SSA, PCA, TDPSC, ACFA: Useful combination of methods for analysis of short and nonstationary time series

Abstract

Singular spectrum analysis (SSA), principal component analysis (PCA), and autocorrelation function analysis (ACFA) are useful tools for extracting information from time series. But the combination of these methods and the time delay phase space construction (TDPSC) is not much used. In this paper we present the opportunities of this bundle of four methods for analysis of short and nonstationary time series. The basis of our analysis are time series for the piglet prices and production in Japan before and after the Japan government intervention in the agriculture sector aiming at stabilization of the agriculture prices after the oil crisis in 1974. As a comparison we analyse long stationary chaotic time series from the classical Lorenz system. We show that SSA, PCA and TDPSC perfectly recognize the dimension of the Lorenz system only on the basis of time series for one of its three variables. The bundle of four methods leads us to enough information to make the conclusion that the intervention of the Japan government in agriculture sector was very successful and leaded (i) to stabilization of prices; (ii) to a coupling between the prices and production cycles and (iii) to decreasing the dimension of the phase space of price and production fluctuations around the year trend thus making their dynamics more forecastable.