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Our macroeconomics research has focused on an extensive evaluation of the nature of financial markets and its interconnections with macroeconomic dynamics and stability. Most of our early research investigated the efficiency of financial markets. This analysis is far from simple. It needs both an appropriate definition of market efficiency and appropriate statistical tools to address this question. Our ambition has been to show that standard tools employed to analyze the efficiency have their limits and therefore, we employed more flexible modeling frameworks. A new measure of the capital market efficiency based on distance from the efficient market state was introduced. Using short-term and long-term memory, entropy measures and measures of fractal dimension, we are able to rank the capital markets according to their efficiency. Compared to the mainstream of the efficient market hypothesis, the fractal market hypothesis considers the financial markets as complex systems consisting of many heterogeneous agents, which are distinguishable mainly with respect to their investment horizons. The fractal capital market hypothesis and its focus on liquidity and investment horizons give reasonable predictions about the dynamics of the financial markets during turbulences such as the Global Financial Crisis of the late 2000s.

Stochastic CUSP Catastrophe Model

The first attempt to fit a stochastic cusp catastrophe model to stock market data was realized through our efforts. The cusp catastrophe model explains the crash of stock exchanges much better than other models. Using the data of U.S. stock markets we demonstrated that the crash of October 19, 1987, may be better explained by the cusp catastrophe theory, which is not, unfortunately, true for the crash of September 11, 2001. With the help of sentiment measures, such as the index put/call options ratio and trading volume (the former models the chartists, the latter the fundamentalists), we have found that the 1987 returns are bimodal, and the cusp catastrophe model fits these data better than alternative models. Therefore we may as well say that internal forces have led the crash.

A reconstruction of the neoclassical theory of inflation

Our target has also been to reconstruct the neoclassical theory of inflation and obtain a model that would generate non-periodical oscillations of price level and be considered a realistic approximation of an actual price level evolution. We started our analysis with the Fisher-type equation of exchange. The assumption on non-variability of the velocity of money circulation parameter is relaxed in favor of dependence on expected inflation. The resulting model of inflation is a two-equation model where price evolution depends on production dynamics, which is assumed to be an exogenous variable. After that, the two-equation model was reformulated as an autonomous system where production dynamics is determined by a Kaldor-type model. By adding the Kaldor model to the two-equation system, the four-equation model was created. Both our models are able to generate more complex dynamics, i.e., non-linear cycles and chaos with the expected inflation playing an important role in money-demand determination. The stability such systems was tested and Lyapunov exponents were computed using appropriate numerical methods. Friedman suggested that money demand decreases as expected inflation increases. He also interpreted the decline of money demand as in the traditional Fisher-type theory. In our construction, the money demand as a non-linear function depending upon both the expected inflation and logistic function has been used. Ramsay growth model was also extended in these directions.

Long Memory Estimation

The generalized Hurst exponent approach makes it possible to study the multi-scaling behavior of different financial time series. This approach is robust and powerful in detecting different types of multi-scaling. A puzzling phenomenon was observed: an apparent increase in the multi-fractality is measured in time series generated from shuffled returns, where all time correlations are destroyed, while the return distributions are conserved. This effect is robust and it is reproduced in several real financial data sets including stock market indices, exchange rates and interest rates. In order to understand the origin of this effect we investigate different simulated time series by means of the Markov switching multi-fractal model, autoregressive fractionally integrated moving average processes with stable innovations, fractional Brownian motion and Levy flights. Overall, we conclude that the multi-fractality observed in financial time series is mainly a consequence of the fat-tailed distribution characteristics of the returns and time correlations having the effect on a decrease of the measured multi-fractality.

DSGE Models and Fiscal Policy

Main ambition is our formation of the DGE or DSGE model that would be included also indicators of capital markets (i.e. stock index and so on). Empirical models with macroeconomic variables and indicators of capital markets are developed. The proposed form of dependence was already analysed by arbitrary pricing models. We consider also application of VAR models, ARMAX, or nonlinear approaches as NARMAX. After empirical verification of dependencies, the construction of DGE or DSGE model with financial market variables should be followed. The model has made use of achieved results from other parts of the research in the field of behavioural finance. As for the linkages between the macroeconomic and financial sectors, we examined how the Czech fiscal and monetary policies affect the domestic economy. We find that both types of these policies matter for the macroeconomic fluctuations, with the fiscal shocks being more unpredictable. The results for the effects of monetary policy largely confirm the findings for any other developed countries. The monetary policy affects prices and output with a lag and its effect disappears after some time. The empirical analysis of the fiscal policy effects on economic growth augmented for potential nonlinearities stemming from different functioning of financial markets under financial stress proves that the fiscal multipliers are higher in downturns than in expansions. Furthermore the differences were highest during the Great Recession. These results support the view that strong and internationally coordinated responses in the Great Recession averted a sharp drop in GDP that could have happened otherwise.



Selected publications

  • Baruník Jozef, Kukačka Jiří :  Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility, Quantitative Finance, forthcoming (2015)
  • Franta M., Baruník Jozef, Horváth Roman, Šmídková K. :  Are Bayesian Fan Charts Useful? The Effect of Zero Lower Bound and Evaluation of Financial Stability Stress Tests , International Journal of Central Banking vol.10, 1 (2014), p. 159-187
  • Horváth Roman, Baxa Jaromír, Vašíček B.:  How Does Monetary Policy Change? Evidence on Inflation Targeting Countries , Macroeconomic Dynamics vol.18, 3 (2014), p. 593-630
  • Krištoufek Ladislav, Vošvrda Miloslav : Measuring capital market efficiency: long-term memory, fractal dimension and approximate entropy , European Physical Journal B vol.87, 7 (2014)
  • Baxa Jaromír, Horváth R., Vašíček B.:  Time-varying monetary-policy rules and financial stress: Does financial instability matter for monetary policy? , Journal of Financial Stability vol.9, 1 (2013), p. 117-138
  • Horváth Roman, Petrovski D.:  International stock market integration: Central and South Eastern Europe compared , Economic Systems vol.37, 1 (2013), p. 81-91
  • Kodera Jan, Van Tran Q., Vošvrda Miloslav : Complex Price Dynamics in the Modified Kaldorian Model , Prague Economic Papers vol.22, 3 (2013), p. 358-384
  • Krištoufek Ladislav, Vošvrda Miloslav : Measuring capital market efficiency: Global and local correlations structure , Physica. A : Statistical Mechanics and its Applications vol.392, 1 (2013), p. 184-193 [2013]
  • Sladký K.: Some Remarks on Stochastic Versions of the Ramsey Growth Model, Bulletin of the Czech Econometric Society vol.19, 29 (2012), p. 139-152
  • Barunik, J., Vosvrda, M. (2009): Can a stochastic cusp catastrophe model explain stock market crashes? Journal of Economic Dynamics and Control 33, pp. 1824-1836  
  • Barunik J., Vacha L., Vosvrda M. (2009): Smart predictors in the heterogeneous agent model, Journal of Economic Interaction and Coordination, vol. 4(2), pp. 163-172, Springer 


Grants and projects

  • Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents
    Miloslav Vošvrda and Jozef Baruník, grant No. FP7-SSH-2013-2 of the European Union's Seventh Framework Programme.
  • DYME - Dynamical models in Economics
    Miloslav Vošvrda, grant No. GAP402/12/G097
  • New Approach to Monitoring and Forecasting Financial Markets
    Miloslav Vošvrda, grant No. 402/09/0965 of the Czech Science Foundation.
  • of the Czech Science Foundation.
  • Nonlinear  Dynamic in Monetary and Financial Economics. Theory and Empirical Models.
    Jan Kodera,  Miloslav Vošvrda, grant No. 402/09/H045 of the Czech Science Foundation, 2009-2011
  • Nonlinear  Dynamic and Stochastics of Economics Systems: Equillibria, Stability, and Bifurcations 
    Jan Kodera, grant No. 402/06/0990 of the Czech Science Foundation,  2006-2008
  • Nonlinear Economic Dynamics
    Miloslav Vošvrda, grant No. 402/03/H057 of the Czech Science Foundation, with University of Economics and Charles University in Prague, 2003-2006. 
  • Economic Dynamics: Analytical and Computational Treatment of Macroeconomic Models
    Karel Sladký, grant No. A 7075202 of the Grant Agency of the Czech Academy of Science, 2002-2006.
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