MODELLING TRENDS AND CYCLES IN MACRONOMIC TIME SERIES

The aim of the article is to look for the estimation of the long-term component by the Hodrick-Presco" filter and after getting residual series to estimate the cyclical component by means of ARMA(p,q) model with complex roots. The method is applied to the quarterly data of the consumer price index (previous year 100 %) in Slovakia and Poland during the period from the first quarter 1998 till the fourth quarter 2005, having sample of 32 observations. The aim of the analysis is to look for how many cycles is covering this period and what is their length. Comparison of two countries could give us picture whether process to harmonize price policy of both countries before and after entering the European unioin is similar or not. It was showen that during the analysed period both series of CPI contain two cycles of the different lenghts. In Slovakia there are shorter cycles of 8 and 10 quarters, first starting at Q1/2001 and the second ending at Q3/2004. In Poland the first cycle has length of 16 quarters starting at Q2/1998 and the second cycle of 13 quarters is ending at Q3/2005.