Stable Distributions



1.6 Financial applications of stable laws

19


Figure 1.6: Stable (cyan) and Gaussian (dashed red) fits to the DJIA returns
(black circles) empirical cdf from the period February 2, 1987 -
December 29, 1994. Right panel is a magnification of the left tail
fit on a double logarithmic scale clearly showing the superiority of
the 1.64-stable law.

θ STFstab06.xpl


Stable, Gaussian, and empirical left tails


puts more weight to the differences in the tails of the distributions. Although
no asymptotic results are known for the stable laws, approximate
p-values for
these goodness-of-fit tests can be obtained via the Monte Carlo technique.
First the parameter vector is estimated for a given sample of size
n, yielding
θ, and the test statistics is calculated assuming that the sample is distributed
according to
F (x; θ), returning a value of d. Next, a sample of size n of F (x; θ)-
distributed variates is generated. The parameter vector is estimated for this
simulated sample, yielding
θ1, and the test statistics is calculated assuming that
the sample is distributed according to
F (x; θ1). The simulation is repeated as
many times as required to achieve a certain level of accuracy. The estimate of
the
p-value is obtained as the proportion of times that the test quantity is at
least as large as
d.

For the α-stable fit of the DJIA returns the values of the Anderson-Darling and
Kolmogorov statistics are 0.6441 and 0.5583, respectively. The corresponding
approximate
p-values based on 1000 simulated samples are 0.02 and 0.5 allowing



More intriguing information

1. Competition In or For the Field: Which is Better
2. The name is absent
3. Distortions in a multi-level co-financing system: the case of the agri-environmental programme of Saxony-Anhalt
4. Investment and Interest Rate Policy in the Open Economy
5. A MARKOVIAN APPROXIMATED SOLUTION TO A PORTFOLIO MANAGEMENT PROBLEM
6. Automatic Dream Sentiment Analysis
7. The Cost of Food Safety Technologies in the Meat and Poultry Industries.
8. Estimating the Technology of Cognitive and Noncognitive Skill Formation
9. Critical Race Theory and Education: Racism and antiracism in educational theory and praxis David Gillborn*
10. Tax Increment Financing for Optimal Open Space Preservation: an Economic Inquiry
11. Handling the measurement error problem by means of panel data: Moment methods applied on firm data
12. The name is absent
13. The name is absent
14. APPLYING BIOSOLIDS: ISSUES FOR VIRGINIA AGRICULTURE
15. Bidding for Envy-Freeness: A Procedural Approach to n-Player Fair Division Problems
16. Reconsidering the value of pupil attitudes to studying post-16: a caution for Paul Croll
17. The name is absent
18. Evolutionary Clustering in Indonesian Ethnic Textile Motifs
19. Can a Robot Hear Music? Can a Robot Dance? Can a Robot Tell What it Knows or Intends to Do? Can it Feel Pride or Shame in Company?
20. The name is absent