Linear algebra is without a doubt a fundamental tool to deal with empirical economic problems. The goal of this paper is to use some of these techniques to treat business cycles. To do that, we present the classic ordinary least square approach to estime the coefficients of a detrended time...

In this short paper I would like to present a rigorous mathematical and yet heuristic description of modelling the economic cycles. The idea behind the cycles is that its dynamics could be decomposed into oscillation of two wave functions with low frequency (long-term cycle) and high frequency...