Simulation of Homogeneous Two-Dimensional Random Fields: Part I—AR and ARMA Models

1992 ◽  
Vol 59 (2S) ◽  
pp. S260-S269 ◽  
Author(s):  
Marc P. Mignolet ◽  
Pol D. Spanos
Keyword(s):  
Power Spectrum ◽  
Random Fields ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Simulation Algorithm ◽  
Two Dimensional ◽  
Arma Models ◽  
Spectral Matrix ◽  
Target Power

The determination of autoregressive (AR) and autoregressive moving average (ARMA) algorithms for simulating realizations of two-dimensional random fields with a specified (target) power spectrum is examined. The form of both of these models is justified first by considering infinite-variate vector processes of appropriate spectral matrix. Next, the AR parameters are selected to achieve the minimum of a positive integral. Then, a technique is formulated to derive an ARM A simulation algorithm from the prior AR approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.

Simulation of Homogeneous Two-Dimensional Random Fields: Part II—MA and ARMA Models

1992 ◽  
Vol 59 (2S) ◽  
pp. S270-S277 ◽  
Author(s):  
Pol D. Spanos ◽  
Marc P. Mignolet
Keyword(s):  
Random Fields ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Mathematical Form ◽  
Simulation Algorithm ◽  
Arma Models ◽  
Spectral Matrix ◽  
Target Power ◽  
Ar Models

Alternatively to the autoregressive (AR) models examined in Part I, the determination of moving average (MA) algorithms for simulating realizations of twodimensional random fields with a specified (target) power spectrum is presented. First, the mathematical form of these models is addressed by considering infinitevariate vector processes of an appropriate spectral matrix. Next, the MA parameters are determined by relying on the maximization of an energy-like quantity. Then, a technique is formulated to derive an autoregressive moving average (ARMA) simulation algorithm from a prior MA approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.

Autoregressive Moving Average (ARMA) Models of Neuromuscular System

1982 ◽  
Vol 15 (4) ◽  
pp. 1205-1210
Author(s):  
G.C. Agarwal ◽  
S.M. Goodarzi ◽  
W.D. O'Neill ◽  
G.L. Cottlieb
Keyword(s):  
Moving Average ◽  
Autoregressive Moving Average ◽  
Neuromuscular System ◽  
Arma Models

scholarly journals A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 324 ◽  
Author(s):  
Dabuxilatu Wang ◽  
Liang Zhang
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Empirical Analysis ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Complex Data ◽  
Arma Models ◽  
Linguistic Data ◽  
Series Analysis

Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fréchet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model.

scholarly journals Predicting IGS RTS Corrections Using ARMA Neural Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Mingyu Kim ◽  
Jeongrae Kim
Keyword(s):  
Neural Network ◽  
Moving Average ◽  
Optimal Order ◽  
Autoregressive Moving Average ◽  
Arma Models ◽  
Time Service ◽  
Prediction Time ◽  
Clock Correction ◽  
Rms Error ◽  
The Difference

An autoregressive moving average neural network (ARMANN) model is applied to predict IGS real time service corrections. ARMA coefficients are determined by applying a neural network to IGS02 orbit/clock corrections. Other than the ARMANN, the polynomial and ARMA models are tested for comparison. An optimal order of each model is determined by fitting the model to the correction data. The data fitting period for training the models is 60 min. and the prediction period is 30 min. The polynomial model is good for the fitting but bad for the prediction. The ARMA and ARMANN have a similar level of accuracies, but the RMS error of the ARMANN is smaller than that of the ARMA. The RMS error of the ARMANN is 0.046 m for the 3D orbit correction and 0.070 m for the clock correction. The difference between the ARMA and ARMANN models becomes significant as the prediction time is increased.

scholarly journals Bootstrap Order Determination for ARMA Models: A Comparison between Different Model Selection Criteria

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Livio Fenga
Keyword(s):  
Selection Criteria ◽  
Moving Average ◽  
Information Criterion ◽  
Autoregressive Moving Average ◽  
Order Selection ◽  
Arma Models ◽  
Final Prediction Error ◽  
Novel Method ◽  
Order Determination ◽  
Selection Of

The present paper deals with the order selection of models of the class for autoregressive moving average. A novel method—previously designed to enhance the selection capabilities of the Akaike Information Criterion and successfully tested—is now extended to the other three popular selectors commonly used by both theoretical statisticians and practitioners. They are the final prediction error, the Bayesian information criterion, and the Hannan-Quinn information criterion which are employed in conjunction with a semiparametric bootstrap scheme of the type sieve.

Time Series Modeling of Earthquake Ground Motions Using ARMA-GARCH Models

2013 ◽  
Vol 470 ◽  
pp. 240-243 ◽  
Author(s):  
Jeng Hsiang Lin
Keyword(s):  
Ground Motion ◽  
Moving Average ◽  
Ground Motions ◽  
Structural Response ◽  
Earthquake Ground Motion ◽  
Response Analysis ◽  
Practical Implementation ◽  
Autoregressive Moving Average ◽  
Arma Models ◽  
Earthquake Models

Engineers are well aware that, due to the stochastic nature of earthquake ground motion, the information obtained from structural response analysis using scant records is quite unreliable. Thus, providing earthquake models for specific sites or areas of research and practical implementation is essential. This paper presents a procedure for the modeling strong earthquake ground motion based on autoregressive moving average (ARMA) models. The Generalized autoregressive conditional heteroskedasticity (GARCH) model is used to simulate the time-varying characteristics of earthquakes.

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