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EN
The aim of the paper is to show that turning points detection can be treated as a problem of pattern recognition. In the paper there are presented the results of applying normal hidden Markov models to a number of survey balances. Beyond a classical two-scale assessment of business activity a slightly more fuzzy classification of states is considered. To determine periods of unclear or difficult to evaluate situation unobservable Markov chains with three and four states are introduced. The outputs of the Viterbi algorithm, i.e. the most likely paths of unobservable states of Markov chains, are a basis of the proposed classification. The comparison of these paths with the business cycle turning points dated by OECD is described. The results obtained for three- and four-state Markov chains are close to those established in the references time series and seem to improve the speed with which, especially downshifts, are signaled. Furthermore, these results are more favorable than outcomes provided by conventional two-state models. The method proposed in this paper seems to be a very effective tool to analyze results of business tendency surveys, in particular, when multistate Markov chains are considered. Moreover, proposed decompositions allow an easy comparison of two time series as far as turning point are concerned. In the paper survey balances are compared with ‘hard’ economic data such as sold manufacturing production. The results confirm the accuracy of assessment provided by survey respondents.
EN
The study of interdependence and the strength of the relationship between finan-cial time series is a quite important area in the financial literature. Hence we discussed the relationships between the main stock indices. The multivariate distributions of returns we modelled basing on copula functions approach. In order to obtain some dynamics of multi-variate distributions we applied the hidden Markov chain. Additionally we assumed that the transition matrix of the Markov chain was dependent on some exogenous variables. The study shows that the volatility indices VIX and VSTOXX which were taken as exogenous variables improved model efficiency.
EN
The aim of this article was the search of the dynamic of dependencies between WSE and other countries coming from Europe, America and Asia. The two-dimensional time series has been modeled by multidimensional GARCH process with dynamic condi-tional correlation or by Markov-switching Copula-GARCH model. The analysis confirms the claim that dependences between financial markets are higher in a period of crisis than during the prosperity time. The dynamic of relationships between Polish market and Euro-pean markets is bigger than the dynamic of relationships between Polish market and Ameri-can or Asian markets.
EN
In the paper the procedure, based on hidden Markov chains with conditional normal distributions and uses algorithms such as time series decompositions (STL), Baum-Welch algorithm, Viterbi algorithm and Monte Carlo simulations, is proposed to analyze data out of the business tendency survey conducted by the Research Institute for Economic Development, Warsaw School of Economics. There are considered three types of models, namely, with two-state, three-state and four-state Markov chains. Results of the procedure could be treated as an approximation of business cycle turning points. The performed analysis speaks in favor of multistate models. Due to, an increasing with the number of states, numerical instability, it is not obvious which model should be considered as the best one. For this purpose various optimization criteria are taken into consideration: information criteria (AIC, BIC) and the maximum-likelihood, but also frequency of obtaining a given set of parameters in the Monte Carlo simulations. The results are confronted with the turning points dated by OECD. The tested models were compared in terms of their effectiveness in detecting of turning points. The procedure is a step into automation of business cycle analysis based on results of business tendency surveys. Though this automation covers only some models from millions of possibilities, the procedure turns out to be extremely accurate in business cycle turning points identification, and the approach seems to be an excellent alternative for classical methods.
PL
Ocena zależności między szeregami czasowymi jest zagadnieniem, które jest często rozwiązywane za pomocą współczynnika korelacji Pearsona. Niestety, czasami wyniki mogą być bardzo mylące. W artykule przedstawiono alternatywną miarę badania zależności, opartą na ukrytych modelach Markowa oraz ścieżkach Viterbiego. Zaproponowana metoda nie jest uniwersalna, ale wydaje się dość dokładnie odzwierciedlać podobieństwo między szeregami czasowymi, eksponując okresy zbieżności i rozbieżności. Przydatność tej nowej miary została zweryfikowana na przykładach, jak również realnych danych makroekonomicznych. Zaletami tej metody są: słabe założenia stosowalności, łatwość interpretacji wyników, możliwość generalizacji i wysoka skuteczność w ocenie zależności różnych szeregów czasowych o charakterze ekonomicznym. Nie należy jej jednak trakto­wać jako substytutu korelacji Pearsona, a raczej jako uzupełniającą metodę pomiaru zależności.
EN
The assessment of dependence between time series is a common dilemma, which is often solved by the use of the Pearson’s correlation coefficient. Unfortunately, sometimes, the results may be highly misleading. In this paper, an alternative measure is presented. It is based on hidden Markov models and Viterbi paths. The proposed method is in no way universal but seems to provide quite an accurate image of the similarities between time series, by disclosing the periods of convergence and divergence. The usefulness of this new measure is verified by specially crafted examples and real‑life macroeconomic data. There are some definite advantages to this method: the weak assumptions of applicability, ease of interpretation of the results, possibility of easy generalization, and high effectiveness in assessing the dependence of different time series of an economic nature. It should not be treated as a substitute for the Pearson’s correlation, but rather as a complementary method of dependence measure.
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