Krzysztof Kompa, Ph.D., Department of Informatics, Warsaw University of Life Sciences, ul. Nowoursynowska 166, Warszawa, 02-787, Poland
Analysis of the periodicity within financial time series is very important for investment theory and applications. If periodicity occurs the EMH is not fulfilled and the investment strategies based on cyclicality are available. For periodicity research statistical methods, as well as financial and dynamic econometric models are usually applied, although the assumptions are often not satisfied.
The aim of this research is to present a concurrent method of time series periodicity analysis based on the vector space theory. We assume that k successive prices yj+1, yj+2, …, yj+k from T-length time series (k width price windows) are vector components in k-dimensional space, on the understanding that k belongs to the interval [2, T]. We take the advantage of the adjacent windows, i.e. j belongs to the interval [ 0, k*Ent(T/k)] >. Then, for each k-width window the explored time series is represented by the group Ent(T/k) of vectors in k-dimensional space. For each of that group the representative vector Tp is computed (Borawski’s algorithm). This vector de facto is a formation of the successive prices which repeats within the time series used for Tp-vector calculation. Borawski’s algorithm allows to find the optimal dimensions (i.e. number k) of vector space. The methodology is applied to the major stock indexes analysis at the Warsaw Stock Exchange (WSE) and NYSE.