The Viterbi paths in an analysis of business cycle synchronization

In the paper we investigate possibility of using the Viterbi paths to analyze two-dimensional macroeconomic time series. We build a two-dimensional Gaussian Markov-switching model with a four-state hidden Markov chain. The model is tested with two pairs of monthly indexes of industrial production for: Poland vs. France, and Poland vs. Germany. The most likely sequence of states of the hidden Markov chain is found for each pair. We compare that sequence with analogous sequences determined for a one-dimensional model with a two-state hidden Markov chain. The results of the comparison suggests the four state Viterbi path provides more valuable information about business cycle synchronization between the two economies than two separate two-state Viterbi paths.