{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import packages\n",
    "import plotly.express as px\n",
    "import pandas as pd\n",
    "\n",
    "# Import packages\n",
    "from scipy.stats import boxcox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read in the data\n",
    "data = pd.read_csv(\"../coal-price-data/AirPassengers.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Month</th>\n",
       "      <th>#Passengers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1949-01</td>\n",
       "      <td>112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1949-02</td>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1949-03</td>\n",
       "      <td>132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1949-04</td>\n",
       "      <td>129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1949-05</td>\n",
       "      <td>121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>139</th>\n",
       "      <td>1960-08</td>\n",
       "      <td>606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>140</th>\n",
       "      <td>1960-09</td>\n",
       "      <td>508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>1960-10</td>\n",
       "      <td>461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>142</th>\n",
       "      <td>1960-11</td>\n",
       "      <td>390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>143</th>\n",
       "      <td>1960-12</td>\n",
       "      <td>432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>144 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Month  #Passengers\n",
       "0    1949-01          112\n",
       "1    1949-02          118\n",
       "2    1949-03          132\n",
       "3    1949-04          129\n",
       "4    1949-05          121\n",
       "..       ...          ...\n",
       "139  1960-08          606\n",
       "140  1960-09          508\n",
       "141  1960-10          461\n",
       "142  1960-11          390\n",
       "143  1960-12          432\n",
       "\n",
       "[144 rows x 2 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data[\"Month\"] = pd.to_datetime(data[\"Month\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Month</th>\n",
       "      <th>#Passengers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1949-01-01</td>\n",
       "      <td>112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1949-02-01</td>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1949-03-01</td>\n",
       "      <td>132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1949-04-01</td>\n",
       "      <td>129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1949-05-01</td>\n",
       "      <td>121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>139</th>\n",
       "      <td>1960-08-01</td>\n",
       "      <td>606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>140</th>\n",
       "      <td>1960-09-01</td>\n",
       "      <td>508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>1960-10-01</td>\n",
       "      <td>461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>142</th>\n",
       "      <td>1960-11-01</td>\n",
       "      <td>390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>143</th>\n",
       "      <td>1960-12-01</td>\n",
       "      <td>432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>144 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         Month  #Passengers\n",
       "0   1949-01-01          112\n",
       "1   1949-02-01          118\n",
       "2   1949-03-01          132\n",
       "3   1949-04-01          129\n",
       "4   1949-05-01          121\n",
       "..         ...          ...\n",
       "139 1960-08-01          606\n",
       "140 1960-09-01          508\n",
       "141 1960-10-01          461\n",
       "142 1960-11-01          390\n",
       "143 1960-12-01          432\n",
       "\n",
       "[144 rows x 2 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_passenger_volumes(df: pd.DataFrame, y: str) -> None:\n",
    "    \"\"\"General function to plot the passenger data.\"\"\"\n",
    "\n",
    "    fig = px.line(df, x=\"Month\", y=y, labels={\"Month\": \"Date\"})\n",
    "    fig.update_layout(\n",
    "        template=\"simple_white\",\n",
    "        font=dict(size=18),\n",
    "        title_text=\"Airline Passengers\",\n",
    "        width=650,\n",
    "        title_x=0.5,\n",
    "        height=400,\n",
    "    )\n",
    "\n",
    "    return fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot the airline passenger data\n",
    "plot_passenger_volumes(df=data, y=\"#Passengers\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = data\n",
    "y = \"#Passengers\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = px.line(df, x=\"Month\", y=y, labels={\"Month\": \"Date\"})\n",
    "fig.update_layout(\n",
    "    template=\"simple_white\",\n",
    "    font=dict(size=18),\n",
    "    title_text=\"Airline Passengers\",\n",
    "    width=650,\n",
    "    title_x=0.5,\n",
    "    height=400,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(fig.show())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make the target stationary\n",
    "data[\"Passengers_boxcox\"], lam = boxcox(data[\"#Passengers\"])\n",
    "data[\"Passenger_stationary\"] = data[\"Passengers_boxcox\"].diff()\n",
    "data.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot the stationary airline passenger data\n",
    "plot_passenger_volumes(df=data, y=\"Passenger_stationary\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import packages\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "\n",
    "\n",
    "# ADF test for stationary\n",
    "def adf_test(series):\n",
    "    \"\"\"Using an ADF test to determine if a series is stationary\"\"\"\n",
    "    test_results = adfuller(series)\n",
    "    print(\"ADF Statistic: \", test_results[0])\n",
    "    print(\"P-Value: \", test_results[1])\n",
    "    print(\"Critical Values:\")\n",
    "    for threshold, adf_stat in test_results[4].items():\n",
    "        print(\"\\t%s: %.2f\" % (threshold, adf_stat))\n",
    "\n",
    "\n",
    "print(adf_test(data[\"Passenger_stationary\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import packages\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.graphics.tsaplots import plot_pacf\n",
    "\n",
    "# Plot partial autocorrelation\n",
    "plt.rc(\"figure\", figsize=(11, 5))\n",
    "plot_pacf(data[\"Passenger_stationary\"], method=\"ywm\")\n",
    "plt.xlabel(\"Lags\", fontsize=18)\n",
    "plt.ylabel(\"Correlation\", fontsize=18)\n",
    "plt.xticks(fontsize=18)\n",
    "plt.yticks(fontsize=18)\n",
    "plt.title(\"Partial Autocorrelation Plot\", fontsize=20)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import packages\n",
    "from statsmodels.tsa.ar_model import AutoReg, ar_select_order\n",
    "\n",
    "# Split train and test\n",
    "train = data.iloc[: -int(len(data) * 0.2)]\n",
    "test = data.iloc[-int(len(data) * 0.2) :]\n",
    "\n",
    "# Build AR model\n",
    "selector = ar_select_order(train[\"Passenger_stationary\"], 15)\n",
    "model = AutoReg(train[\"Passenger_stationary\"], lags=selector.ar_lags).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import packages\n",
    "from scipy.special import inv_boxcox\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "# Get forecasts and convert to actual passenger volumes\n",
    "transformed_forecasts = list(model.forecast(steps=len(test)))\n",
    "boxcox_forecasts = []\n",
    "for idx in range(len(test)):\n",
    "    if idx == 0:\n",
    "        boxcox_forecast = (\n",
    "            transformed_forecasts[idx] + train[\"Passengers_boxcox\"].iloc[-1]\n",
    "        )\n",
    "    else:\n",
    "        boxcox_forecast = transformed_forecasts[idx] + boxcox_forecasts[idx - 1]\n",
    "\n",
    "    boxcox_forecasts.append(boxcox_forecast)\n",
    "\n",
    "forecasts = inv_boxcox(boxcox_forecasts, lam)\n",
    "\n",
    "\n",
    "def plot_forecasts(forecasts: list[float], title: str) -> None:\n",
    "    \"\"\"Function to plot the forecasts.\"\"\"\n",
    "    fig = go.Figure()\n",
    "    fig.add_trace(\n",
    "        go.Scatter(x=train[\"Month\"], y=train[\"#Passengers\"], name=\"Train\")\n",
    "    )\n",
    "    fig.add_trace(\n",
    "        go.Scatter(x=test[\"Month\"], y=test[\"#Passengers\"], name=\"Test\")\n",
    "    )\n",
    "    fig.add_trace(go.Scatter(x=test[\"Month\"], y=forecasts, name=\"Forecast\"))\n",
    "    fig.update_layout(\n",
    "        template=\"simple_white\",\n",
    "        font=dict(size=18),\n",
    "        title_text=title,\n",
    "        width=650,\n",
    "        title_x=0.5,\n",
    "        height=400,\n",
    "        xaxis_title=\"Date\",\n",
    "        yaxis_title=\"Passenger Volume\",\n",
    "    )\n",
    "\n",
    "    return fig.show()\n",
    "\n",
    "\n",
    "# Plot the forecasts\n",
    "plot_forecasts(forecasts, \"Autoregression\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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