INARMA Modeling of Count Time Series

While most of the literature about INARMA models (integer-valued autoregressive moving-average) concentrates on the purely autoregressive INAR models, we consider INARMA models that also include a moving-average part. We study moment properties and show how to efficiently implement maximum likelihood estimation. We analyze the estimation performance and consider the topic of model selection. We also analyze the consequences of choosing an inadequate model for the given count process. Two real-data examples are presented for illustration.

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Maximum Likelihood Estimation for Vector Autoregressive Moving Average Models

10.21236/ada060867 ◽

1978 ◽

Cited By ~ 2

Author(s):

Theodore W. Anderson

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Moving Average ◽

Likelihood Estimation ◽

Autoregressive Moving Average ◽

Vector Autoregressive ◽

Moving Average Models ◽

Vector Autoregressive Moving Average ◽

Autoregressive Moving Average Models

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On Maximum Likelihood Estimation of Parameters of Autoregressive Moving Average Processes

Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians ◽

10.1007/978-94-010-9910-3_4 ◽

1977 ◽

pp. 37-45 ◽

Cited By ~ 1

Author(s):

T. W. Anderson

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Moving Average ◽

Likelihood Estimation ◽

Autoregressive Moving Average ◽

Estimation Of Parameters ◽

Moving Average Processes

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Continuous Autoregressive Moving Average Models

Methodologies and Applications of Computational Statistics for Machine Intelligence - Advances in Systems Analysis, Software Engineering, and High Performance Computing ◽

10.4018/978-1-7998-7701-1.ch007 ◽

2021 ◽

pp. 118-141

Author(s):

Yakup Ari

Keyword(s):

Time Series ◽

Parameter Estimation ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Discrete Time ◽

Moving Average ◽

Likelihood Estimation ◽

Real Data ◽

Autoregressive Moving Average ◽

The Difference

The financial time series have a high frequency and the difference between their observations is not regular. Therefore, continuous models can be used instead of discrete-time series models. The purpose of this chapter is to define Lévy-driven continuous autoregressive moving average (CARMA) models and their applications. The CARMA model is an explicit solution to stochastic differential equations, and also, it is analogue to the discrete ARMA models. In order to form a basis for CARMA processes, the structures of discrete-time processes models are examined. Then stochastic differential equations, Lévy processes, compound Poisson processes, and variance gamma processes are defined. Finally, the parameter estimation of CARMA(2,1) is discussed as an example. The most common method for the parameter estimation of the CARMA process is the pseudo maximum likelihood estimation (PMLE) method by mapping the ARMA coefficients to the corresponding estimates of the CARMA coefficients. Furthermore, a simulation study and a real data application are given as examples.

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