Extreme Value Theorem - Pareto Distribution
Posted: Tue Aug 07, 2012 7:48 am
Dear Sir/Madam,
Currently I am conducting research for my master thesis and I am struggling with EViews 7. My research is somewhat the same as: “Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach” from McNeil and Frey (2000). In the first part of my research I fit a GARCH (1,1) model to a historical return series by using pseudo maximum likelihood. Secondly, I calculate the residuals from the fitted model in EViews. So far so good. However, than I would like to apply extreme value theorem to the residuals. To be more specifically, I would like to apply the: “peaks over threshold approach” of the extreme value theorem. Meaning that a fixed high threshold value is chosen, it is assumed that the excess residuals over this threshold follow a generalized Pareto Distribution (GPD). Maximum likelihood should be used to fit the formula on page 8 of the attachment (the formula second formula on the page, immediately after formula eigth)
It would be of great help if you could help me with the proper programming language. I am not sure whether you are acquainted with Extreme Value Theorem. So, if I should give more information, please let me know!
Thanks you very much,
Alexander Vaartjes
Currently I am conducting research for my master thesis and I am struggling with EViews 7. My research is somewhat the same as: “Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach” from McNeil and Frey (2000). In the first part of my research I fit a GARCH (1,1) model to a historical return series by using pseudo maximum likelihood. Secondly, I calculate the residuals from the fitted model in EViews. So far so good. However, than I would like to apply extreme value theorem to the residuals. To be more specifically, I would like to apply the: “peaks over threshold approach” of the extreme value theorem. Meaning that a fixed high threshold value is chosen, it is assumed that the excess residuals over this threshold follow a generalized Pareto Distribution (GPD). Maximum likelihood should be used to fit the formula on page 8 of the attachment (the formula second formula on the page, immediately after formula eigth)
It would be of great help if you could help me with the proper programming language. I am not sure whether you are acquainted with Extreme Value Theorem. So, if I should give more information, please let me know!
Thanks you very much,
Alexander Vaartjes