Nonlinear Time-Series Prediction with Missing and Noisy Data

1998 ◽  
Vol 10 (3) ◽  
pp. 731-747 ◽  
Author(s):  
Volker Tresp ◽  
Reimar Hofmann
Keyword(s):  
Time Series ◽  
Stochastic Simulation ◽  
Time Series Prediction ◽  
Noisy Data ◽  
Nonlinear Time Series ◽  
Point Of View ◽  
Data Set ◽  
Sunspot Data ◽  
Error Bars ◽  
Probabilistic Point

We derive solutions for the problem of missing and noisy data in nonlinear time-series prediction from a probabilistic point of view. We discuss different approximations to the solutions—in particular, approximations that require either stochastic simulation or the substitution of a single estimate for the missing data. We show experimentally that commonly used heuristics can lead to suboptimal solutions. We show how error bars for the predictions can be derived and how our results can be applied to K-step prediction. We verify our solutions using two chaotic time series and the sunspot data set. In particular, we show that for K-step prediction, stochastic simulation is superior to simply iterating the predictor.

scholarly journals A Period-Aware Hybrid Model Applied for Forecasting AQI Time Series

2020 ◽  
Vol 12 (11) ◽  
pp. 4730 ◽  
Author(s):  
Ping Wang ◽  
Hongyinping Feng ◽  
Guisheng Zhang ◽  
Daizong Yu
Keyword(s):  
Time Series ◽  
Air Quality ◽  
Hybrid Model ◽  
Prediction Models ◽  
Time Series Prediction ◽  
Input Vector ◽  
Period Function ◽  
Data Set ◽  
Luenberger Observer ◽  
Extraction Algorithm

An accurate, reliable and stable air quality prediction system is conducive to the public health and management of atmospheric ecological environment; therefore, many models, individual or hybrid, have been implemented widely to deal with the prediction problem. However, many of these models do not take into consideration or extract improperly the period information in air quality index (AQI) time series, which impacts the models’ learning efficiency greatly. In this paper, a period extraction algorithm is proposed by using a Luenberger observer, and then a novel period-aware hybrid model combined the period extraction algorithm and tradition time series models is build to exploit the comprehensive forecasting capacity to the AQI time series with nonlinear and non-stationary noise. The hybrid model requires a multi-phase implementation. In the first step, the Luenberger observer is used to estimate the implied period function in the one-dimensional AQI series, and then the analyzed time series is mapped to the period space through the function to obtain the period information sub-series of the original series. In the second step, the period sub-series is combined with the original input vector as input vector components according to the time points to establish a new data set. Finally, the new data set containing period information is applied to train the traditional time series prediction models. Both theoretical proof and experimental results obtained on the AQI hour values of Beijing, Tianjin, Taiyuan and Shijiazhuang in North China prove that the hybrid model with period information presents stronger robustness and better forecasting accuracy than the traditional benchmark models.

A Novel Modeling Method Based on Multi-Dimensional Taylor Network and its Application in Time Series Prediction

2014 ◽  
Vol 940 ◽  
pp. 480-484 ◽  
Author(s):  
Yi Lin ◽  
Hong Sen Yan ◽  
Bo Zhou
Keyword(s):  
Time Series ◽  
Prior Knowledge ◽  
Dynamic Characteristics ◽  
Prediction Accuracy ◽  
Time Series Prediction ◽  
Nonlinear Time Series ◽  
Modeling Method ◽  
Input Output ◽  
Output Data ◽  
Bridge Tower

A novel modeling method based on multi-dimensional Taylor network is proposed. The structure and the principle of the multi-dimensional Taylor network are introduced. Based on this, the method is applied in the nonlinear time series prediction based on multi-dimensional Taylor network. It provides a new method to predict the time series, which can describe the dynamic characteristics without prior knowledge and can realize the prediction of the nonlinear time series just with input-output data. An example of predicting the stress data of a large span bridge tower induced by strong typhoon is taken at last in this paper. Results indicate the validity and the better prediction accuracy of this method in nonlinear time series prediction.

scholarly journals Predicting Spatio-temporal Time Series Using Dimension Reduced Local States

2019 ◽  
Vol 30 (3) ◽  
pp. 713-735 ◽  
Author(s):  
Jonas Isensee ◽  
George Datseris ◽  
Ulrich Parlitz
Keyword(s):  
Time Series ◽  
Principle Component Analysis ◽  
Temporal Dynamics ◽  
Time Series Prediction ◽  
Noisy Data ◽  
Nearest Neighbour ◽  
Reduction Techniques ◽  
Spatio Temporal ◽  
Delay Coordinates ◽  
Dimension Reduction Techniques

Abstract We present a method for both cross-estimation and iterated time series prediction of spatio-temporal dynamics based on local modelling and dimension reduction techniques. Assuming homogeneity of the underlying dynamics, we construct delay coordinates of local states and then further reduce their dimensionality through Principle Component Analysis. The prediction uses nearest neighbour methods in the space of dimension reduced states to either cross-estimate or iteratively predict the future of a given frame. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio–Cherry–Fenton model, and the Kuramoto–Sivashinsky model.

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