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Track irregularity time series analysis and trend forecasting. (English) Zbl 1255.62235
Summary: The combination of linear and nonlinear methods is widely used in the prediction of time series data. This paper analyzes track irregularity time series data by using gray incidence degree models and methods of data transformation, trying to find the connotative relationship between the time series data. In this paper, $GM\left(1,1\right)$ is based on first-order, single variable linear differential equations; after an adaptive improvement and error correction, it is used to predict the long-term changing trend of track irregularity at a fixed measuring point; the stochastic linear AR, Kalman filtering model, and artificial neural network model are applied to predict the short-term changing trend of track irregularity at unit section. Both long-term and short-term changes prove that the model is effective and can achieve the expected accuracy.
##### MSC:
 62M10 Time series, auto-correlation, regression, etc. (statistics) 62M20 Prediction; filtering (statistics) 68T05 Learning and adaptive systems
##### Keywords:
stochastic linear AR; Kalman filtering model