Parameter estimation for stable distributions with application to commodity futures log-returns
This paper explores the theory behind the rich and robust family of $ \alpha $-stable distributions to estimate parameters from financial asset log-returns data. We discuss four-parameter estimation methods including the quantiles, logarithmic moments method, maximum likelihood (ML), and the empiric...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2017-01-01
|
| Series: | Cogent Economics & Finance |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/23322039.2017.1318813 |
| _version_ | 1818415426169733120 |
|---|---|
| author | M. Kateregga S. Mataramvura D. Taylor |
| author_facet | M. Kateregga S. Mataramvura D. Taylor |
| author_sort | M. Kateregga |
| collection | DOAJ |
| description | This paper explores the theory behind the rich and robust family of $ \alpha $-stable distributions to estimate parameters from financial asset log-returns data. We discuss four-parameter estimation methods including the quantiles, logarithmic moments method, maximum likelihood (ML), and the empirical characteristics function (ECF) method. The contribution of the paper is two-fold: first, we discuss the above parametric approaches and investigate their performance through error analysis. Moreover, we argue that the ECF performs better than the ML over a wide range of shape parameter values, $ \alpha $ including values closest to 0 and 2 and that the ECF has a better convergence rate than the ML. Secondly, we compare the t location-scale distribution to the general stable distribution and show that the former fails to capture skewness which might exist in the data. This is observed through applying the ECF to commodity futures log-returns data to obtain the skewness parameter. |
| first_indexed | 2024-12-14T11:34:48Z |
| format | Article |
| id | doaj.art-264de8d1279d437b9426e4fc9110e28e |
| institution | Directory Open Access Journal |
| issn | 2332-2039 |
| language | English |
| last_indexed | 2024-12-14T11:34:48Z |
| publishDate | 2017-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Cogent Economics & Finance |
| spelling | doaj.art-264de8d1279d437b9426e4fc9110e28e2022-12-21T23:03:06ZengTaylor & Francis GroupCogent Economics & Finance2332-20392017-01-015110.1080/23322039.2017.13188131318813Parameter estimation for stable distributions with application to commodity futures log-returnsM. Kateregga0S. Mataramvura1D. Taylor2University of Cape TownUniversity of Cape TownUniversity of Cape TownThis paper explores the theory behind the rich and robust family of $ \alpha $-stable distributions to estimate parameters from financial asset log-returns data. We discuss four-parameter estimation methods including the quantiles, logarithmic moments method, maximum likelihood (ML), and the empirical characteristics function (ECF) method. The contribution of the paper is two-fold: first, we discuss the above parametric approaches and investigate their performance through error analysis. Moreover, we argue that the ECF performs better than the ML over a wide range of shape parameter values, $ \alpha $ including values closest to 0 and 2 and that the ECF has a better convergence rate than the ML. Secondly, we compare the t location-scale distribution to the general stable distribution and show that the former fails to capture skewness which might exist in the data. This is observed through applying the ECF to commodity futures log-returns data to obtain the skewness parameter.http://dx.doi.org/10.1080/23322039.2017.1318813stable distributionparameter estimationdensity estimation |
| spellingShingle | M. Kateregga S. Mataramvura D. Taylor Parameter estimation for stable distributions with application to commodity futures log-returns Cogent Economics & Finance stable distribution parameter estimation density estimation |
| title | Parameter estimation for stable distributions with application to commodity futures log-returns |
| title_full | Parameter estimation for stable distributions with application to commodity futures log-returns |
| title_fullStr | Parameter estimation for stable distributions with application to commodity futures log-returns |
| title_full_unstemmed | Parameter estimation for stable distributions with application to commodity futures log-returns |
| title_short | Parameter estimation for stable distributions with application to commodity futures log-returns |
| title_sort | parameter estimation for stable distributions with application to commodity futures log returns |
| topic | stable distribution parameter estimation density estimation |
| url | http://dx.doi.org/10.1080/23322039.2017.1318813 |
| work_keys_str_mv | AT mkateregga parameterestimationforstabledistributionswithapplicationtocommodityfutureslogreturns AT smataramvura parameterestimationforstabledistributionswithapplicationtocommodityfutureslogreturns AT dtaylor parameterestimationforstabledistributionswithapplicationtocommodityfutureslogreturns |