Additional metric added based on the quasi-likekilhood loss function (qlike).

[edjanga]

• closes #xxxx
• tests added / passed.
• code/documentation is well formatted.
• properly formatted commit message. See
  NumPy's guide.

Notes:

• It is essential that you add a test when making code changes. Tests are not
  needed for doc changes.
• When adding a new function, test values should usually be verified in another package (e.g., R/SAS/Stata).
• When fixing a bug, you must add a test that would produce the bug in main and
  then show that it is fixed with the new code.
• New code additions must be well formatted. Changes should pass flake8. If on Linux or OSX, you can
  verify you changes are well formatted by running

  git diff upstream/main -u -- "*.py" | flake8 --diff --isolated
  

  assuming flake8 is installed. This command is also available on Windows
  using the Windows System for Linux once flake8 is installed in the
  local Linux environment. While passing this test is not required, it is good practice and it help
  improve code quality in statsmodels.
• Docstring additions must render correctly, including escapes and LaTeX.

[josef-pkt]

something wrong here
Many unrelated changes, several look like they are reverting previous PRs and would reintroduce bugs or revert enhancements.

[josef-pkt]

Do you have a reference for this definition of quasi-likelihood?

[edjanga]

One can refer to the following paper for the definition of quasi-likelihood: https://doi.org/10.1093/jjfinec/nbab028 [https://oup.silverchair-cdn.com/oup/backfile/Content_public/Journal/jfec/PAP/10.1093_jjfinec_nbab028/1/m_nbab028f1.jpeg?Expires=1740164861&Signature=PlNdRdFE-UmYWlZpK6xDcX4Fi823-nIaA~yUJ5cLCYbzvLLUFuuQ5D8I~uk0nS6ekV3KYwcp0FEp~l3OoaEGr~4276sXy30LzICBlXTnCdv~z5mS29bXMkmKuI9LLQjycslG5Tf2BM0Kzna5jIMLuLI8wijWFtEOdhm52AIm-Dy2rFp6CqYDcS3j0rsXaKslXIjhBW0SOjEugMopRsoajJnlaZGR1saNo77oNBa3CoksxNYEzjoVSXcYOUoqX1WBkY6HBx7lSVWr41ci8W4~6Uu2XNXrmeMXvRPRCOHTQUH8GPPLz49knN-NiJq~QZ~jkgKTLvRgUP5bEObhRtKvCw__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA]<https://doi.org/10.1093/jjfinec/nbab028> Increasing the information content of realized volatility forecasts*<https://doi.org/10.1093/jjfinec/nbab028> Abstract. Assuming N available calendar days, each with M intraday returns, the realized volatility literature suggests creating N end-of-day estimators by summ doi.org

…

________________________________ From: Josef Perktold ***@***.***> Sent: 03 March 2023 18:53 To: statsmodels/statsmodels ***@***.***> Cc: Emmanuel Djanga ***@***.***>; Author ***@***.***> Subject: Re: [statsmodels/statsmodels] Additional metric added based on the quasi-likekilhood loss function (qlike). (PR #8715) Do you have a reference for this definition of quasi-likelihood? — Reply to this email directly, view it on GitHub<#8715 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ANZ5GCO5GCZEY2E5LJ2GD63W2I4Y7ANCNFSM6AAAAAAVO5CAS4>. You are receiving this because you authored the thread.Message ID: ***@***.***>

[edjanga]

I tried to fork the latest code from GitHub. I shall give it another try then.

…

________________________________ From: Josef Perktold ***@***.***> Sent: 03 March 2023 18:49 To: statsmodels/statsmodels ***@***.***> Cc: Emmanuel Djanga ***@***.***>; Author ***@***.***> Subject: Re: [statsmodels/statsmodels] Additional metric added based on the quasi-likekilhood loss function (qlike). (PR #8715) something wrong here Many unrelated changes, several look like they are reverting previous PRs and would reintroduce bugs or revert enhancements. — Reply to this email directly, view it on GitHub<#8715 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ANZ5GCJLD3WZUXJ4ONHRXJDW2I4NDANCNFSM6AAAAAAVO5CAS4>. You are receiving this because you authored the thread.Message ID: ***@***.***>

[josef-pkt]

The article uses qlike for volatility forecast and not for mean. equ. 16b

I'm not sure we can use the same definition.
AFAICS, this does not correspond what is usually called quasi-likelihood in GLM, including gaussian.

[josef-pkt]

the qlike looks more like the quasi-likelihood for the gamma family, which would be the distribution of the variance if the underlying random variable is gaussian.

Also it looks like the definition differs from equ 35 in
Patton, Andrew J., and Kevin Sheppard. “Evaluating Volatility and Correlation Forecasts.” In Handbook of Financial Time Series, edited by Thomas Mikosch, Jens-Peter Kreiß, Richard A. Davis, and Torben Gustav Andersen, 801–38. Berlin, Heidelberg: Springer, 2009. https://doi.org/10.1007/978-3-540-71297-8_36.

Also if it's used for forecasting, then it should be an out of sample evaluation measure.

I'm just skimming a few things

@bashtage any comment here