Piecewise Linear Representation of Finance Time Series: Quantum Mechanical Tool

Piecewise Linear Time Series Estimation with GRASP

This paper describes a heuristic to build piecewise linear statistical models with multivariate thresholds, based on a Greedy Randomized Adaptive Search Procedure (GRASP). GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. In this paper we describe a GRASP to sequentially split an n-dimen...

Piecewise Trend Approximation: A Ratio-Based Time Series Representation

and Applied Analysis 3 can identify segments of variable length. Also, the APCA algorithm is able to produce high quality approximations of a time series by resorting to solutions adopted in the wavelet domain. In SAX method, dimensionality of original time series is first reduced by applying PAA, then the PAA coefficients are quantized, and finally each quantization level is represented by a s...

Neural network piecewise linear preprocessing for time-series prediction

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 f...

Max-Min Representation of Piecewise Linear Functions

It is shown that a piecewise linear function on a convex domain in R can be represented as a boolean polynomial in terms of its linear components.