On the Estimation of Nonstationary Functional Series TARMA Models: An Isomorphic Matrix Algebra Based Method1

2001 ◽  
Vol 123 (4) ◽  
pp. 601-610 ◽  
Author(s):  
George N. Fouskitakis ◽  
Spilios D. Fassois
Keyword(s):  
Matrix Algebra ◽  
Moving Average ◽  
Estimation Method ◽  
Algebraic Approach ◽  
Autoregressive Moving Average ◽  
Excellent Performance ◽  
Functional Series ◽  
Monte Carlo Experiments ◽  
Polynomial Operators ◽  
Improved Accuracy

Functional Series Time-dependent AutoRegressive Moving Average (TARMA) models form an important class of nonstationary stochastic models offering high parsimony, tracking of “fast” and “slow” variations, high accuracy and resolution, as well as accurate capturing of both resonances and antiresonances. This paper considers the estimation of Functional Series TARMA models with polynomial functional spaces based upon a novel matrix algebra that is isomorphic to that of the noncommutative ring of time-varying polynomial operators expressed in terms of the model’s functional spaces. The Generalized estimation method introduced offers important advantages, such as the use of properly contracted functional spaces that is necessary for the elimination of asymptotic bias errors, the ability to handle AR and MA functional spaces of different dimensionalities, as well as improved accuracy through a streamlined realization. The method’s excellent performance characteristics are confirmed via Monte Carlo experiments and comparisons with an earlier Polynomial-Algebraic approach and the adaptive Recursive Maximum Likelihood ARMA method.

Using The Fully Modified M Method In Estimating The Effect Of Cultivated Area On Barley Production In Iraq For The Period 1970-2018

2020 ◽  
Vol 2020 (66) ◽  
pp. 101-110
Author(s):  
. Azhar Kadhim Jbarah ◽  
Prof Dr. Ahmed Shaker Mohammed
Keyword(s):  
Regression Model ◽  
Moving Average ◽  
Estimation Method ◽  
Estimation Methods ◽  
Autoregressive Moving Average ◽  
Moving Average Models ◽  
Error Terms ◽  
Relationship Of ◽  
The Relationship ◽  
Barley Crop

The research is concerned with estimating the effect of the cultivated area of barley crop on the production of that crop by estimating the regression model representing the relationship of these two variables. The results of the tests indicated that the time series of the response variable values is stationary and the series of values of the explanatory variable were nonstationary and that they were integrated of order one ( I(1) ), these tests also indicate that the random error terms are auto correlated and can be modeled according to the mixed autoregressive-moving average models ARMA(p,q), for these results we cannot use the classical estimation method to estimate our regression model, therefore, a fully modified M method was adopted, which is a robust estimation methods, The estimated results indicate a positive significant relation between the production of barley crop and cultivated area.

Identification of Armax Models With Time Dependent Coefficients

2002 ◽  
Vol 124 (3) ◽  
pp. 464-467 ◽  
Author(s):  
R. Ben Mrad ◽  
E. Farag
Keyword(s):  
Moving Average ◽  
Estimation Method ◽  
Initial Guess ◽  
Autoregressive Moving Average ◽  
Hydraulic Actuator ◽  
Prediction Ability ◽  
Signal Prediction ◽  
Highly Nonlinear ◽  
Good Signal ◽  
Stochastic Time

A method that uses input/output measurements is developed for the estimation of the coefficients of stochastic Time-varying AutoRegressive Moving Average with eXogeneous imputs (TARMAX) models. The TARMAX coefficients are expressed as linear combinations of a set of pre-selected functions. The model coefficients estimation method is fully based on linear operations, does not require initial guess values and is suitable for micro-computer implementation. The good performance of the estimation method is verified through numerical examples. A TARMAX model is also used to capture the dynamics of a detailed highly nonlinear model of an automobile hydraulic active suspension system. The TARMAX model is used to relate a desired force provided by a corner processor to the actual force generated by the hydraulic actuator. The TARMAX model is shown to provide good signal prediction ability.

scholarly journals Semiparametric estimation of the canonical permanent‐transitory model of earnings dynamics

2019 ◽  
Vol 10 (4) ◽  
pp. 1495-1536 ◽  
Author(s):  
Yingyao Hu ◽  
Robert Moffitt ◽  
Yuya Sasaki
Keyword(s):  
Moving Average ◽  
State Space Model ◽  
Estimation Method ◽  
Higher Order ◽  
Autoregressive Moving Average ◽  
Earnings Mobility ◽  
Arma Process ◽  
Earnings Dynamics ◽  
Prior Literature ◽  
Transitory Component

This paper presents identification and estimation results for a flexible state space model. Our modification of the canonical model allows the permanent component to follow a unit root process and the transitory component to follow a semiparametric model of a higher‐order autoregressive‐moving‐average (ARMA) process. Using panel data of observed earnings, we establish identification of the nonparametric joint distributions for each of the permanent and transitory components over time. We apply the identification and estimation method to the earnings dynamics of U.S. men using the Panel Survey of Income Dynamics (PSID). The results show that the marginal distributions of permanent and transitory earnings components are more dispersed, more skewed, and have fatter tails than the normal and that earnings mobility is much lower than for the normal. We also find strong evidence for the existence of higher‐order ARMA processes in the transitory component, which lead to much different estimates of the distributions of and earnings mobility in the permanent component, implying that misspecification of the process for transitory earnings can affect estimated distributions of the permanent component and estimated earnings dynamics of that component. Thus our flexible model implies earnings dynamics for U.S. men different from much of the prior literature.

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

2021 ◽  
Vol 15 ◽  
pp. 1607-1612
Author(s):  
Adnan M Al-Smadi
Keyword(s):  
Moving Average ◽  
Estimation Method ◽  
Qr Decomposition ◽  
New Technique ◽  
Autoregressive Moving Average ◽  
Third Order ◽  
Power Spectral ◽  
Q Model ◽  
A New Technique ◽  
Non Gaussian

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.

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