Online Non-stationary Time Series Analysis and Processing
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Time series analysis is critical in academic communities ranging from economics, transportation science and meteorology, to engineering, genetics and environmental sciences. In this paper, we will firstly model a time series as a non-stationary stochastic process presenting the properties of variant mean and variant variance. Then the Time-variant Local Autocorrelated Polynomial model with Kalman filter, and Envelope Detecting method is proposed to dynamically estimate the instantaneous mean (trend) and variance of the interested time series. After that, we could forecast the time series. The advantages of our methods embody: (1) training free, which means that no complete a priori history data is required to train a model, compared to Box-Jenkins methodology (ARMA, ARIMA); (2) automatically identifying and predicting the peak and valley values of a time series; (3) automatically reporting and forecasting the current changing pattern (increasing or decreasing of the trend); (4) being able to handle the general variant variance problem in time series analysis, compared to the canonical but limited Box-Cox transformation; and (5) being real-time and workable for the sequential data, not just block data. More interestingly, we could also use the method we propose to explain the philosophy and nature of motion modeling in physics.
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