A Better Alternative to Piecewise Linear Time Series Segmentation

Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast linear time algorithms. The popular piecewise linear model can determine where the data goes up or down and at what rate. Unfortunately, when the data does not follow a linear model, the computation of the local slope creates overfitting. We propose an adaptive time series model where the polynomial degree of each interval vary (constant, linear and so on). Given a number of regressors, the cost of each interval is its polynomial degree: constant intervals cost 1 regressor, linear intervals cost 2 regressors, and so on. Our goal is to minimize the Euclidean (l2) error for a given model complexity. Experimentally, we investigate the model where intervals can be either constant or linear. Over synthetic random walks, historical stock market prices, and...

• Type: Conference
• Year: 2007
• Where: SDM
• Authors: Daniel Lemire
• Keywords: Data Mining, Linear Model, Piecewise Linear Model, SDM 2007, Time Series