Common stochastic features and their economic interpretation
DOI:
https://doi.org/10.26485/SPE/2023/126/6Keywords:
cointegration, co-autocorrelation, equilibrium and adjustment mechanisms, shocks.Abstract
Background: Cointegration analysis has been part of the research literature for almost 40 years. However, other common features that cause disequilibrium of economic categories have so far attracted less attention. This leads to an interesting question about the degree to which studies in the alternative fields are substitutive or complementary, and what conditions must be met in order to undertake the appropriate analysis (cointegration, co-cyclical, co-autocorrelation or other, less frequently discussed co-behaviors) is purposeful.
Research purpose: The purpose of this paper is the comparison of different types of common stochastic behaviors. The type of common factors and the resulting analysis of movements that should be chosen, naturally depends on the time horizon, which can be long, medium, or short, but a reliable study should not ignore any of these perspectives. This study tries to demonstrate that the key role in this choice is played by the reduced rank of the most important matrices that occur in the appropriate VAR model representations or the isomorphic representations thereof. Another research goal was to show that the above-mentioned analyses of stochastic co-movements are largely complementary.
Methods: Multidimensional dynamic econometrics based on VAR models was selected for the study because it contains tools that enable the different methods of analyzing common behaviors to be analyzed. Possible combinations of full and reduced cointegrating matrix ranks and the medium- and long-run relationships matrices were considered and economically interpreted. Relationships between the matrices have been identified, and the iterative mechanism that causes the system to return to equilibrium is described.
Conclusions: The study confirms that the analyzed investigations on common dominant components were essentially complementary. Extending the analysis to seasonal cointegration or deterministic co-trending would allow substitutive elements to be revealed. For example, a cointegration analysis using a relatively short time horizon is an alternative to co-trending (the stochastic trend expires only in a very long perspective), and an analysis that considers a more integrated process could be an alternative to co-deterministic cyclical analysis.
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