{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "[![Binder](img/badge-binder.svg)](https://mybinder.org/v2/gh/nhirschey/teaching/gh-pages?filepath=premiums.ipynb)\u0026emsp;\n",
    "[![Script](img/badge-script.svg)](/Teaching//premiums.fsx)\u0026emsp;\n",
    "[![Notebook](img/badge-notebook.svg)](/Teaching//premiums.ipynb)\n",
    "\n",
    "# Equity Premium usings CAPE\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 1, "outputs": [],
   "source": [
    "#r \"nuget: NovaSBE.Finance, 0.5.0\"\n",
    "#r \"nuget: FSharp.Stats, 0.5.0\"\n",
    "#r \"nuget: FSharp.Data, 5.0.2\"\n",
    "#r \"nuget: Plotly.NET, 3.*\"\n",
    "#r \"nuget: Plotly.NET.Interactive, 3.*\"\n",
    "#r \"nuget: ExcelProvider,2.*\"\n",
    "\n",
    "open System\n",
    "open NovaSBE.Finance\n",
    "open NovaSBE.Finance.Utils\n",
    "open FSharp.Stats\n",
    "open Plotly.NET\n",
    "open Plotly.NET.Interactive\n",
    "open FSharp.Data\n",
    "open NovaSBE.Finance.Ols\n",
    "open FSharp.Interop.Excel\n",
    "\n",
    "Environment.CurrentDirectory \u003c- __SOURCE_DIRECTORY__\n",
    "\n",
    "let goyal2022Id = \"1g4LOaRj4TvwJr9RIaA_nwrXXWTOy46bP\"\n",
    "let sheetToCsv id sheet = $\"https://docs.google.com/spreadsheets/d/{id}/gviz/tq?tqx=out:csv\u0026sheet={sheet}\"\n",
    "\n",
    "download (sheetToCsv goyal2022Id \"Monthly\") \"goyalMonthly.csv\"\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "Shiller data\n",
    "\n",
    "Download the excel file from Robert Shiller\u0027s website to your current directory.\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 2, "outputs": [],
   "source": [
    "download \"http://www.econ.yale.edu/~shiller/data/ie_data.xls\" \"shiller_data.xls\"\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "Now loading the excel data.\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 3, "outputs": [],
   "source": [
    "let [\u003cLiteral\u003e] shillerFile = __SOURCE_DIRECTORY__ + \"/shiller_data.xls\"\n",
    "type ShillerXls = ExcelFile\u003cshillerFile,SheetName=\"Data\",Range=\"A8:V2000\",ForceString = true\u003e\n",
    "\n",
    "let shillerDate (x: ShillerXls.Row) =\n",
    "    let year = int x.Date[..3]\n",
    "    let month = \n",
    "        let m = x.Date[5..]\n",
    "        if m = \"1\" then 10 else int m\n",
    "    DateTime(year, month, 1)\n",
    "\n",
    "type ShillerData = \n",
    "    { Month: DateTime\n",
    "      CAPE: float\n",
    "      Ret: float }\n",
    "let shiller = \n",
    "    ShillerXls().Data \n",
    "    |\u003e Seq.toList\n",
    "    |\u003e Seq.takeWhile (fun x -\u003e \n",
    "        not (isNull x.Date) \u0026\u0026\n",
    "        not (isNull x.D) \u0026\u0026 \n",
    "        not (isNull x.CAPE)\n",
    "        )\n",
    "    |\u003e Seq.pairwise\n",
    "    |\u003e Seq.map (fun (x0, x1) -\u003e\n",
    "        let cape = \n",
    "            match x1.CAPE with\n",
    "            | \"NA\" -\u003e nan\n",
    "            | cape -\u003e cape |\u003e float\n",
    "        shillerDate x1,\n",
    "        { Month = shillerDate x1\n",
    "          CAPE = cape \n",
    "          Ret = (float x1.P + float x1.D / 12.0) / float x0.P - 1.0})\n",
    "    |\u003e Map     \n",
    "\n",
    "\n",
    "/// Goyal and Welch Monthly Excel worksheet\n",
    "let gwXlMd = CsvProvider\u003c\"goyalMonthly.csv\",ResolutionFolder = __SOURCE_DIRECTORY__\u003e.GetSample().Rows\n",
    "let parseMonth (yyyyMM) = DateTime.ParseExact(string yyyyMM,\"yyyyMM\",Globalization.CultureInfo.InvariantCulture)\n",
    "\n",
    "type Predictors =\n",
    "    { Month: DateTime\n",
    "      CAPE: float\n",
    "      R: float }\n",
    "let capePredictor=\n",
    "    gwXlMd\n",
    "    |\u003e Seq.filter (fun x -\u003e\n",
    "        x.Yyyymm \u003e= 188102 \u0026\u0026\n",
    "        x.Yyyymm \u003c= 202303)\n",
    "    |\u003e Seq.map (fun x -\u003e\n",
    "        let month = parseMonth x.Yyyymm\n",
    "        let r =\n",
    "            if month \u003c DateTime(1927,1,1) then\n",
    "                shiller[month].Ret - x.Rfree\n",
    "            else\n",
    "                x.CRSP_SPvw - x.Rfree\n",
    "        { Month = month\n",
    "          CAPE = shiller[month.AddMonths(-1)].CAPE \n",
    "          R = r })\n",
    "    |\u003e Seq.toArray\n",
    "\n",
    "let crspRet = gwXlMd |\u003e Seq.map (fun x -\u003e parseMonth x.Yyyymm, x) |\u003e Map\n",
    "\n",
    "type ReturnPrediction = { Month: DateTime; R: float }\n",
    "let muHistorical =\n",
    "    let mutable acc = 0.0\n",
    "    let mutable n = 0.0\n",
    "    let mutable dt = shiller.Keys |\u003e Seq.min\n",
    "    [| while dt \u003c= DateTime(2022,12,1) do \n",
    "        if dt \u003c DateTime(1927,1,1) then \n",
    "          acc \u003c- acc + shiller[dt].Ret - crspRet[dt].Rfree\n",
    "        else\n",
    "          acc \u003c- acc + crspRet[dt].CRSP_SPvw - crspRet[dt].Rfree\n",
    "        n \u003c- n + 1.0\n",
    "        dt \u003c- dt.AddMonths(1)\n",
    "        { Month = dt.AddMonths(1)\n",
    "          R = acc / n}\n",
    "    |]\n",
    "let muHistoricalMap = muHistorical |\u003e Seq.map (fun x -\u003e x.Month, x.R) |\u003e Map\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "Might have seen a chart like this before. Looks like CAPE is a good predictor.\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 4, "outputs": [],
   "source": [
    "let capeBarChart =\n",
    "    capePredictor\n",
    "    |\u003e Seq.filter (fun x -\u003e x.Month \u003c= DateTime(2005,12,1))\n",
    "    |\u003e Seq.sortBy (fun x -\u003e x.CAPE)\n",
    "    |\u003e Seq.splitInto 5\n",
    "    |\u003e Seq.map (fun xs -\u003e \n",
    "        let cape = xs |\u003e Seq.map (fun x -\u003e x.CAPE) |\u003e Seq.average\n",
    "        let r = xs |\u003e Seq.map (fun x -\u003e x.R * 12.0) |\u003e Seq.average\n",
    "        $\"%.2f{cape}\", r)\n",
    "    |\u003e Chart.Column\n",
    "    |\u003e Chart.withXAxisStyle (\"CAPE\")\n",
    "    |\u003e Chart.withYAxisStyle (\"Annualized Excess Return\")\n",
    "    |\u003e Chart.withYAxis(LayoutObjects.LinearAxis.init(TickFormat = \".1%\"))\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 5, "outputs": [
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   "source": [
    "capeBarChart\n"
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   "cell_type": "markdown",
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   "source": [
    "Though simple OLS results are not too special.\n",
    "\n"
   ]
  }
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    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 7, "outputs": [
          {
           "data": {
            "text/plain": ["\"=======================================================================================",
"Dep. Variable:                   R    R-squared:                0.002",
"Model:                         OLS    Adj. R-squared:           0.001",
"Method:              Least Squares    F-statistic:             3.4424",
"Date:                   2024-02-20    Prob (F-statistic):      0.0637",
"Time:                     12:52:23                                   ",
"No. Observations:             1703                                   ",
"Df Residuals:                 1701                                   ",
"Df Model:                        1                                   ",
"Covariance Type:         Nonrobust                                   ",
"---------------------------------------------------------------------------------------",
"                   coef      std err            t       P\u003e|t|       [0.025       0.975]",
"Intercept        0.0108        0.003        3.513    0.000455        0.005        0.017",
"CAPE            -0.0003        0.000       -1.855      0.0637       -0.001     1.74e-05",
"=======================================================================================\""]
        },
           "execution_count": 7,
           "metadata": {},
           "output_type": "execute_result"
          }],
   "source": [
    "Ols(\"R~CAPE\", capePredictor).fit().summary()\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "Until 2005\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 8, "outputs": [
          {
           "data": {
            "text/plain": ["\"=======================================================================================",
"Dep. Variable:                   R    R-squared:                0.003",
"Model:                         OLS    Adj. R-squared:           0.003",
"Method:              Least Squares    F-statistic:             5.0264",
"Date:                   2024-02-20    Prob (F-statistic):      0.0251",
"Time:                     12:52:23                                   ",
"No. Observations:             1499                                   ",
"Df Residuals:                 1497                                   ",
"Df Model:                        1                                   ",
"Covariance Type:         Nonrobust                                   ",
"---------------------------------------------------------------------------------------",
"                   coef      std err            t       P\u003e|t|       [0.025       0.975]",
"Intercept        0.0123        0.003        3.647    0.000275        0.006        0.019",
"CAPE            -0.0004        0.000       -2.242      0.0251       -0.001    -5.42e-05",
"=======================================================================================\""]
        },
           "execution_count": 8,
           "metadata": {},
           "output_type": "execute_result"
          }],
   "source": [
    "Ols(\"R~CAPE\", \n",
    "    capePredictor \n",
    "    |\u003e Array.filter (fun x -\u003e x.Month \u003c= DateTime(2005,12,1))).fit().summary()\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "We can do rolling regressions.\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 9, "outputs": [
          {
           "data": {
            "text/plain": ["{ Month = 6/1/1889 12:00:00 AM",
"  R = -0.001028701056 }"]
        },
           "execution_count": 9,
           "metadata": {},
           "output_type": "execute_result"
          }],
   "source": [
    "let capePrediction (xs: array\u003cPredictors\u003e) =\n",
    "    let mdl = Ols(\"R~CAPE\",xs[..xs.Length-2]).fit()\n",
    "    let lastObs = xs |\u003e Array.last\n",
    "    { Month = lastObs.Month \n",
    "      R = mdl.predict([lastObs])[0] }\n",
    "\n",
    "capePrediction capePredictor[..100]\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "Restricted predictor\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 10, "outputs": [],
   "source": [
    "let capePredictionRestricted (xs: array\u003cPredictors\u003e) =\n",
    "    let mdl = Ols(\"R~CAPE\",xs[..xs.Length-2]).fit()\n",
    "    let lastObs = xs |\u003e Array.last\n",
    "    let slope = min 0.0 mdl.coefs[\"CAPE\"]\n",
    "    let prediction = max 0.0 (mdl.coefs[\"Intercept\"] + slope * lastObs.CAPE)\n",
    "    { Month = lastObs.Month \n",
    "      R = prediction }\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "Restricted vs. unrestricted predictions\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 11, "outputs": [
          {
           "data": {
            "text/plain": ["Unrestricted:",
"{ Month = 1/1/1999 12:00:00 AM",
"  R = -0.005161117975 }",
"",
"Restricted:",
"{ Month = 1/1/1999 12:00:00 AM",
"  R = 0.0 }"]
        },
           "execution_count": 11,
           "metadata": {},
           "output_type": "execute_result"
          }],
   "source": [
    "let index1999 = capePredictor |\u003e Array.findIndex (fun x -\u003e x.Month = DateTime(1999,1,1))\n",
    "printfn $\"Unrestricted:\\n{capePrediction capePredictor[..index1999]}\"\n",
    "printfn $\"Restricted:\\n{capePredictionRestricted capePredictor[..index1999]}\"\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "the CAPE predictons.\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 12, "outputs": [],
   "source": [
    "let cape1927Index =\n",
    "    capePredictor\n",
    "    |\u003e Array.findIndex (fun x -\u003e x.Month = DateTime(1927,1,1))\n",
    "\n",
    "let muCAPE =\n",
    "    [| for i = cape1927Index to capePredictor.Length-1 do \n",
    "        capePrediction capePredictor[..i] |]\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "Historical sample average.\n",
    "\n",
    "Compare predictions\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 13, "outputs": [],
   "source": [
    "[ Chart.Line (muCAPE |\u003e Array.map (fun x -\u003e x.Month, 12.0*x.R),\n",
    "              Name = \"CAPE\")\n",
    "  Chart.Line (muHistorical |\u003e Array.map (fun x -\u003e x.Month, 12.0*x.R),\n",
    "              Name = \"Historical\")]\n",
    "|\u003e Chart.combine\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "Accuracy\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 14, "outputs": [
          {
           "data": {
            "text/plain": ["[|{ Month = 1/1/1929 12:00:00 AM",
"    Actual = 0.624876",
"    PredRegression = 0.04718276909",
"    PredHistAvg = 0.04755984426 }; { Month = 1/1/2000 12:00:00 AM",
"                                     Actual = -0.64476",
"                                     PredRegression = -0.04524778738",
"                                     PredHistAvg = 0.06599267524 };",
"  { Month = 12/1/2022 12:00:00 AM",
"    Actual = -0.745008",
"    PredRegression = 0.02755284611",
"    PredHistAvg = 0.06546170231 }|]"]
        },
           "execution_count": 14,
           "metadata": {},
           "output_type": "execute_result"
          }],
   "source": [
    "let muCAPEMap = muCAPE |\u003e Array.map (fun x -\u003e x.Month, x.R) |\u003e Map\n",
    "\n",
    "type PredictionCombo =\n",
    "    { Month: DateTime \n",
    "      Actual: float \n",
    "      PredRegression: float \n",
    "      PredHistAvg: float }\n",
    "let accuracyComps =\n",
    "    [| for i = cape1927Index to capePredictor.Length-1 do\n",
    "        let month = capePredictor[i].Month \n",
    "        {  Month = month\n",
    "           Actual = 12.0*capePredictor[i].R \n",
    "           PredRegression = 12.0*muCAPEMap[month]\n",
    "           PredHistAvg = 12.0*muHistoricalMap[month] }|]\n",
    "\n",
    "accuracyComps\n",
    "|\u003e Array.filter (fun x -\u003e\n",
    "    x.Month = DateTime(1929,1,1) ||\n",
    "    x.Month = DateTime(2000,1,1) ||\n",
    "    x.Month = DateTime(2022,12,1))\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "root mean squared errors\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 15, "outputs": [],
   "source": [
    "let rmse xy = \n",
    "    xy \n",
    "    |\u003e Array.averageBy (fun (x,y) -\u003e (x - y) ** 2.0)\n",
    "    |\u003e sqrt\n",
    "\n",
    "let rmses =\n",
    "    [| for i = 1 to accuracyComps.Length-1 do \n",
    "        let mseCAPE = \n",
    "            accuracyComps[..i]\n",
    "            |\u003e Array.map (fun x -\u003e x.Actual, x.PredRegression)\n",
    "            |\u003e rmse \n",
    "        let mseHist =\n",
    "            accuracyComps[..i]\n",
    "            |\u003e Array.map (fun x -\u003e x.Actual, x.PredHistAvg)\n",
    "            |\u003e rmse\n",
    "        {| Month = accuracyComps[i].Month \n",
    "           mseCAPE = mseCAPE\n",
    "           mseHist = mseHist |}|]\n",
    "\n",
    "let rmseChart = \n",
    "    [ Chart.Line(rmses |\u003e Array.map (fun x -\u003e x.Month, x.mseCAPE),\n",
    "                 Name =\"CAPE\")\n",
    "      Chart.Line(rmses |\u003e Array.map (fun x -\u003e x.Month, x.mseHist),\n",
    "                 Name = \"Hist\")]\n",
    "    |\u003e Chart.combine\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 16, "outputs": [
          {
           "data": {
            "text/html": ["\u003cdiv id=\"d8ec7918-7c19-4f77-8e96-a227fd8f31c7\"\u003e\u003c!-- Plotly chart will be drawn inside this DIV --\u003e\u003c/div\u003e",
"",
"\u003cscript type=\"text/javascript\"\u003e",
"",
"",
"",
"            var renderPlotly_d8ec79187c194f778e96a227fd8f31c7 = function() {",
"",
"            var fsharpPlotlyRequire = requirejs.config({context:\u0027fsharp-plotly\u0027,paths:{plotly:\u0027https://cdn.plot.ly/plotly-2.6.3.min\u0027}}) || require;",
"",
"            fsharpPlotlyRequire([\u0027plotly\u0027], function(Plotly) {",
"",
"",
"",
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"",
"            var config = {\"responsive\":true};",
"",
"            Plotly.newPlot(\u0027d8ec7918-7c19-4f77-8e96-a227fd8f31c7\u0027, data, layout, config);",
"",
"});",
"",
"            };",
"",
"            if ((typeof(requirejs) !==  typeof(Function)) || (typeof(requirejs.config) !== typeof(Function))) {",
"",
"                var script = document.createElement(\"script\");",
"",
"                script.setAttribute(\"src\", \"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js\");",
"",
"                script.onload = function(){",
"",
"                    renderPlotly_d8ec79187c194f778e96a227fd8f31c7();",
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"                renderPlotly_d8ec79187c194f778e96a227fd8f31c7();",
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"",
"\u003c/script\u003e",
"",
""]
        },
           "execution_count": 16,
           "metadata": {},
           "output_type": "execute_result"
          }],
   "source": [
    "rmseChart\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "The difference, much easier to interpret.\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 18, "outputs": [],
   "source": [
    "let rmsesDiffChart =\n",
    "    rmses\n",
    "    |\u003e Array.map (fun x -\u003e\n",
    "        x.Month, (x.mseHist - x.mseCAPE))\n",
    "    |\u003e Chart.Line\n",
    "    |\u003e Chart.withTitle(\"Hist Avg. RMSE - CAPE RMSE\")\n",
    "    |\u003e Chart.withYAxisStyle(TitleText=\"Positive means that CAPE has lower error\")\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": null, "outputs": [
          {
           "data": {
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"",
"\u003cscript type=\"text/javascript\"\u003e",
"",
"",
"",
"            var renderPlotly_a607450e1b334a9da84460c3f8fb88f9 = function() {",
"",
"            var fsharpPlotlyRequire = requirejs.config({context:\u0027fsharp-plotly\u0027,paths:{plotly:\u0027https://cdn.plot.ly/plotly-2.6.3.min\u0027}}) || require;",
"",
"            fsharpPlotlyRequire([\u0027plotly\u0027], function(Plotly) {",
"",
"",
"",
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240, 248, 1.0)\"},\"line\":{\"color\":\"rgba(255, 255, 255, 1.0)\"}},\"header\":{\"fill\":{\"color\":\"rgba(200, 212, 227, 1.0)\"},\"line\":{\"color\":\"rgba(255, 255, 255, 1.0)\"}}}]}},\"title\":{\"text\":\"Hist Avg. 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"",
"            var config = {\"responsive\":true};",
"",
"            Plotly.newPlot(\u0027a607450e-1b33-4a9d-a844-60c3f8fb88f9\u0027, data, layout, config);",
"",
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"",
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"",
"                var script = document.createElement(\"script\");",
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"\u003c/script\u003e",
"",
""]
        },
           "execution_count": null,
           "metadata": {},
           "output_type": "execute_result"
          }],
   "source": [
    "rmsesDiffChart\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "OOS R2\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 20, "outputs": [],
   "source": [
    "let oosR2 (xs: seq\u003cPredictionCombo\u003e) =\n",
    "    let sseHist = xs |\u003e Seq.sumBy (fun x -\u003e (x.Actual - x.PredHistAvg) ** 2.0)\n",
    "    let sseRegression = xs |\u003e Seq.sumBy (fun x -\u003e (x.Actual - x.PredRegression) ** 2.0)\n",
    "    1.0 - sseRegression / sseHist\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "Pre 2005\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 21, "outputs": [
          {
           "data": {
            "text/plain": ["0.001295581388"]
        },
           "execution_count": 21,
           "metadata": {},
           "output_type": "execute_result"
          }],
   "source": [
    "accuracyComps\n",
    "|\u003e Array.filter (fun x -\u003e x.Month \u003c= DateTime(2005,12,1))\n",
    "|\u003e oosR2\n"
   ]
  }
,
  {
   "cell_type": "markdown",
   "metadata": {},
   
   "source": [
    "Plot of OOS R2\n",
    "\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 22, "outputs": [],
   "source": [
    "let oosr2Chart =\n",
    "    [| for i = 1 to accuracyComps.Length-1 do \n",
    "        accuracyComps[i].Month,\n",
    "        accuracyComps[..i] |\u003e oosR2 |]\n",
    "    |\u003e Array.filter (fun (dt, xs) -\u003e dt \u003c= DateTime(2005,12,1))\n",
    "    |\u003e Chart.Line\n",
    "    |\u003e Chart.withYAxis(LayoutObjects.LinearAxis.init(TickFormat = \".1%\",TickVals = [| -0.01;0.0;0.01;0.02|]))\n",
    "    |\u003e Chart.withYAxisStyle(MinMax = (-0.01,0.02))\n",
    "    |\u003e Chart.withSize(Width=1000,Height=500)\n"
   ]
  }
,
  {
   "cell_type": "code",
   "metadata": {
    "dotnet_interactive": {
     "language": "fsharp"
    },
    "polyglot_notebook": {
     "kernelName": "fsharp"
    }
   },
   "execution_count": 23, "outputs": [
          {
           "data": {
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"            var fsharpPlotlyRequire = requirejs.config({context:\u0027fsharp-plotly\u0027,paths:{plotly:\u0027https://cdn.plot.ly/plotly-2.6.3.min\u0027}}) || require;",
"",
"            fsharpPlotlyRequire([\u0027plotly\u0027], function(Plotly) {",
"",
"",
"",
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