The computing problem in the analysis of non-stochastic time series using an auto-regression model

1956 ◽  
Author(s):  
Z. Szatrowski
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Stochastic Time Series ◽  
Stochastic Time ◽  
Auto Regression

scholarly journals Identification of an unstable ARMA equation

2001 ◽  
Vol 7 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Yulia R. Gel ◽  
Vladimir N. Fomin
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Infinite Order ◽  
Time Series Model ◽  
Identification Algorithm ◽  
Data Handling ◽  
Stochastic Time Series ◽  
Stochastic Time ◽  
Strongly Consistent ◽  
Minimal Phase

Usually the coefficients in a stochastic time series model are partially or entirely unknown when the realization of the time series is observed. Sometimes the unknown coefficients can be estimated from the realization with the required accuracy. That will eventually allow optimizing the data handling of the stochastic time series.Here it is shown that the recurrent least-squares (LS) procedure provides strongly consistent estimates for a linear autoregressive (AR) equation of infinite order obtained from a minimal phase regressive (ARMA) equation. The LS identification algorithm is accomplished by the Padé approximation used for the estimation of the unknown ARMA parameters.

Using the AR–SVR–CPSO hybrid model to forecast vibration signals in a high-speed train transmission system

2018 ◽  
Vol 233 (7) ◽  
pp. 701-714
Author(s):  
Yumei Liu ◽  
Ningguo Qiao ◽  
Congcong Zhao ◽  
Jiaojiao Zhuang ◽  
Guangdong Tian
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Support Vector Regression ◽  
Hybrid Model ◽  
High Speed ◽  
Support Vector ◽  
High Speed Train ◽  
Support Vector Regression Model ◽  
Vibration Time ◽  
Auto Regression

Accurate vibration time series modeling can mine the internal law of data and provide valuable references for reliability assessment. To improve the prediction accuracy, this study proposes a hybrid model – called the AR–SVR–CPSO hybrid model – that combines the auto regression (AR) and support vector regression (SVR) models, with the weights optimized by the chaotic particle swarm optimization (CPSO) algorithm. First, the auto regression model with the difference method is employed to model the vibration time series. Second, the support vector regression model with the phase space reconstruction is constructed for predicting the vibration time series once more. Finally, the predictions of the AR and SVR models are weighted and summed together, with the weights being optimized by the CPSO. In addition, the data collected from the reliability test platform of high-speed train transmission systems and the “NASA prognostics data repository” are used to validate the hybrid model. The experimental results demonstrate that the hybrid model proposed in this study outperforms the traditional AR and SVR models.

Fractal and Multifractal in Stochastic Time Series

2020 ◽  
pp. 129-151
Author(s):  
Santo Banerjee ◽  
M K Hassan ◽  
Sayan Mukherjee ◽  
A Gowrisankar
Keyword(s):  
Time Series ◽  
Stochastic Time Series ◽  
Stochastic Time

A Recurrent Probabilistic Neural Network for EMG Pattern Recognition

2011 ◽  
pp. 130-153 ◽  
Author(s):  
Toshio Tsuji ◽  
Nan Bu ◽  
Osamu Fukuda
Keyword(s):  
Time Series ◽  
Pattern Recognition ◽  
Hidden Markov ◽  
Probabilistic Neural Network ◽  
Temporal Characteristic ◽  
Gaussian Mixture ◽  
Neural Computation ◽  
Emg Pattern Recognition ◽  
Stochastic Time Series ◽  
Stochastic Time

In the field of pattern recognition, probabilistic neural networks (PNNs) have been proven as an important classifier. For pattern recognition of EMG signals, the characteristics usually used are: (1) amplitude, (2) frequency, and (3) space. However, significant temporal characteristic exists in the transient and non-stationary EMG signals, which cannot be considered by traditional PNNs. In this article, a recurrent PNN, called recurrent log-linearized Gaussian mixture network (R-LLGMN), is introduced for EMG pattern recognition, with the emphasis on utilizing temporal characteristics. The structure of R-LLGMN is based on the algorithm of a hidden Markov model (HMM), which is a routinely used technique for modeling stochastic time series. Since R-LLGMN inherits advantages from both HMM and neural computation, it is expected to have higher representation ability and show better performance when dealing with time series like EMG signals. Experimental results show that R-LLGMN can achieve high discriminant accuracy in EMG pattern recognition.

scholarly journals Coercively Adjusted Auto Regression Model for Forecasting in Epilepsy EEG

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Sun-Hee Kim ◽  
Christos Faloutsos ◽  
Hyung-Jeong Yang
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Regression Model ◽  
Random Coefficients ◽  
Experimental Results ◽  
Ar Model ◽  
Forecasting Method ◽  
Eeg Data ◽  
Future Value ◽  
Auto Regression

Recently, data with complex characteristics such as epilepsy electroencephalography (EEG) time series has emerged. Epilepsy EEG data has special characteristics including nonlinearity, nonnormality, and nonperiodicity. Therefore, it is important to find a suitable forecasting method that covers these special characteristics. In this paper, we propose a coercively adjusted autoregression (CA-AR) method that forecasts future values from a multivariable epilepsy EEG time series. We use the technique of random coefficients, which forcefully adjusts the coefficients with−1and 1. The fractal dimension is used to determine the order of the CA-AR model. We applied the CA-AR method reflecting special characteristics of data to forecast the future value of epilepsy EEG data. Experimental results show that when compared to previous methods, the proposed method can forecast faster and accurately.

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