. The operator is then used to define a first-order integer-valued autoregressive \inar1 process. Distributional…
In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from…
In economic and financial applications, there is often the need for analysing multivariate time series, comprising of time series for a range of quantities. In some applications such complex systems can be associated with some underlying…
Integer-valued time series models have been a recurrent theme considered in many papers in the last three decades, but only a few of them have dealt with models on $\mathbb Z$ (that is, including both negative and positive integers). Our…
The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…
Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have…
Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector…
In this paper, we present a nonparametric estimation procedure for the multivariate Hawkes point process. The timeline is cut into bins and -- for each component process -- the number of points in each bin is counted. The distribution of…
The thinning-based integer-valued autoregressive moving-average (INARMA) models are popular for count time series. Recently, types of INARMA models have also been developed for count random fields, i.e., for spatial count data located on a…
Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable…
This paper proposes an autoregressive (AR) model for sequences of graphs, which generalises traditional AR models. A first novelty consists in formalising the AR model for a very general family of graphs, characterised by a variable…
Change in the coefficients or in the mean of the innovation distribution of an INAR(p) process is a sign of disturbance that is important to detect. The methods of this paper can test for change in any one of these quantities separately, or…
A bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with copula-joint innovations is studied. Different parameter estimation methods are analyzed and compared via Monte Carlo simulations with emphasis on estimation of…
We propose a factor network autoregressive (FNAR) model for time series with complex network structures. The coefficients of the model reflect many different types of connections between economic agents ("multilayer network"), which are…
An inhomogeneous first--order integer--valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient slowly converges to one. It is shown that the process converges weakly to a Poisson or a compound…
Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…
The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…