https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1980.tb01126.x

Threshold Autoregression, Limit Cycles and Cyclical Data

SUMMARY This paper discusses the fitting and use of models for daily rainfall observations. Nonstationary Markov chains are fitted to the occurrence of rain, and gamma distributions, with parameters which vary with-the time of year, are fitted to the rainfall amounts. Numerical methods are used to derive results from these models that are important in agricultural planning. Examples include the distributions of soil water content and lengths of dry spells. The process of fitting and using these models provides a straightforward and flexible analysis for rainfall records.

A model fitting analysis of daily rainfall data

On introduit un modele pour des chaines de Markov du leme ordre qui comporte seulement un parametre additionnel pour chaque retard

A model for high-order Markov chains

https://rss.onlinelibrary.wiley.com/doi/pdf/10.2307/2981736

A Model Fitting Analysis of Daily Rainfall Data

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

Some arma models for dependent sequences of Poisson counts

supported by funds provided directly from
the Chief of Naval Research under Grant NR-42-284, and the National Science
Foundation under Grant NSF-75-02026

https://www.jstor.org/stable/info/2984870

Discrete Time Series Generated by Mixtures. I: Correlational and Runs Properties

Discrete Time Series Generated by Mixtures Ii: Asymptotic Properties

: A scheme for obtaining a stationary sequence of discrete random variables which has p-th order Markov dependence and a specified marginal distribution is presented. This DAR(p) process, which is a particular p-th order Markov chain, has the physical and correlation structure of an autoregressive process of order p. The process and its transition matrix are determined by the specified marginal distribution and by several other parameters which, independently of the marginal distribution, determine the correlation structure. Correlational properties and initial conditions for stationarity of the process are studied. Asymptotic properties for the process are also obtained. (Author)

https://calhoun.nps.edu/bitstream/10945/29821/1/discretetimeseri00jaco.pdf

Patricia A. Jacobs

Papers

Discrete Time Series Generated by Mixtures. I: Correlational and Runs Properties

Discrete Time Series Generated by Mixtures Ii: Asymptotic Properties

Discrete time series generated by mixtures III: Autoregressive processes (DAR(p))