scholarly journals Autoregressive moving average modeling for spectral parameter estimation from a multigradient echo chemical shift acquisition

2009 ◽  
Vol 36 (3) ◽  
pp. 753-764 ◽  
Author(s):  
Brian A. Taylor ◽  
Ken-Pin Hwang ◽  
John D. Hazle ◽  
R. Jason Stafford
Keyword(s):  
Parameter Estimation ◽  
Chemical Shift ◽  
Spectral Parameter ◽  
Moving Average ◽  
Autoregressive Moving Average

Continuous Autoregressive Moving Average Models

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.

scholarly journals Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Weili Xiong ◽  
Wei Fan ◽  
Rui Ding
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Least Squares ◽  
Moving Average ◽  
Estimation Algorithm ◽  
Autoregressive Moving Average ◽  
Parameter Estimates ◽  
Persistent Excitation ◽  
Estimation Algorithms ◽  
Parameter Estimation Algorithm

This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.

Consistency of model selection and parameter estimation

1986 ◽  
Vol 23 (A) ◽  
pp. 127-141 ◽  
Author(s):  
Ritei Shibata
Keyword(s):  
Parameter Estimation ◽  
Model Selection ◽  
Lower Order ◽  
Moving Average ◽  
Information Matrix ◽  
Autoregressive Moving Average ◽  
Moving Average Models ◽  
The Cost ◽  
The Relationship ◽  
Autoregressive Moving Average Models

The relationship between consistency of model selection and that of parameter estimation is investigated. It is shown that the consistency of model selection is achieved at the cost of a lower order of consistency of the resulting estimate of parameters in some domain. The situation is different when selecting autoregressive moving average models, since the information matrix becomes singular when overfitted. Some detailed analyses of the consistency are given in this case.

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