| Abstract [eng] |
To estimate the roughness of the sample function the methodology introdused in Norvaiša and Salopek (2002) was applied. The roughness is defined as p-variation index of the sample function graph. Methodology is based on linear regression of the oscilation index. This master thesis tests the assumptions of linear regression residuals and constructs estimator which fulfill these assumptions. The model was used for the generated α-stable process and fractional Brownian motion. Conclusions are generalized using Monte-Carlo procedure. The confidence intervals for the p-variation index was constructed making assumption that the process is the realisation of -stable or fractional Brownian motion. The p-variation index was estimated for the „Vallourec” stock price data, sampled at irregular time. In addidion the variability in time of p-variation index was studied for different segments of intervals. |
