Journal ArticleDOI
Integer-Valued Self-Exciting Threshold Autoregressive Processes
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In this paper, a class of self-exciting threshold integer-valued autoregressive models driven by independent Poisson-distributed random variables is introduced and parameter estimation is also addressed.Abstract:
In this article, we introduce a class of self-exciting threshold integer-valued autoregressive models driven by independent Poisson-distributed random variables. Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the least squares-type and likelihood-based ones. Their performance is compared through a simulation study.read more
Citations
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Journal ArticleDOI
Statistical Inference for Markov Processes
TL;DR: In this article, Statistical Inference for Markov Processes (SINP) is used for statistical inference for the Markov process, and it is shown that SINP can be used to identify Markov processes.
Journal ArticleDOI
Thinning-based models in the analysis of integer-valued time series: a review
TL;DR: A comprehensive survey of recent developments in the field of integer-valued time series modelling, paying particular attention to models obtained as discrete counterparts of conventional autoregressive moving average and bilinear models, and based on the concept of thinning.
Discrete analogues of self-decomposability and stability
FW Fred Steutel,van K Klaas Harn +1 more
TL;DR: In this article, analogues for the concepts of self-decomposability and stability for distributions on the nonnegative integers were proposed, and it turns out that these "discrete self-Decomposable" and "Discrete Stable" distributions have properties that are quite similar to those of their continuous counterparts.
Journal ArticleDOI
Binomial autoregressive processes with density-dependent thinning
TL;DR: In this paper, an extension of the usual binomial AR(1) process on {0,1,N} that allows the thinning probabilities to depend on the current state N only through the density' n/N, a natural assumption in many real contexts is presented.
References
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Book
Probability and Measure
TL;DR: In this paper, the convergence of distributions is considered in the context of conditional probability, i.e., random variables and expected values, and the probability of a given distribution converging to a certain value.
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Non-linear time series. A dynamical system approach
TL;DR: Non-linear least-squares prediction based on non-linear models and case studies and an introduction to dynamical systems.
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Threshold models in non-linear time series analysis
TL;DR: This chapter discusses SETAR Modelling, Threshold Models and Discrete-Time Non-Linear Vibrations, and some Advantages and Some Limitations of Arma Models.
Journal ArticleDOI
Discrete analogues of self-decomposability and stability
FW Fred Steutel,van K Klaas Harn +1 more
TL;DR: In this paper, analogues for the concepts of self-decomposability and stability for distributions on the nonnegative integers were proposed, and it turns out that these "discrete self-Decomposable" and "Discrete Stable" distributions have properties that are quite similar to those of their continuous counterparts.