China 
Africa 
Explore chapters and articles related to this topic
Applications of Artificial Neural Networks to Time Series Prediction
Published in Yu Hen Hu, Jenq-Neng Hwang, Handbook of Neural Network Signal Processing, 2018
Yuansong Liao, John Moody, Lizhong Wu
Traditional time series techniques [7, 11, 20, 21, 29, 31, 46] usually assume that a signal is stationary and can be described by a set of linear equations. Popular models include AR (autoregressive), ARX (AR with external input series), VAR (vector autoregression [45]), ARMA (autoregressive moving average), ARMAX (ARMA with external input series), ARIMA (autoregressive integrated moving average), ARIMAX (ARIMA with external input series), and ARFIMA (autoregressive fractionally integrated moving average [19, 26, 70]).3 Advantages of linear time series models are that: (1) they have been studied for a long time and can be understood in great detail, and (2) they are straightforward to implement. However, because of the limitation of linearity, they cannot be applied to many more complicated problems. Instead, nonlinear models, such as TAR (threshold autoregressive model) [64, 65, 72, 73] and state-space models [3], are used for nonlinear time series modeling. For these techniques, model types and complexities need to be predefined. Some of these models work very well for specific problems, for example, TAR for Sunspots series prediction [74]. However, for most time series, a priori models are unknown and it is difficult to obtain a good guess due to the large number of variables involved, the high level of noise, and the limited amount of training data.
Fractals
Published in Nicholas Stergiou, Nonlinear Analysis for Human Movement Variability, 2018
Methodological issues have challenged the existence of true long-range correlations in movement time series. If a researcher goes in search of a power law in his or her data by applying fractal analysis when the data are not actually governed by a power law, these methods will always give a result, but the result might very well be misleading. This is somewhat analogous to applying parametric statistical tests to nonparametric data. The tests will yield a result, but the result may not be valid. It is therefore advised that researchers include a number of safeguards in their data analysis to ensure that they have correctly identified long-range temporal correlations, as opposed to short-range correlations, which can also be found in biological data. Multiple measures of the fractal dimension are recommended in order to corroborate evidence of long-range correlations. Additionally, it has been recommended that a relevant null hypothesis for testing for the presence of long-range correlations should consider the possible short-range nature of serial correlations [40,87]. An inferential test for the presence of long-range dependence in time series, based on ARFIMA (autoregressive fractionally integrated moving average) modeling has been proposed to test this hypothesis. While this method constitutes a valuable, complementary solution for addressing some of the challenges of fractal estimation, it is not without its problems either [88]. Finally, a surrogation method is recommended when using any of the fractal methods. This is where the original, experimental time series is shuffled multiple times so that the presumed temporal correlations are destroyed, and then the fractal methods are applied to the surrogate time series. Hypothesis testing reveals whether or not the shuffled time series are different from the original time series, suggesting that the empirical time series indeed possesses a different fractal structure to a randomly shuffled time series.
ARFIMA and ARTFIMA Processes in Time Series with Applications
Published in Dinesh C. S. Bisht, Mangey Ram, Recent Advances in Time Series Forecasting, 2021
Kuldeep Kumar, Priya Chaturvedi
The interesting feature of the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process is that its autocorrelation functions decay much slower than exponential decay, which makes it a strong candidate for modeling a time series having a long memory. For time series possessing long memory, these ARFIMA processes provide an improved fit and better predictions in comparison to ARMA processes.
A hybrid autoregressive fractionally integrated moving average and nonlinear autoregressive neural network model for short-term traffic flow prediction
Published in Journal of Intelligent Transportation Systems, 2023
Xuecai Xu, Xiaofei Jin, Daiquan Xiao, Changxi Ma, S. C. Wong
Tsekeris and Stathopoulos (2006) generalized the modeling method for forecasting traffic volatility, in which the mean was modeled by ARIMA while the variance was modeled by an autoregressive conditional heteroscedastic process. Kumar and Vanajakshi (2015) extended to seasonal ARIMA model for short-term traffic flow prediction using only limited input data, and the accuracy was acceptable, and Ghosh et al. (2007; 2009) estimated the parameters of the seasonal ARIMA with Bayesian method. Another trend of ARIMA is to extend into autoregressive fractionally integrated moving average (ARFIMA) by addressing the long-term memory. Ravishanker and Ray (2002) presented ARFIMA and described a Bayesian method for the evaluation. Markov chain Monte Carlo methods were employed to generate samples, but the approach was illustrated using sea surface temperatures along the California coast, instead of traffic flow prediction. In order to capture long memory properties, Karlaftis and Vlahogianni (2009) proposed fractionally integrated dual memory models to deal with mean and variance of a time-series, but the differentiation parameter of ARIMA was forced to equal 1, which caused over-inflated moving average terms. Recently, a seasonal ARIMA plus generalized autoregressive conditional heteroscedasticity (GARCH) structure has been received increasing attention for traffic flow prediction (Guo et al., 2014, 2015), in which the seasonal ARIMA was used to predict the traffic flow levels, and the GARCH part was adopted to predict the conditional variance, which provided some idea for our model. Similar study by Zhang et al. (2014) presented a hybrid model for multi-step ahead traffic flow forecasting on freeway with real-time traffic flow data. Three modeling components were included, an intra-day or periodic trend by introducing the spectral analysis technique, a deterministic part modeled by the ARIMA model and the volatility estimated by the GARCH model. The experimental results demonstrated that the proposed model showed promising abilities in improving the accuracy and reliability of freeway traffic flow. With missing data, Zhang and Zhang (2016) compared historical average, vector autoregressive and general regression neural network for traffic flow forecasting. It was indicated that the accuracy of vector regressive was more sensitive to the missing ratio while the general regression neural network provided more robust and accurate forecasting. Pointed at fractal nature of traffic flow, Krause et al. (2017) demonstrated that traffic flow revealed antipersistence property, which can be described with a fractional Brownian motion with certain dependence of fluctuations. Actually the Brownian motion reflected the long-term memory property partly, and can be considered as the foundation of our study.