We propose a new method of tail analysis for data featuring a high degree of leptokurtosis. Heavy tails can typically be found in financial series, like for example, the stock returns or durations between arrivals of trades. In our framework, the shape of tails can be assessed by fitting some...

In certain cases the distribution of the normalized maximumof a sample can be better approximated by a sequence ofdifferent extreme value distributions than by the final one. Weshow that these cases are rather restricted and that the possibleimprovement is not spectacular.

Large data sets in finance with millions of observations have becomewidely available. Such data sets enable the construction of reliablesemi-parametric estimates of the risk associated with extreme pricemovements. Our approach is based on semi-parametric statisticalextreme value analysis, and...

We advocate the use of absolute moment ratio statistics in conjunctionwith standard variance ratio statistics in order to disentangle lineardependence, non-linear dependence, and leptokurtosis in financial timeseries. Both statistics are computed for multiple return horizonssimultaneously, and...

The techniques of exploratory data analysis include a resistant rule, based on a linear combination of quartiles, for identification of outliers. This paper shows that the substitution of the quartiles with the median leads to a better performance in the non-Gaussian case. The improvement occurs...

A new kind of even and odd nonlinear coherent states (EONLCSs) is introduced. Using the Pegg–Barnett formalism of phase operator we study the phase probability distributions of the new kind of EONLCSs. The numerical computation results show that the phase probability distributions for the new...

We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a ‘potential’ or ‘objective’ function. This allows us to rescale data from different assets (or sources) such that each data set then has similar statistical properties in...

We study the dynamical behavior of high-frequency data from the Korean Stock Price Index (KOSPI) using the movement of returns in Korean financial markets. The dynamical behavior of a binarized series of our models is not completely random. In addition, the conditional probability is numerically...