Cyclicality on CEE stock markets: Vector calculus approach

The subject of the investigation is cyclicality of capital markets in Central and Eastern Europe (CEE). The aim of the research is to verify the assumption about occurrence of cyclicality on CEE markets and to examine the nature of the occurring cyclicality. The analysis of the phenomenon of cyclicality uses a unique method based on the properties of vector calculus, proposed by Borawski & Nermend (2008). The idea of this method is to find a vector, that is the best approximation of a set of vectors. This set is created by dividing the financial time series into N contiguous, equinumerous parts, wherein the quotations contained in each of these parts are the coordinates of one vector from the set. The best approximating vector is a certain price formation of any shape. This formation is treated as a cyclical phenomenon - a certain repetitive formation of quotations, by means of which is possible to approximate (restore) a series of quotations. The purpose of the paper is also practical confirmation of utility of the vector-based methodology for cyclicality analysis of the real financial time series.

The research covers selected capital markets of CEE countries: Austria, the Czech Republic, Slovenia, Hungary and Poland, where the following exchanges are functioning: Vienna Stock Exchange (VSE), Praque Stock Exchange (PSE), Lubljana Stock Exchange (LJSE), Budapest Stock Exchange (BSE) and Warsaw Stock Exchange (WSE). With the exception of the VSE, all the remaining ones were created after the collapse of the communist regime in the early 1990s and their development is strongly related to the development of free market economies in the countries in which they operate.

Presented empirical studies use quotations of daily closing rates of the following exchange indexes - ATX, PX, SBITOP, BUX and WIG20. CECE index is a benchmark for the Central and Eastern Europe region. Not all selected indexes are the main indexes for analyzed exchanges. However, as indexes of the largest and the most liquid (so-called blue-chip) companies, cover a significant range of capitalization of broad market indexes and seem to be appropriate measures to study market behavior, including cyclicality.

The analysis of the cyclical phenomenon was carried out for the entire adopted time ranges and for business cycles defined for each of the markets. The time range of quotations used for research has been individually determined for each index and covers data from year 1995 till 2013.