2013/02/27 by Jozef Baruník, Barunik, Jozef, Jiří Kukačka +1
Economics, Econometrics and Finance · Environmental Science · #Complex Systems and Time Series Analysis #Market Dynamics and Volatility #Ecosystem dynamics and resilience
paper · pdf · doi:10.48550/arxiv.1302.7036
This paper develops a two-step estimation methodology, which allows us to\napply catastrophe theory to stock market returns with time-varying volatility\nand model stock market crashes. Utilizing high frequency data, we estimate the\ndaily realized volatility from the returns in the first step and use stochastic\ncusp catastrophe on data normalized by the estimated volatility in the second\nstep to study possible discontinuities in markets. We support our methodology\nby simulations where we also discuss the importance of stochastic noise and\nvolatility in deterministic cusp catastrophe model. The methodology is\nempirically tested on almost 27 years of U.S. stock market evolution covering\nseveral important recessions and crisis periods. Due to the very long sample\nperiod we also develop a rolling estimation approach and we find that while in\nthe first half of the period stock markets showed marks of bifurcations, in the\nsecond half catastrophe theory was not able to confirm this behavior. Results\nsuggest that the proposed methodology provides an important shift in\napplication of catastrophe theory to stock markets.\n