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.

scholarly journals Order Selection of AR Models of Hydrologic Time Series

1982 ◽  
Vol 13 (2) ◽  
pp. 93-104 ◽  
Author(s):  
G. Padmanabhan ◽  
A.R. Rao
Keyword(s):  
Time Series ◽  
Posterior Probability ◽  
Information Criterion ◽  
Order Selection ◽  
Hydrologic Time Series ◽  
Hydrologic Analysis ◽  
Final Prediction Error ◽  
Probability Criterion ◽  
Ar Models ◽  
Selection Of

Recently several criteria have been proposed for selection of orders of AR models. One of these, namely the AIC has been used in hydrologic analysis. However, the results given by these criteria when observed hydrologic data are analyzed by using them have not been studied to determine the variability in the results obtained by these criteria. Some of the more widely discussed of these criteria have been analyzed in this paper by using both hydrologic and nonhydrologic time series. The orders of AR models given by Akaike's information criterion, the final prediction error criterion, the criterion autoregression transfer function, Schwarz's criterion and the posterior probability criterion have been analyzed, and the results are discussed. Although the results obtained by these criteria are often similar, the posterior probability criterion has been recommended for use because it is possible to estimate the probability of the order being correct by using it.

scholarly journals A MISO-ARX-Based Method for Single-Trial Evoked Potential Extraction

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Nannan Yu ◽  
Lingling Wu ◽  
Dexuan Zou ◽  
Ying Chen ◽  
Hanbing Lu
Keyword(s):  
Evoked Potential ◽  
Moving Average ◽  
Extraction Process ◽  
Autoregressive Moving Average ◽  
Single Trial ◽  
Model Driven ◽  
Single Output ◽  
Multiple Input ◽  
Novel Method ◽  
Electroencephalographic Activity

In this paper, we propose a novel method for solving the single-trial evoked potential (EP) estimation problem. In this method, the single-trial EP is considered as a complex containing many components, which may originate from different functional brain sites; these components can be distinguished according to their respective latencies and amplitudes and are extracted simultaneously by multiple-input single-output autoregressive modeling with exogenous input (MISO-ARX). The extraction process is performed in three stages: first, we use a reference EP as a template and decompose it into a set of components, which serve as subtemplates for the remaining steps. Then, a dictionary is constructed with these subtemplates, and EPs are preliminarily extracted by sparse coding in order to roughly estimate the latency of each component. Finally, the single-trial measurement is parametrically modeled by MISO-ARX while characterizing spontaneous electroencephalographic activity as an autoregression model driven by white noise and with each component of the EP modeled by autoregressive-moving-average filtering of the subtemplates. Once optimized, all components of the EP can be extracted. Compared with ARX, our method has greater tracking capabilities of specific components of the EP complex as each component is modeled individually in MISO-ARX. We provide exhaustive experimental results to show the effectiveness and feasibility of our method.

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

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.

scholarly journals Future Trend Forecast by Empirical Wavelet Transform and Autoregressive Moving Average

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2621 ◽  
Author(s):  
Qiusheng Wang ◽  
Haipeng Li ◽  
Jinyong Lin ◽  
Chunxia Zhang
Keyword(s):  
Complex System ◽  
Wavelet Transform ◽  
Moving Average ◽  
Parametric Model ◽  
Future Trend ◽  
Autoregressive Moving Average ◽  
System A ◽  
Empirical Wavelet Transform ◽  
Novel Method ◽  
System States

In engineering and technical fields, a large number of sensors are applied to monitor a complex system. A special class of signals are often captured by those sensors. Although they often have indirect or indistinct relationships among them, they simultaneously reflect the operating states of the whole system. Using these signals, the field engineers can evaluate the operational states, even predict future behaviors of the monitored system. A novel method of future operational trend forecast of a complex system is proposed in this paper. It is based on empirical wavelet transform (EWT) and autoregressive moving average (ARMA) techniques. Firstly, empirical wavelet transform is used to extract the significant mode from each recorded signal, which reflects one aspect of the operating system. Secondly, the system states are represented by the indicator function which are obtained from those normalized and weighted significant modes. Finally, the future trend is forecast by the parametric model of ARMA. The effectiveness and practicality of the proposed method are verified by a set of numerical experiments.

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.

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.

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