Modelling with parameter mixture copulas
Interactive Supplement CD-ROM
hank you for your interest in my thesis. This CD-ROM is a collection of supplementary material relating to my thesis, titled Modelling with parameter mixture copulas. This thesis was written in 2006 at the University of Sydney as a component of the Bachlor of Commerce (Honours) program.
The supplementary material is divided into the following parts:
Click on each link above to see the detailed list, along with descriptions of each item, and instructions on opening and reading each part. I hope you enjoy this material as much as I have enjoyed writing this thesis. If you would like to contact me, please click here.
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Thesis
This thesis was written using Scientific Workplace. The thesis is available as a single PDF file, and also in individual PDFs by chapter for convenient reading and/or transferring. Note that Adobe Acrobat Reader or another compatible program is required to open PDF files. The Adobe Acrobat Reader is available to download for free at: Get Adobe Reader.
Single file:
Modelling with parameter mixture copulas
PDF 2204 KB
By chapter [browse]:
Acknowledgements
PDF 12 KBAbstract
PDF 12 KB
Introduction
PDF 70 KB
Copulas and mixture copulas [show/hide
details]
PDF 372 KB
Copulas
Sklar's theorem
Families of Copulas
Dependence Coverage
Modelling using copulas
Parameter-mixing
Parameter-mixing applied to copulas
Properties of mixture copulas
[show/hide details]
PDF 237 KB
Overview
Example of mixture copulas
Equivalent functional form
Identification
Dependence measure
Dependence structures covered
Informative mixing
Simulation [show/hide
details]
PDF 120 KB
Overview
Simulation algorithms
Estimation
Comparing results from mixture copulas with parent copulas
Comparing results at different dependence levels
Application [show/hide
details]
PDF 1653 KB
Overview
NBA Data
Estimation
Estimated marginal distributions
Comparing mixture copulas with parent copulas
Effect of partitioning
Conclusion [show/hide
details]
PDF 62 KB
Further research
Conclusion
Note on appendices
Bibliography
PDF 62 KB
Presentation
Modelling with parameter mixture copulas - Thesis presentation Microsoft Powerpoint Presentation 2840 KB
Thesis presentation as presented to the Discipline of Econometrics and Business Statistics, 6 Oct 2006
Data
The following data sets are used in the thesis. Note that Microsoft Excel is required to open Excel files (extension .xls). A text editor or spreadsheet program, such as Microsoft Excel, is required to open CSV files (Comma Separated Values; extension .csv).
Raw data in excel format
Data in csv format
Mathematica codes and results
Computation for this thesis was, for the most part, conducted using Mathematica. Note that Mathematica is required to open Mathematica Notebook files (extension .nb). Note also that some of these notebooks require mathStatica, the add-on to Mathematica. For more information on Mathematica and mathStatica see http://www.wolfram.com/products/mathematica/index.html and http://www.mathstatica.com/ respectively.
Simulations
Application
Miscellaenous
Graphics
The following graphics were used in writing this thesis. The file types of each graphic is as noted. Jpeg and Gif files can be viewed in standard web browsers. However, graphics are best viewed at original size. Animated gifs may not display correctly when viewed inside web browser. Choose "Browse" to view these files in a graphics program.
3Dplots.jpg Jpeg 608 KB; 964 x
794
3D plots of several
copulas, illustrating the W, M, and Π copulas, and one example of the
AMH family.
animation2.gif
Gif 323 KB; 408 x
321
3D Animation of AMH
copula as parameter changes.
animation3.gif
Gif 274 KB; 408 x
321
3D Animation of GB
copula as parameter changes.
contours.jpg Jpeg 1090 KB; 1134 x 1757
Contour plots of a series of AMH
copulas, and a series of Beta-mixture AMH copulas.
contours_shade.jpg
Jpeg 1122 KB; 1134 x 1757
The same
contour plots, with shading.
nba_histo.jpg Jpeg 650 KB 4017 x 3367
Histograms and scatterplot of the
NBA data.
nba_histo_simonoff.jpg
Jpeg 1722 KB 4001 x 3341
Histograms and scatterplot of the
NBA data, with Simonoff's dataset highlighted.
2by2marginals.jpg Jpeg 870 KB 3307 x 2244
Marginal frequency polygons and
fitted marginal distributions for each partition.
3by2marginals.jpg Jpeg 225 KB 800 x 950
Marginal frequency polygons and
fitted marginal distribution for the whole NBA dataset, and each
partition.