Fast change point analysis on the Hurst index of piecewise fractional Brownian motion

In this presentation, we introduce a new method for change point analysis on the Hurst index for a piecewise fractional Brownian motion. We first set the model and the statistical problem. The proposed method is a transposition of the FDpV (Filtered Derivative with p-value) method introduced for the detection of change points on the mean in Bertrand et al. (2011) to the case of changes on the Hurst index. The underlying statistics of the FDpV technology is a new statistic estimator for Hurst index, so-called Increment Bernoulli Statistic (IBS). Both FDpV and IBS are methods with linear time and memory complexity, with respect to the size of the series. Thus the resulting method for change point analysis on Hurst index reaches also a linear complexity

Identifying financial crises in real time

Following the thermodynamic formulation of multifractal measure that was shown to be capable of detecting large fluctuations at an early stage, here we propose a new index which permits us to distinguish events like financial crisis in real time . We calculate the partition function from where we obtain thermodynamic quantities analogous to free energy and specific heat. The index is defined as the normalized energy variation and it can be used to study the behavior of stochastic time series, such as financial market daily data. Famous financial market crashes - Black Thursday (1929), Black Monday (1987) and Subprime crisis (2008) - are identified with clear and robust results. The method is also applied to the market fluctuations of 2011. From these results it appears as if the apparent crisis of 2011 is of a different nature from the other three. We also show that the analysis has forecasting capabilities.Comment: 8 pages, 6 figure

Long-Range Dependence in Daily Interest Rate

We employ a number of parametric and non-parametric techniques to establish the existence of long-range dependence in daily interbank o er rates for four countries. We test for long memory using classical R=S analysis, variance-time plots and Lo's (1991) modi ed R=S statistic. In addition we estimate the fractional di erencing parameter using Whittle's (1951) maximum likelihood estimator and we shu e the data to destroy long and short memory in turn, and we repeat our non-parametric tests. From our non-parametric tests we And strong evidence of the presence of long memory in all four series independently of the chosen statistic. We nd evidence that supports the assertion of Willinger et al (1999) that Lo's statistic is biased towards non-rejection of the null hypothesis of no long-range dependence. The parametric estimation concurs with these results. Our results suggest that conventional tests for capital market integration and other similar hypotheses involving nominal interest rates should be treated with cautio