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The normality of financial data after an extraction of jumps in the jump-diffusion model

100%
Gardoń A.
Mathematical Economics
|
2011
|
issue 7 (14)
93-106
EN
When modelling financial data the jump-diffusion processes, driven by Wiener (W) and Poisson (N) processes, gain increasing importance. On the one hand, they explain better than the Itô diffusion the heavy tails of distributions of percentage changes of stock prices; on the other hand, unlike for example α-stable processes, they are based on the well developed mathematical tools for the Wiener and Poisson processes. After the identification of the jump times, e.g. by means of one of the so-called threshold methods, which are not linked with the continuous part of the model, the parameters from the continuous terms may be estimated similarly as for the Itô diffusion. But it is not obvious if the financial data after an extraction of jumps are already normally distributed. Therefore results of several normality tests will be presented here for chosen data from the Polish stock exchange market.
2

Rozkład statystyki t-studenta przy danej wariancji z próby o rozkładzie normalnym

100%
Gardoń A.
Didactics of Mathematics
|
2011
|
issue 8 (12)
17-30
EN
It is not so easy to lecture on higher mathematics for economy students. Advanced notions must be often presented for people without an appropriate theoretical background, which forces the teacher to simplify. Unfortunately, the praxis shows that the frontier between a simplification and a factual error is often very subtle and it happens this frontier is sometimes crossed. Such a situation occurs just in the case of the problem, which will be described in this paper. It is a known fact that the so called Student’s T statistics from a normal distributed sample is t-Student distributed, without any doubt. But in handbooks for economy students several authors try to use this statistics for exercises with mathematical tables of the t-Student distribution, ordering a calculation of the probability that the sample average will belong to the given interval, in the case when the theoretical variance is unknown but the sample variance has been calculated. Unfortunately, such a situation has nothing to do with the t-Student distribution and this error is systematically copied in successive handbooks.
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