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Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
Autoregressive moving average model (ARMA). An autoregressive moving average time series of order n is defined via yk=-∑m=1namyk-m+∑m=0ncmwk-m. The sequence wk is usually assumed to consist of zero-mean identically distributed stochastic variables wk.
A spatiotemporal graph generative adversarial networks for short-term passenger flow prediction in urban rail transit systems
Published in International Journal of General Systems, 2023
Jinlei Zhang, Hua Li, Shuxin Zhang, Lixing Yang, Guangyin Jin, Jianguo Qi
As an important topic of spatiotemporal data mining, traffic flow prediction (Shu, Cai, and Xiong 2021; Ma, Dai, and Zhou 2021; Zhang et al. 2021a; Wu 2021) has been extensively studied in recent years. Conventional traffic prediction models are statistic-based, such as the autoregressive model (AR), moving average model (MA), autoregressive moving average model (ARIMA), and linear regression (Sun, Zhang, and Yin 2014). Williams, Durvasula, and Brown (1998) proposed a seasonal ARIMA to conduct traffic flow prediction for urban freeways. Williams (2001) applied the ARIMA model to short-term predictions for motorways. Yan (2010) extended the ARIMA model with spatial dimension and further applied it for trajectory predictions. However, the statistic-based passenger flow prediction models cannot effectively capture the complex nonlinear relationship in the time series, thus exhibiting limited performance and adaptability.
R-Peak Detection in ECG Signal Using Yule–Walker and Principal Component Analysis
Published in IETE Journal of Research, 2021
The state transition matrix (STM) can be modified in terms of as [44] where is expressed as , can be estimated if is expressed as where In general, generalized expression for model order m is given as And, ARMA (Autoregressive moving average) model is given by m = 0 and Y(z) = 1 for AR signals, therefore it can be expressed mathematically as
Prediction method of autoregressive moving average models for uncertain time series
Published in International Journal of General Systems, 2020
Jingwen Lu, Jin Peng, Jinyang Chen, Kiki Ariyanti Sugeng
Assuming and are stable. That is, the autoregressive moving average model is stable and reversible. The way to deal with the problem is to quote Ding's (2018) article. Thus, the model is equivalent to the infinite order autoregressive where . Let be large enough, for example, . This infinite model (5) is approximately equal to the higher-order model where .