Parameter Estimation of Moving Average Processes Using Cumulants and Nonlinear Optimization Algorithms (original) (raw)

A New Algorithm for Blind Identification of MA Models Using Cumulants

This paper addresses the problem of blind identifi- cation of Moving Average (MA) models. We propose a new al- gorithm utilizing Higher-Order Statistics (HOS), namely fourth- order cumulants and autocorrelation functions of output signal of the MA model, to estimate the parameters of this model. A general relationship linking cumulants of the output signal of the model and the coefficients of this model is exploited to generate a Least-Squares (LS) solution. This new method is compared with C(q;k;0) algorithm, named also Giannakis algorithm. Input signal is considered like digital communications signal, non observable, but its statistical properties are known. Simulation results are presented demonstrating the performance of this algorithm.

Identification of non-skewed MA processes using a fourth-order cumulant-based approach

Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics. SPW-HOS '99, 1999

The purpose of this communication is the formulation of three new linear algorithms for blind non-minimum phase MA system identification. These methods have been derived starting from new equations involving system coefficients and -slices of the ¡ £ ¢ ¥ ¤¦ order cumulant sequence of the ouput MA system. In particular, these new algorithms use only fourth-order cumulants, and thus, are specially useful when the driving system noise has symmetric probability density function and a possible additive Gaussian noisy process contaminates the system ouput.

Higher-order statistics based blind estimation of non-Gaussian bidimensional moving average models

Signal Processing, 2006

In this paper, four batches least squares linear approaches are developed for non-minimum phase bidimensional non-Gaussian moving average (MA) models identification. A relationship between autocorrelation and cumulant sequences is established. One of the proposed methods is cumulant based. The others exploit both autocorrelation and mth-order cumulants (m42). Three of these proposed methods are obtained by transforming Brillinger-Rosenblatt's non-linear equation into linear one using the Tugnait's closed-form solution. We also generalize the 2-D version of Giannakis-Mendel's method to mth-order cumulant. The simulation results show that one of the three autocorrelation and cumulants based methods gives the best estimates in free-noise environments, but in a Gaussian noisy case, the cumulant-based one is more adequate when large data are available. We also show the usefulness of the relationship to improve the estimates of the autocorrelation-based method in colored noise environment.

Identification of autoregressive moving-average parameters of time series

IEEE Transactions on Automatic Control, 1975

A procedure for sequentially estimating the parameters and orders of mixed autoregressive moving-average signal models from time-series data is presented. Identification is performed by first identifying a purely autoregressive signal model. The parameters and orders of the mixed autoregressive moving-average process are then given from the solution of simple algebraic equations involving the purely autoregressive model parameters.

Identification of Coefficients in a Quadratic Moving Average Process Using the Generalized Method of Moments

The output of a causal, stable, time-invariant nonlinear filter can be approximately represented by the linear and quadratic terms of a finite parameter Volterra series expansion. We call this representation the "quadratic nonlinear MA model" since it is the logical extension of the usual linear MA process. Where the actual generating mechanism for the data is fairly smooth, this quadratic MA model should provide a better approximation to the true dynamics than the two- state threshold autoregression and Markov switching models usually considered. As with linear MA processes, the nonlinear MA model coefficients can be estimated via least squares fitting, but it is essential to begin with a reasonably parsimonious model identification and non-arbitrary preliminary estimates for the parameters. In linear ARMA modeling these are derived from the sample correlogram and the sample partial correlogram, but these tools are confounded by nonlinearity in the generating mechanism. H...

The compact genetic algorithm for likelihood estimator of first order moving average model

2012 2nd International Conference on Digital Information and Communication Technology and its Applications, DICTAP 2012, 2012

Recently Genetic Algorithms (GAs) have frequently been used for optimizing the solution of estimation problems. One of the main advantages of using these techniques is that they require no knowledge or gradient information about the response surface. The poor behavior of genetic algorithms in some problems, sometimes attributed to design operators, has led to the development of other types of algorithms. One such class of these algorithms is compact Genetic Algorithm (cGA), it dramatically reduces the number of bits reqyuired to store the poulation and has a faster convergence speed. In this paper compact Genetic Algorithm is used to optimize the maximum likelihood estimator of the first order moving avergae model MA(1). Simulation results based on MSE were compared with those obtained from the moments method and showed that the Canonical GA and compact GA can give good estimator of θ for the MA(1) model. Another comparison has been conducted to show that the cGA method has less number of function evaluations, minimum searched space percentage, faster convergence speed and has a higher optimal precision than that of the Canonical GA.

A new stable feedback ladder algorithm for the identification of moving average processes

A novel algorithm for the direct identification of the coefficients of a moving average model is presented. The scheme can be represented in a feedback ladder form, recursive in time and order, hence allowing sequential processing of data observed from a process. Potential applications are numerous in different fields such as spectral estimation, automatic control or econometrics. The paper briefly discusses the underlying principles of the method. Results from simulations are included in order to display the general behaviour of the algorithm and its sensitivity to uncertainty in the model order.

ARMA model parameter estimation based on the equivalent MA approach

Digital Signal Processing, 2006

The paper investigates the relation between the parameters of an autoregressive moving average (ARMA) model and its equivalent moving average (EMA) model. On the basis of this relation, a new method is proposed for determining the ARMA model parameters from the coefficients of a finite-order EMA model. This method is a three-step approach: in the first step, a simple recursion relating the EMA model parameters and the cepstral coefficients of an ARMA process is derived to estimate the EMA model parameters; in the second step, the AR parameters are estimated by solving the linear equation set composed of EMA parameters; then, the MA parameters are obtained via simple computations using the estimated EMA and AR parameters. Simulations including both low-and high-order ARMA processes are given to demonstrate the performance of the new method. The end results are compared with the existing method in the literature over some performance criteria. It is observed from the simulations that our new algorithm produces the satisfactory and acceptable results.

A New Technique for ARMA-System Identification Based on QR-Decomposition of Third Order Cumulants Matrix

International Journal of Circuits, Systems and Signal Processing, 2021

In this paper a new technique to estimate the coefficients of a general Autoregressive Moving Average (ARMA) (p, q) model is proposed. The ARMA system is excited by an un-observable independently identically distributed (i.i.d) non-Gaussian process. The proposed ARMA coefficients estimation method uses the QR-Decomposition (QRD) of a special matrix built with entries of third order cumulants (TOC) of the available output data only. The observed output may be corrupted with additive colored or white Gaussian noise of unknown power spectral density. The proposed technique was compared with several good methods such as the residual time series (RTS) and the Q-slice algorithm (QSA) methods. Simulations for several examples were tested. The results for these examples confirm the good performance of the proposed technique with respect to existing well-known methods.