English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse
  1. Start / 
  2. Item Summary

Item

ITEM ACTIONSEXPORT
Add to Basket
  Local TagsRelease HistoryDetailsSummary

Released
Journal Article

Autoregressive processes with exponentially decaying probability distribution functions: Applications to daily variations of a stock market index

MPS-Authors
/persons/resource/persons184864

Porto,  M.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

/persons/resource/persons184895

Roman,  H. E.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available
Citation

Porto, M., & Roman, H. E. (2002). Autoregressive processes with exponentially decaying probability distribution functions: Applications to daily variations of a stock market index. Physical Review E, 65(4): 046149. Retrieved from http://ojps.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLEEE8000065000004046149000001&idtype=cvips&gifs=yes.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-37CC-7
Abstract
We consider autoregressive conditional heteroskedasticity (ARCH) processes in which the variance sigma(y)(2) depends linearly on the absolute value of the random variable y as sigma(y)(2)=a+b\y\. While for the standard model, where sigma(y)(2)=a+by(2), the corresponding probability distribution function (PDF) P(y) decays as a power law for \y\-->infinity, in the linear case it decays exponentially as P(y)similar toexp(-alpha\y\), with alpha=2/b. We extend these results to the more general case sigma(y)(2)=a+b\y\(q), with 0<q<2. We find stretched exponential decay for 1<q<2 and stretched Gaussian behavior for 0<q<1. As an application, we consider the case q=1 as our starting scheme for modeling the PDF of daily (logarithmic) variations in the Dow Jones stock market index. When the history of the ARCH process is taken into account, the resulting PDF becomes a stretched exponential even for q=1, with a stretched exponent beta=2/3, in a much better agreement with the empirical data.