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Yanxin Wang – 1st expert on this subject based on the ideXlab platform
modwt ARMA Model for time series predictionApplied Mathematical Modelling, 2014Co-Authors: Yanxin WangAbstract:
Abstract Many time series in the applied sciences display a time-varying second order structure and long-range dependence (LRD). In this paper, we present a hybrid MODWT-ARMA Model by combining the maximal overlap discrete wavelet transform (MODWT) and the ARMA Model to deal with the non-stationary and LRD time series. We prove theoretically that the details series obtained by MODWT are stationary and short-range dependent (SRD). Then we derive the general form of MODWT-ARMA Model. In the experimental study, the daily rainfall and Mackey–Glass time series are used to assess the performance of the hybrid Model. Finally, the normalized error comparison with DWT-ARMA, EMD-ARMA and ARIMA Model indicates that this combined Model is an effective way to improve forecasting accuracy.
A H Kayran – 2nd expert on this subject based on the ideXlab platform
ARMA Model parameter estimation based on the equivalent ma approachDigital Signal Processing, 2006Co-Authors: Aydin Kizilkaya, A H KayranAbstract:
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.
estimation of 2 d ARMA Model parameters by using equivalent ar approachJournal of The Franklin Institute-engineering and Applied Mathematics, 2005Co-Authors: Aydin Kizilkaya, A H KayranAbstract:
Abstract In this paper, the problem of estimating the parameters of a two-dimensional autoregressive moving-average (2-D ARMA) Model driven by an unobservable input noise is addressed. In order to solve this problem, the relation between the parameters of a 2-D ARMA Model and their 2-D equivalent autoregressive (EAR) Model parameters is investigated. Based on this relation, a new algorithm is proposed for determining the 2-D ARMA Model parameters from the coefficients of the 2-D EAR Model. This algorithm is a three-step approach. In the first step, the parameters of the 2-D EAR Model that is approximately equivalent to the 2-D ARMA Model are estimated by applying 2-D modified Yule–Walker (MYW) equation to the process under consideration. Then, the moving-average parameters of the 2-D ARMA Model are obtained solving the linear equation set constituted by using the EAR coefficients acquired in the first step. Finally, the autoregressive parameters of the 2-D ARMA Model are found by exploiting the values obtained in first and second steps. The performance of the proposed algorithm is compared with other 2-D ARMA parameter and spectral estimation algorithms available in the technical literature by means of three different criteria. As a result of this comparison, it is shown that the parameters and the corresponding power spectrums estimated by using the proposed algorithm are converged to the original parameters and the original power spectrums, respectively.
Ki H Chon – 3rd expert on this subject based on the ideXlab platform
a new algorithm for linear and nonlinear ARMA Model parameter estimation using affine geometry and application to blood flow pressure dataIEEE Transactions on Biomedical Engineering, 2001Co-Authors: Sheng Lu, Ki Hwan Ju, Ki H ChonAbstract:
A linear and nonlinear autoregressive (AR) moving average (MA) (ARMA) identification algorithm is developed for Modeling time series data. The new algorithm is based on the concepts of affine geometry in which the salient feature of the algorithm is to remove the linearly dependent ARMA vectors from the pool of candidate ARMA vectors. For noiseless time series data with a priori incorrect Model-order selection, computer simulations show that accurate linear and nonlinear ARMA Model parameters can be obtained with the new algorithm. Many algorithms, including the fast orthogonal search (FOS) algorithm, are not able to obtain correct parameter estimates in every case, even with noiseless time series data, because their Model-order search criteria are suboptimal. For data contaminated with noise, computer simulations show that the new algorithm performs better than the FOS algorithm for MA processes, and similarly to the FOS algorithm for ARMA processes. However, the computational time to obtain the parameter estimates with the new algorithm is faster than with FOS. Application of the new algorithm to experimentally obtained renal blood flow and pressure data show that the new algorithm is reliable in obtaining physiologically understandable transfer function relations between blood pressure and flow signals.