Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

bugfix FIGARCH(1, d, 1) formula in the function description #759

Open
wants to merge 1 commit into
base: main
Choose a base branch
from

Conversation

pavelkrotkov
Copy link

E.g. in the original paper of Baililie et al. / Journal of Econometrics 74 (1996) 3-30 at the top o p.14 in the table caption:

$\sigma_t^2 = \omega + [1 - \beta L - (1 - \phi L)(1 - L)^d] R_t^2 + \beta \sigma_{t-1}^2$

so $\phi(L)=1-\phi L$ for first order model.

In ARCH($\infty$) form:

$\sigma_t^2 = (1 - \beta(L))^{-1} \omega + \lambda(L) R_t^2$

where

$\lambda(L) = (1 - (1 - \beta L)^{-1} (1 - \phi L)(1 - L)^d) = \sum_{k=0}^\infty \lambda_k L^k$

Having $1-\phi L$ is necessary for $\lambda_0$ to be 0, as is correctly written in the recursive formulas.

Copy link

codecov bot commented Nov 16, 2024

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.51%. Comparing base (8ff5a5e) to head (5e0c969).

Additional details and impacted files
@@           Coverage Diff           @@
##             main     #759   +/-   ##
=======================================
  Coverage   99.51%   99.51%           
=======================================
  Files          74       74           
  Lines       15634    15634           
  Branches     1274     1274           
=======================================
  Hits        15558    15558           
  Misses         51       51           
  Partials       25       25           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
None yet
Projects
None yet
Development

Successfully merging this pull request may close these issues.

1 participant