scholarly journals Adaptive Gradient-Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jian Pan ◽  
Hao Ma ◽  
Xiao Jiang ◽  
Wenfang Ding ◽  
Feng Ding
Keyword(s):  
Moving Average ◽  
Measurement Data ◽  
Identification Problem ◽  
Autoregressive Moving Average ◽  
Data Filtering ◽  
Moving Average Process ◽  
Output Data ◽  
Gradient Based ◽  
Filtering Technique ◽  
Negative Gradient

The identification problem of multivariable controlled autoregressive systems with measurement noise in the form of the moving average process is considered in this paper. The key is to filter the input–output data using the data filtering technique and to decompose the identification model into two subidentification models. By using the negative gradient search, an adaptive data filtering-based gradient iterative (F-GI) algorithm and an F-GI with finite measurement data are proposed for identifying the parameters of multivariable controlled autoregressive moving average systems. In the numerical example, we illustrate the effectiveness of the proposed identification methods.

Parameter Estimation Algorithms for Hammerstein–Wiener Systems With Autoregressive Moving Average Noise

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Yanjiao Wang ◽  
Feng Ding
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Data Filtering ◽  
Estimation Algorithms ◽  
Gradient Based ◽  
Wiener Systems ◽  
Filtering Technique ◽  
Identification Theory

Hammerstein–Wiener (H–W) systems are a class of typical nonlinear systems. This paper studies the gradient-based parameter estimation algorithms for H–W nonlinear systems based on the multi-innovation identification theory and the data filtering technique. The proposed methods include a generalized extended stochastic gradient (GESG) algorithm, a multi-innovation GESG (MI-GESG) algorithm, a data filtering based GESG (F-GESG) algorithm and a data filtering based MI-GESG algorithm. Finally, the computational efficiency of the proposed algorithms are analyzed and compared. The simulation example verifies the theoretical results.

ARMA processes have maximal entropy among time series with prescribed autocovariances and impulse responses

1985 ◽  
Vol 17 (04) ◽  
pp. 810-840 ◽  
Author(s):  
Jürgen Franke
Keyword(s):  
Time Series ◽  
Impulse Response ◽  
Moving Average ◽  
Autoregressive Process ◽  
Natural Generalization ◽  
Maximal Entropy ◽  
Autoregressive Moving Average ◽  
Moving Average Process ◽  
Arma Process ◽  
Arma Processes

The maximum-entropy approach to the estimation of the spectral density of a time series has become quite popular during the last decade. It is closely related to the fact that an autoregressive process of order p has maximal entropy among all time series sharing the same autocovariances up to lag p. We give a natural generalization of this result by proving that a mixed autoregressive-moving-average process (ARMA process) of order (p, q) has maximal entropy among all time series sharing the same autocovariances up to lag p and the same impulse response coefficients up to lag q. The latter may be estimated from a finite record of the time series, for example by using a method proposed by Bhansali (1976). By the way, we give a result on the existence of ARMA processes with prescribed autocovariances up to lag p and impulse response coefficients up to lag q.

Parametric estimators for stationary time series with missing observations

1981 ◽  
Vol 13 (01) ◽  
pp. 129-146 ◽  
Author(s):  
W. Dunsmuir ◽  
P. M. Robinson
Keyword(s):  
Unknown Parameter ◽  
Strong Consistency ◽  
Moving Average ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Missing Observations ◽  
Parameter Vector ◽  
Moving Average Process ◽  
The Third ◽  
Unknown Parameter Vector

Three related estimators are considered for the parametrized spectral density of a discrete-time process X(n), n = 1, 2, · · ·, when observations are not available for all the values n = 1(1)N. Each of the estimators is obtained by maximizing a frequency domain approximation to a Gaussian likelihood, although they do not appear to be the most efficient estimators available because they do not fully utilize the information in the process a(n) which determines whether X(n) is observed or missed. One estimator, called M3, assumes that the second-order properties of a(n) are known; another, M2, lets these be known only up to an unknown parameter vector; the third, M1, requires no model for a(n). Under representative sets of conditions, which allow for both deterministic and stochastic a(n), the strong consistency and asymptotic normality of M1, M2, and M3 are established. The conditions needed for consistency when X(n) is an autoregressive moving-average process are discussed in more detail. It is also shown that in general M1 and M3 are equally efficient asymptotically and M2 is never more efficient, and may be less efficient, than M1 and M3.

On the inverses of some patterned matrices arising in the theory of stationary time series

1974 ◽  
Vol 11 (01) ◽  
pp. 63-71 ◽  
Author(s):  
R. F. Galbraith ◽  
J. I. Galbraith
Keyword(s):  
Moving Average ◽  
Autoregressive Process ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
First Order ◽  
Explicit Formulae ◽  
Patterned Matrices ◽  
Autoregressive Moving Average Process

Expressions are obtained for the determinant and inverse of the covariance matrix of a set of n consecutive observations on a mixed autoregressive moving average process. Explicit formulae for the inverse of this matrix are given for the general autoregressive process of order p (n ≧ p), and for the first order mixed autoregressive moving average process.

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