A multinomial autoregressive model for finite-range time series of counts

In view of the complexity and asymmetry of finite range multi-state integer-valued time series data, we propose a first-order random coefficient multinomial autoregressive model in this paper. Basic probabilistic and statistical properties of the model are discussed. Conditional least squares (CLS) and weighted conditional least squares (WCLS) estimators of the model parameters are derived, and their asymptotic properties are established. In simulation studies, we compare these two methods with the conditional maximum likelihood (CML) method to verify the proposed procedure. A real example is applied to illustrate the advantages of our model.

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Extreme Overdispersion and Persistence in Time-Series of Counts

SSRN Electronic Journal ◽

10.2139/ssrn.3661266 ◽

2020 ◽

Author(s):

Leopoldo Catania ◽

Eduardo Rossi ◽

Paolo Santucci de Magistris

Keyword(s):

Time Series ◽

Time Series Of Counts

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Modeling Best Practice Life Expectancy Using Gumbel Autoregressive Models

Risks ◽

10.3390/risks9030051 ◽

2021 ◽

Vol 9 (3) ◽

pp. 51

Author(s):

Anthony Medford

Keyword(s):

Time Series ◽

Life Expectancy ◽

Extreme Value Theory ◽

Autoregressive Model ◽

Best Practice ◽

Gumbel Distribution ◽

Value Theory ◽

Model Diagnostics ◽

Temporal Dependence ◽

Simulation Results

Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best practice life expectancy. This class of model represents a neat and coherent framework for modeling time series extremes. The Gumbel distribution accounts for the extreme nature of best practice life expectancy, while the AR structure accounts for the temporal dependence in the time series. Model diagnostics and simulation results indicate that these models present a viable alternative to Gaussian AR(1) models when dealing with time series of extremes and merit further exploration.

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GQL Versus Conditional GQL Inferences for Non-Stationary Time Series of Counts with Overdispersion

Journal of Time Series Analysis ◽

10.1111/j.1467-9892.2007.00570.x ◽

2008 ◽

Vol 29 (2) ◽

pp. 402-420 ◽

Cited By ~ 10

Author(s):

Taslim S. Mallick ◽

Brajendra C. Sutradhar

Keyword(s):

Time Series ◽

Stationary Time Series ◽

Time Series Of Counts ◽

Stationary Time

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An autoregressive model for irregular time series of variable stars

Proceedings of the International Astronomical Union ◽

10.1017/s1743921317000448 ◽

2016 ◽

Vol 12 (S325) ◽

pp. 259-262

Author(s):

Susana Eyheramendy ◽

Felipe Elorrieta ◽

Wilfredo Palma

Keyword(s):

Time Series ◽

Gravitational Lensing ◽

Autoregressive Model ◽

Likelihood Estimation ◽

Estimation Procedure ◽

Variable Stars ◽

Light Curves ◽

Finite Sample ◽

Harmonic Model ◽

Dependency Structure

AbstractThis paper discusses an autoregressive model for the analysis of irregularly observed time series. The properties of this model are studied and a maximum likelihood estimation procedure is proposed. The finite sample performance of this estimator is assessed by Monte Carlo simulations, showing accurate estimators. We implement this model to the residuals after fitting an harmonic model to light-curves from periodic variable stars from the Optical Gravitational Lensing Experiment (OGLE) and Hipparcos surveys, showing that the model can identify time dependency structure that remains in the residuals when, for example, the period of the light-curves was not properly estimated.

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