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Merge remote-tracking branch 'origin/main' into update_business_cycle
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‎.github/dependabot.yml‎

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# https://docs.github.com/code-security/dependabot/dependabot-version-updates/configuration-options-for-the-dependabot.yml-file
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version: 2
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enable-beta-ecosystems: true
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updates:
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- package-ecosystem: github-actions
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directory: /
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commit-message:
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prefix: ⬆️
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schedule:
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interval: weekly
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- package-ecosystem: "conda"
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directory: "/"
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commit-message:
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prefix: ⬆️
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schedule:
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interval: "weekly"
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ignore:
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- dependency-name: "jupyter-book"
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versions: [">=2.0"]
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- dependency-name: "python"
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# Python version should be constrained by the anaconda distribution version

‎.github/workflows/cache.yml‎

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runs-on: ubuntu-latest
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steps:
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- name: Checkout
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uses: actions/checkout@v4
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uses: actions/checkout@v6
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with:
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fetch-depth: 0
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- name: Setup Anaconda
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uses: conda-incubator/setup-miniconda@v3
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uses: conda-incubator/setup-miniconda@v4
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with:
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auto-update-conda: true
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auto-activate-base: true
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run: |
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jb build lectures --path-output ./ -W --keep-going
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- name: Upload Execution Reports (HTML)
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uses: actions/upload-artifact@v4
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uses: actions/upload-artifact@v7
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if: failure()
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with:
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name: execution-reports
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path: _build/html/reports
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- name: Upload "_build" folder (cache)
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uses: actions/upload-artifact@v4
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uses: actions/upload-artifact@v7
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with:
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name: build-cache
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path: _build

‎.github/workflows/ci.yml‎

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runs-on: ubuntu-latest
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steps:
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- name: Checkout
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uses: actions/checkout@v4
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uses: actions/checkout@v6
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with:
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fetch-depth: 0
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- name: Setup Anaconda
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uses: conda-incubator/setup-miniconda@v3
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uses: conda-incubator/setup-miniconda@v4
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with:
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auto-update-conda: true
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auto-activate-base: true
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shell: bash -l {0}
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run: pip list
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- name: Download "build" folder (cache)
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uses: dawidd6/action-download-artifact@v11
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uses: dawidd6/action-download-artifact@v21
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with:
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workflow: cache.yml
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branch: main
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mkdir -p _build/html/_pdf
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cp -u _build/latex/*.pdf _build/html/_pdf
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- name: Upload Execution Reports (LaTeX)
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uses: actions/upload-artifact@v4
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uses: actions/upload-artifact@v7
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if: failure()
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with:
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name: execution-reports
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rm -r _build/.doctrees
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jb build lectures --path-output ./ -nW --keep-going
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- name: Upload Execution Reports (HTML)
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uses: actions/upload-artifact@v4
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uses: actions/upload-artifact@v7
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if: failure()
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with:
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name: execution-reports

‎.github/workflows/collab.yml‎

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container:
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image: us-docker.pkg.dev/colab-images/public/runtime:latest
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steps:
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- uses: actions/checkout@v4
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- uses: actions/checkout@v6
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with:
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ref: ${{ github.event.pull_request.head.sha }}
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- name: Check for dockerenv file
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shell: bash -l {0}
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run: pip list
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- name: Download "build" folder (cache)
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uses: dawidd6/action-download-artifact@v11
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uses: dawidd6/action-download-artifact@v21
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with:
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workflow: cache.yml
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branch: main
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- name: Install Build Software
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shell: bash -l {0}
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run: |
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pip install jupyter-book==0.15.1 docutils==0.17.1 quantecon-book-theme==0.7.2 sphinx-tojupyter==0.3.0 sphinxext-rediraffe==0.2.7 sphinx-exercise==0.4.1 sphinxcontrib-youtube==1.1.0 sphinx-togglebutton==0.3.1 arviz==0.13.0 sphinx_proof==0.2.0 sphinx_reredirects==0.1.3
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pip install jupyter-book==1.0.4post1 quantecon-book-theme==0.20.2 sphinx-tojupyter==0.6.0 sphinxext-rediraffe==0.3.0 sphinx-exercise==1.2.1 sphinxcontrib-youtube==1.4.1 sphinx-togglebutton==0.4.5 sphinx_proof==0.4.0 sphinx_reredirects==1.1.0
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# Build of HTML (Execution Testing)
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- name: Build HTML
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shell: bash -l {0}
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run: |
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jb build lectures --path-output ./ -n -W --keep-going
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- name: Upload Execution Reports
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uses: actions/upload-artifact@v4
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uses: actions/upload-artifact@v7
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if: failure()
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with:
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name: execution-reports

‎.github/workflows/linkcheck.yml‎

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steps:
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# Checkout the live site (html)
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- name: Checkout
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uses: actions/checkout@v4
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uses: actions/checkout@v6
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with:
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ref: gh-pages
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- name: Link Checker
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args: --accept 403,503 *.html
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- name: Create Issue From File
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if: steps.lychee.outputs.exit_code != 0
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uses: peter-evans/create-issue-from-file@v5
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uses: peter-evans/create-issue-from-file@v6
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with:
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title: Link Checker Report
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content-filepath: ./lychee/out.md

‎.github/workflows/publish.yml‎

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runs-on: ubuntu-latest
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steps:
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- name: Checkout
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uses: actions/checkout@v4
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uses: actions/checkout@v6
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with:
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fetch-depth: 0
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- name: Setup Anaconda
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uses: conda-incubator/setup-miniconda@v3
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uses: conda-incubator/setup-miniconda@v4
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with:
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auto-update-conda: true
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auto-activate-base: true
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shell: bash -l {0}
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run: pip list
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- name: Download "build" folder (cache)
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uses: dawidd6/action-download-artifact@v11
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uses: dawidd6/action-download-artifact@v21
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with:
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workflow: cache.yml
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branch: main
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run: |
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rm -r _build/.doctrees
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jb build lectures --path-output ./
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# Create HTML archive for release assets
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- name: Create HTML archive
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shell: bash -l {0}
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run: |
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tar -czf lecture-python-intro-html-${{ github.ref_name }}.tar.gz -C _build/html .
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sha256sum lecture-python-intro-html-${{ github.ref_name }}.tar.gz > html-checksum.txt
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# Create metadata manifest
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cat > html-manifest.json << EOF
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{
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"tag": "${{ github.ref_name }}",
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"commit": "${{ github.sha }}",
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"timestamp": "$(date -Iseconds)",
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"size_mb": $(du -sm _build/html | cut -f1),
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"file_count": $(find _build/html -type f | wc -l)
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}
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EOF
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- name: Upload archives to release
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uses: softprops/action-gh-release@v3
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with:
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files: |
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lecture-python-intro-html-${{ github.ref_name }}.tar.gz
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html-checksum.txt
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html-manifest.json
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env:
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GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
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- name: Deploy to Netlify
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uses: nwtgck/actions-netlify@v3.0
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with:
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publish_dir: _build/html/
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cname: intro.quantecon.org
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- name: Upload "_build" folder (cache)
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uses: actions/upload-artifact@v4
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uses: actions/upload-artifact@v7
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with:
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name: build-publish
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path: _build

‎environment.yml‎

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- default
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dependencies:
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- python=3.13
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- anaconda=2025.06
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- anaconda=2025.12
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- pip
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- pip:
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- jupyter-book==1.0.4post1
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- quantecon-book-theme==0.8.3
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- sphinx-tojupyter==0.3.1
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- sphinxext-rediraffe==0.2.7
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- sphinx-exercise==1.0.1
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- sphinx-proof==0.2.1
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- sphinxcontrib-youtube==1.4.1
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- sphinx-togglebutton==0.3.2
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- sphinx-reredirects==1.0.0
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- quantecon-book-theme==0.20.3
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- sphinx-tojupyter==0.6.0
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- sphinxext-rediraffe==0.3.0
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- sphinx-exercise==1.2.1
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- sphinx-proof==0.4.0
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- sphinxcontrib-youtube==1.5.0
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- sphinx-togglebutton==0.4.5
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- sphinx-reredirects==1.1.0
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‎lectures/_config.yml‎

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nb_render_image_options:
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width: 80%
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nb_code_prompt_show: "Show {type}"
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nb_merge_streams: true
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nb_mime_priority_overrides: [
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# HTML
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['html', 'application/vnd.jupyter.widget-view+json', 10],
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['html', 'application/javascript', 20],
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['html', 'text/html', 30],
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['html', 'text/latex', 40],
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['html', 'image/svg+xml', 50],
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['html', 'image/png', 60],
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['html', 'image/jpeg', 70],
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['html', 'text/markdown', 80],
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['html', 'text/plain', 90],
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# Jupyter Notebooks
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['jupyter', 'application/vnd.jupyter.widget-view+json', 10],
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['jupyter', 'application/javascript', 20],
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['jupyter', 'text/html', 30],
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['jupyter', 'text/latex', 40],
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['jupyter', 'image/svg+xml', 50],
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['jupyter', 'image/png', 60],
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['jupyter', 'image/jpeg', 70],
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['jupyter', 'text/markdown', 80],
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['jupyter', 'text/plain', 90],
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# LaTeX
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['latex', 'text/latex', 10],
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['latex', 'application/pdf', 20],
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['latex', 'image/png', 30],
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['latex', 'image/jpeg', 40],
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['latex', 'text/markdown', 50],
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['latex', 'text/plain', 60],
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# Link Checker
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['linkcheck', 'text/plain', 10],
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]
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suppress_warnings: [mystnb.unknown_mime_type, myst.domains]
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# sphinx-proof
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# -------------
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html_js_files:
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header_organisation: QuantEcon
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repository_url: https://github.com/QuantEcon/lecture-python-intro
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nb_repository_url: https://github.com/QuantEcon/lecture-python-intro.notebooks
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path_to_docs: lectures
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twitter: quantecon
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twitter_logo_url: https://assets.quantecon.org/img/qe-twitter-logo.png
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og_logo_url: https://assets.quantecon.org/img/qe-og-logo.png

‎lectures/_static/lecture_specific/long_run_growth/tooze_ch1_graph.png‎

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‎lectures/ar1_processes.md‎

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* productivity, etc.
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We are going to study AR(1) processes partly because they are useful and
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partly because they help us understand important concepts.
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partly because they help us understand important concepts.
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Let's start with some imports:
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X_{t+1} = a X_t + b + c W_{t+1}
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```
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where $a, b, c$ are scalar-valued parameters
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where $a, b, c$ are scalar-valued parameters
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(Equation {eq}`can_ar1` is sometimes called a **stochastic difference equation**.)
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```{prf:example}
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:label: ar1_ex_ar
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For example, $X_t$ might be
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For example, $X_t$ might be
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* the log of labor income for a given household, or
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* the log of money demand in a given economy.
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And we can use a theoretical AR(1) model to calculate the right hand side.
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If $\frac{1}{m} \sum_{t = 1}^m X_t$ is not close to $\psi^(x)$, even for many
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observations, then our theory seems to be incorrect and we will need to revise
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it.
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If $\frac{1}{m} \sum_{t = 1}^m h(X_t)$ is not close to $\int h(x)\psi^*(x) dx$, even for many observations, then our theory seems to be incorrect and we will need to revise it.
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## Exercises
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return 0
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k_vals = np.arange(6) + 1
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sample_moments = np.empty_like(k_vals)
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true_moments = np.empty_like(k_vals)
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sample_moments = np.empty(len(k_vals), dtype=float)
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true_moments = np.empty(len(k_vals), dtype=float)
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for k_idx, k in enumerate(k_vals):
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sample_moments[k_idx] = sample_moments_ar1(k)
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For $K$ use the Gaussian kernel ($K$ is the standard normal
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density).
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Write the class so that the bandwidth defaults to Silverman’s rule (see
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the “rule of thumb” discussion on [this
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Write the class so that the bandwidth defaults to Silverman's rule (see
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the "rule of thumb" discussion on [this
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page](https://en.wikipedia.org/wiki/Kernel_density_estimation)). Test
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the class you have written by going through the steps
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