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[var_dmd, svd_intro, measurement_models] Correct math, add exercises - #1055

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tom_sept
Sep 15, 2026
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@jstac jstac commented Sep 12, 2026

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Revisions by @thomassargent30 to var_dmd.md, svd_intro.md and measurement_models.md, plus new bib entries (branch tom_sept, see Tom's email "tom_sept branch(es)"). Tom notes that the live versions of the DMD and VAR material contained substantive mathematical errors that this PR corrects.

var_dmd.md

  • Reframe DMD as a rank-$r$ VAR (principal components regression).
  • Replace the incorrect identity $A = \Phi \Lambda \Phi^+$ with the exact modal representation $A = \Phi \Lambda \Psi$, $\Psi = (W \Lambda)^{-1} U_r^\top$.
  • Add a state-space form, long-run responses, a simulated example, and three exercises.
  • Cite the published Sargent–Selvakumar–Yang (IER 2026) paper.

svd_intro.md

  • Fix the "not not" typo and several errors: four-subspaces code mislabeled $V^\top$, the Eckart–Young statement, reduced-SVD identities, PCA score dimensions and indices, and the polar decomposition.
  • Fix DecomAnalysis for tall matrices and use it.
  • Add two exercises bridging to var_dmd.

measurement_models.md

  • Use the innovation covariance $\Sigma_\eta$ (not the unconditional $R$) in the quasi-differenced Kalman filter.
  • Fix the bracket in the consumption rule and the shock timing.
  • Add an ordering-free Granger causality check, note the exact identity in filtered data, and add three exercises.

Other

  • _static/quant-econ.bib: 49 lines of new references.

Note: the branch is one commit behind main; should merge cleanly but CI will confirm.

🤖 Generated with Claude Code

https://claude.ai/code/session_01UZWhdWQnrKdbgHbyvX4UYs

var_dmd: reframe DMD as a rank-r VAR (principal components regression);
replace the incorrect identity A = Phi Lambda Phi^+ with the exact modal
representation A = Phi Lambda Psi, Psi = (W Lambda)^{-1} U_r^T; add a
state-space form, long-run responses, a simulated example, and three
exercises. Cite the published Sargent-Selvakumar-Yang (IER 2026) paper.

svd_intro: fix the "not not" typo and other errors (four-subspaces code
mislabeled V^T, Eckart-Young statement, reduced-SVD identities, PCA
score dimensions and indices, polar decomposition); fix DecomAnalysis
for tall matrices and use it; add two exercises bridging to var_dmd.

measurement_models: use the innovation covariance Sigma_eta (not the
unconditional R) in the quasi-differenced Kalman filter; fix the bracket
in the consumption rule and shock timing; add an ordering-free Granger
causality check, note the exact identity in filtered data, and add three
exercises.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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Commit: 051b9ba

📚 Changed Lectures


Build Info

jstac and others added 2 commits September 15, 2026 18:08
…ntouts, docstring timing, heading case

- measurement_models: print V2 eigenvalues in scientific notation so the
  tiny second eigenvalue and the third (= ε) are visible, as the text claims
- measurement_models: relabel the Friedman step in the meas_ex1 solution
  as the second claim; align steady_state_kalman docstring with the w_t
  timing convention
- svd_intro: sentence-case section headings per the style manual
- var_dmd: i.i.d. -> IID
- quant-econ.bib: add trailing newline

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
@jstac
jstac merged commit 63880c0 into main Sep 15, 2026
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@jstac
jstac deleted the tom_sept branch September 15, 2026 09:53
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2 participants