We closely examine and compare two promising techniques helpful in es� ma� ng the moment an asset bubble bursts. Namely, the Log-Periodic Power Law model and Generalized Hurst Exponent approaches are considered. Sequen� al LPPL fi � ng to empirical fi nancial � me series exhibi� ng evident bubble behavior is presented. Es� ma� ng the cri� cal crash-� me works sa� sfactorily well also in the case of GHE, when substan� al "decorrela� on" prior to the event is visible. An extensive simula� on study carried out on empirical data: stock indices and commodi� es, confi rms very good performance of the two approaches.

No abstract

We investigate several promising algorithms, proposed in literature, devised to detect sudden changes (structural breaks) in the volatility of financial time series. Comparative study of three techniques: ICSS, NPCPM and Cheng's algorithm is carried out via numerical simulation in the case of simulated T-GARCH models and two real series, namely German and US stock indices. Simulations show that the NPCPM algorithm is superior to ICSS because is not over-sensitive either to heavy tails of market returns or to their serial dependence. Some signals generated by ICSS are falsely classified as structural breaks in volatility, while Cheng's technique works well only when a single break occurs. JEL classification: C19, C22, C58. Abstract 33Volatility is one of the all-important terms in financial econometrics, where dynamics of asset price processes, currency valuations and various economic data are the subject of research. Even though its multiple quantitative definitions are proposed, volatility can be viewed as a measure of the unpredictability of a given time series' (like asset returns) behavior within an analyzed time span. It has been an object of intensive research for several decades now, as its proper understanding and description provides a cutting edge in trading on stock exchanges, portfolio and risk management, stress testing, etc. Formally, financial volatility can be a parameter (either constant or another stochastic process itself) present in the model driving the given price dynamics, eg. σ in Geometric Brownian Motion. The crucial role of this parameter in derivatives pricing emerges in the celebrated

We reconsider the problem of the power (also called shape) parameter estimation within symmetric, zero-mean, unit-variance one-parameter Generalized Error Distribution family. Focusing on moment estimators for the parameter in question, through extensive Monte Carlo simulations we analyze the probability of non-existence of moment estimators for small and moderate samples, depending on the shape parameter value and the sample size. We consider a nonparametric bootstrap approach and prove its consistency. However, despite its established asymptotics, bootstrap does not substantially improve the statistical inference based on moment estimators once they fall into the non-existence area in case of small and moderate sample sizes.