An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint matrices and hence a spectral representation. As a result,...

An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint matrices and hence a spectral representation. As a result,...

The dynamic comovement between time series is a key concept in macroeconomic analysis. The extent to which series are cyclically synchronized is particularly important for evaluating the feasibility of common policy measures for groups of countries. This paper investigates concepts in the time...

The prediction of stock prices is studied extensively, because of the demand from private investors and financial institutions. However, long-term prediction is difficult due to the large number of factors that affect the real market. Previous research has focused on the fluctuation patterns and...

We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (complexity) is of order T 2, where T is the length of the time series. Our algorithm allows calculation speed of order T log2 T . For moderate and large...