Piecewise Linear Representation of Finance Time Series: Quantum Mechanical Tool

In this work, a piecewise linear representation of economic time series is presented. The representation is based on calculating local maxima and minima in time series. Then, we study the localization properties of the 1D tight-binding equation, where the on-site potential is replaced by a piecewise linear function. The piecewise linear representation is derived from economic time series databases. We carry out numerical work involving direct diagonalization to study eigenvalues of the system. This numerical scheme is applied to different segments of the time series. It is shown that this mathematical tool could be used as a moving indicator to study finance charts.