Autoregressive Moving Average Parameter Estimation Research Articles

ARMA model order and parameter estimation using genetic algorithms

A new method for simultaneously determining the order and the parameters of autoregressive moving average (ARMA) models is presented in this article. Given an ARMA (p, q) model in the absence of any information for the order, the correct order of the model (p, q) as well as the correct parameters will be simultaneously determined using genetic algorithms (GAs). These algorithms simply search the order and the parameter spaces to detect their correct values using the GA operators. The proposed method works on the principle of maximizing the GA fitness value relying on the deviation between the actual plant output, with or without an additive noise, and the estimated plant output. Simulation results show in detail the efficiency of the proposed approach. In addition to that, a practical model identification and parameter estimation is conducted in this article with results obtained as desired. The new method is compared with other well-known methods for ARMA model order and parameter estimation.

Electricity demand loads modeling using AutoRegressive Moving Average (ARMA) models

This study addresses the problem of modeling the electricity demand loads in Greece. The provided actual load data is deseasonilized and an AutoRegressive Moving Average (ARMA) model is fitted on the data off-line, using the Akaike Corrected Information Criterion (AICC). The developed model fits the data in a successful manner. Difficulties occur when the provided data includes noise or errors and also when an on-line/adaptive modeling is required. In both cases and under the assumption that the provided data can be represented by an ARMA model, simultaneous order and parameter estimation of ARMA models under the presence of noise are performed. The produced results indicate that the proposed method, which is based on the multi-model partitioning theory, tackles successfully the studied problem. For validation purposes the produced results are compared with three other established order selection criteria, namely AICC, Akaike's Information Criterion (AIC) and Schwarz's Bayesian Information Criterion (BIC). The developed model could be useful in the studies that concern electricity consumption and electricity prices forecasts.

Modeling of the grounding resistance variation using ARMA models

This study addresses the problem of modeling the variation of the grounding resistance during the year. An AutoRegressive Moving Average (ARMA) model is fitted (off-line) on the provided actual data using the Corrected Akaike Information Criterion (AICC). The developed model is shown to fit the data in a successful manner. Difficulties occur when the provided data includes noise or errors and also when an on line/adaptive modeling is required. In both cases, and under the assumption that the provided data can be represented by an ARMA model, simultaneous order and parameter estimation of ARMA models under the presence of noise is necessary. In this paper, a new method based on the multi-model partitioning theory which is also applicable to on line/adaptive operation, is used for the solution of the above mentioned problem. The simulations show that the proposed method succeeds in selecting the correct ARMA model order and estimates the parameters accurately in very few steps and even with a small sample size. For validation purposes the method introduced is compared with three other established order selection criteria presenting very good results. The proposed method can be extremely useful in the studies of electrical engineer designers, since the variation of the grounding resistance during the year affects significantly power systems performance and must be definitely considered.

An analog architecture on parameter estimation of ARMA models

An analog architecture that is suitable for parameter estimation of autoregressive moving average (ARMA) models is proposed. The convergence theorem that connects this architecture with ARMA parameter estimation is presented. Simulation results indicate that its convergence takes only a few microseconds. Hence, this architecture can lead to online implementations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

ARMA parameter estimation using a novel recursive estimation algorithm with selective updating

The authors investigate an extension of a recursive estimation algorithm (the so-called optimal bounding ellipsoid or OBE algorithm) which features a discerning update strategy. In particular, an extension of the algorithm to ARMA (autoregressive moving-average) parameter estimation is presented along with a convergence analysis. The extension is similar to the extended least-squares (ELS) algorithm. However, the convergence analysis is complicated due to the discerning update strategy, which incorporates an information-dependent updating factor. The virtues of such an update strategy are more efficient use of the input data in terms of information processing and a modular adaptive filter structure which would facilitate the development of a parallel-pipelined signal processing architecture. It is shown that if the input noise is bounded and the moving-average parameters satisfy a certain magnitude bound, then the a posteriori prediction errors are uniformly bounded. With an additional persistence-of-excitation condition, the parameter estimates are shown to converge to a neighborhood of the true parameters, and the a priori prediction errors are shown to be asymptotically bounded. Simulation results show that the parameter estimation error for the EOBE algorithm is comparable to that for the ELS algorithm. >

Optimal ARMA parameter estimation based on the sample covariances for data with missing observations

The problem of spectral estimation through the autoregressive moving-average (ARMA) modeling of stationary processes with missing observations is considered. A class of estimators based on the sample covariances is presented, and an asymptotically optimal estimator in this class is proposed. The proposed algorithm is based on a nonlinear-least-squares fit of the sample covariances computed from the data to the true covariances of the assumed ARMA model. The statistical properties of the algorithm are explored and used to show that it is asymptotically optimal, in the sense of achieving the smallest possible asymptotic variance. The performance of the algorithm is illustrated by some numerical examples. >

ARMA parameter estimation of speech

Autoregressive moving average (ARMA) or pole‐zero modeling techniques are known to provide better spectral estimation capabilities than autoregressive (AR) or all‐pole methods such as linear prediction for nasalized speech and speech corrupted by noise. This paper describes the results of applying two ARMA modeling techniques to synthesized and natural segments of noisy and clean speech. The overdetermined normal equation (ODNE) and the extended‐order singular value decomposition (SVD) methods of ARMA parameter estimation are compared to the covariance method of linear prediction and are evaluated using parametric distance measures in the cepstral domain. Use of the AR part of the ARMA model to estimate the envelope of noisy speech is demonstrated. Coefficient transformations among ARMA, AR, and cepstral parameters are also discussed.