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  "Title": "Butterworth-Induced Autoregressive Model",
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  "Description": "Implements the Butterworth-Induced Autoregressive\n('BTWAR') model, where autoregressive coefficients are obtained\nfrom analog Butterworth filter prototypes mapped into the\ndiscrete-time domain using the Matched Z-Transform. The\nframework establishes a structured connection between\nfrequency-domain filter design and time-domain autoregressive\nmodeling. Model order selection is performed via nested\nrolling-origin cross-validation. Method described in\nBras-Geraldes, Rocha and Martins (2026)\n<doi:10.3390/math14030479>.",
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  "Encoding": "UTF-8",
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  "URL": "https://doi.org/10.3390/math14030479,\nhttps://github.com/cgeraldes/BTWAR",
  "BugReports": "https://github.com/cgeraldes/BTWAR/issues",
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  "Date/Publication": "2026-03-15 20:01:27 UTC",
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    "btwar_fit",
    "compute_spectrum",
    "mse",
    "plot_bode",
    "plot_freq_amplitude",
    "plot_zpoles",
    "poles_AR",
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    "simulate_ar_split",
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    {
      "page": "apply_stationarity",
      "title": "Apply Stationarity Transformation to a Train/Test Split",
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        "apply_stationarity"
      ]
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    {
      "page": "btwar_fit",
      "title": "Fit a Butterworth-Induced Autoregressive Model",
      "topics": [
        "btwar_fit"
      ]
    },
    {
      "page": "coef.btwar",
      "title": "Extract AR Coefficients from a BTWAR Model",
      "topics": [
        "coef.btwar"
      ]
    },
    {
      "page": "compute_spectrum",
      "title": "Compute the One-Sided Power Spectrum",
      "topics": [
        "compute_spectrum"
      ]
    },
    {
      "page": "fitted.btwar",
      "title": "Fitted Values from a BTWAR Model",
      "topics": [
        "fitted.btwar"
      ]
    },
    {
      "page": "mse",
      "title": "Mean Squared Error",
      "topics": [
        "mse"
      ]
    },
    {
      "page": "plot_bode",
      "title": "Plot the Bode Magnitude Diagram of a BTWAR Model",
      "topics": [
        "plot_bode"
      ]
    },
    {
      "page": "plot_freq_amplitude",
      "title": "Plot the Frequency Amplitude Spectrum of a Time Series",
      "topics": [
        "plot_freq_amplitude"
      ]
    },
    {
      "page": "plot_zpoles",
      "title": "Plot Z-Plane Poles from a BTWAR Model",
      "topics": [
        "plot_zpoles"
      ]
    },
    {
      "page": "plot.btwar",
      "title": "Plot Predictions from a BTWAR Model",
      "topics": [
        "plot.btwar"
      ]
    },
    {
      "page": "poles_AR",
      "title": "Compute Z-Plane Poles of an AR Model",
      "topics": [
        "poles_AR"
      ]
    },
    {
      "page": "predict.btwar",
      "title": "Predict from a BTWAR Model",
      "topics": [
        "predict.btwar"
      ]
    },
    {
      "page": "print.btwar",
      "title": "Print a BTWAR Model",
      "topics": [
        "print.btwar"
      ]
    },
    {
      "page": "print.summary.btwar",
      "title": "Print a BTWAR Model Summary",
      "topics": [
        "print.summary.btwar"
      ]
    },
    {
      "page": "residuals.btwar",
      "title": "Residuals from a BTWAR Model",
      "topics": [
        "residuals.btwar"
      ]
    },
    {
      "page": "rmse",
      "title": "Root Mean Squared Error",
      "topics": [
        "rmse"
      ]
    },
    {
      "page": "simulate_ar_split",
      "title": "Simulate an AR(p) Series and Split into Train/Test Sets",
      "topics": [
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    },
    {
      "page": "summary.btwar",
      "title": "Summarise a BTWAR Model",
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        "summary.btwar"
      ]
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      "title": "One-Step-Ahead AR Predictions",
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      "title": "Introduction to the BTWAR Package",
      "author": "Carlos Brás-Geraldes, J. Leonel Rocha",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "Methodology",
        "Butterworth Filter Prototype",
        "Matched Z-Transform",
        "Correspondence Between Filter Order and AR Order",
        "The Butterworth-Induced Autoregressive Model",
        "Practical Properties of BTW-AR",
        "Model Fitting Pipeline",
        "End-to-End Example",
        "Setup",
        "Simulating Data",
        "Exploratory Analysis",
        "Fitting the BTW-AR Model",
        "Time-Series Predictions",
        "Spectral Interpretation: Bode Magnitude Diagram",
        "Frequency Amplitude Spectrum",
        "Z-Plane Pole Structure",
        "Robustness Options",
        "Conclusion",
        "Session Information",
        "References"
      ],
      "created": "2026-03-01 13:56:31",
      "modified": "2026-03-15 04:08:59",
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