herding.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly.express as px\n",
    "import plotly.graph_objects as go\n",
    "from plotly.subplots import make_subplots\n",
    "from matplotlib import cm\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "coin_df = pd.read_csv('Crypto_Price_20240108.csv')\n",
    "coin_df = coin_df.drop(columns=['BSV', 'LTC'])\n",
    "crix_df = pd.read_csv('new_crix.csv')\n",
    "df = coin_df.merge(crix_df)\n",
    "df = df.rename(columns={'price':'CRIX'})\n",
    "df.index = pd.to_datetime(df['date'])\n",
    "df = df.drop(columns=['date'])\n",
    "df = df.apply(lambda x: np.log(x)-np.log(x.shift(1)))\n",
    "df = df.dropna(how='any')\n",
    "df = df[df.index >= '2017-09-06']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "vcrix_df = pd.read_csv('vcrix.csv')\n",
    "vcrix_df.index = vcrix_df['date']\n",
    "vcrix_df = vcrix_df[vcrix_df.index >= '2022-01-01']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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     "data": {
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       "config": {
        "plotlyServerURL": "https://plot.ly"
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           "ticks": "",
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           "zerolinewidth": 2
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          "yaxis": {
           "automargin": true,
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           "zerolinewidth": 2
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        "width": 1200,
        "xaxis": {
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        }
       }
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     },
     "metadata": {},
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   ],
   "source": [
    "fig = make_subplots(rows=1, cols=1, shared_xaxes=True, vertical_spacing=0)\n",
    "\n",
    "fig.update_layout(\n",
    "    height=600,\n",
    "    width=1200,\n",
    "    title='',\n",
    "    showlegend=False,\n",
    "    font=dict(family='Times New Roman', size=14),\n",
    "    plot_bgcolor='rgba(0,0,0,0)',\n",
    "    paper_bgcolor='rgba(0,0,0,0)',\n",
    ")\n",
    "\n",
    "    \n",
    "fig.add_trace(go.Scatter(\n",
    "    y=vcrix_df['vcrix'], \n",
    "    x=vcrix_df.index,\n",
    "    line=dict(color='black', width=1),\n",
    "    # mode='markers', marker_size=1,  \n",
    "    ), row=1, col=1)\n",
    "\n",
    "\n",
    "fig.update_xaxes(\n",
    "    title='',\n",
    "    tickformat='%Y-%m',  \n",
    "    # dtick='M3',  \n",
    "    showline=True,\n",
    "    linewidth=1,\n",
    "    linecolor='black',\n",
    "    mirror=True,\n",
    "    showgrid=False,\n",
    "    row=1, col=1  \n",
    ")\n",
    "\n",
    "fig.update_yaxes(\n",
    "    showticklabels=True,\n",
    "    title='VCRIX',\n",
    "    showline=True,\n",
    "    linewidth=1,\n",
    "    linecolor='black',\n",
    "    mirror=True,\n",
    "    showgrid=False,\n",
    ")\n",
    "\n",
    "fig.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### CSAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rolling_csad(coin_returns, market_returns, window):\n",
    "    csad_values = []\n",
    "    for i in range(len(coin_returns) - window + 1):\n",
    "        window_data = coin_returns.iloc[i:i+window]\n",
    "        window_market = market_returns[i:i+window].mean()\n",
    "        N = len(window_data.columns)\n",
    "        csad = (N / (N - 1)) * np.sum(np.abs(window_data.sub(window_market, axis=0)).mean(axis=1))\n",
    "        csad_values.append(csad)\n",
    "    return pd.Series(csad_values, index=coin_returns.index[window-1:])\n",
    "\n",
    "# # E(R_{m,t})\n",
    "# def moving_average(market_returns, n=30):\n",
    "#     ret = np.cumsum(market_returns, dtype=float)\n",
    "#     ret[n:] = ret[n:] - ret[:-n]\n",
    "#     return ret[n - 1:] / n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "window=1\n",
    "rolling_csad_values = rolling_csad(df[df.columns[:-1]], df['CRIX'], window)\n",
    "avg_crix = df['CRIX'].rolling(window=window).mean()\n",
    "avg_crix = avg_crix.iloc[window:]\n",
    "df = df.iloc[window:]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "csad_df = pd.DataFrame()\n",
    "csad_df['csad'] = rolling_csad_values\n",
    "csad_df['CRIX'] = df['CRIX']\n",
    "csad_df = csad_df[1:]\n",
    "csad_df.index = df.index\n",
    "csad_df['abs_CRIX'] = abs(df['CRIX'])\n",
    "csad_df['sq_CRIX'] = np.square(df['CRIX'])\n",
    "csad_df = csad_df[(csad_df.index >= '2022-01-01') & (csad_df.index <= '2023-12-31')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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         "anchor": "x",
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         "linewidth": 1,
         "mirror": true,
         "showgrid": false,
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         "showticklabels": true,
         "title": {
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        },
        "yaxis2": {
         "anchor": "x2",
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         "linewidth": 1,
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          "text": "CSAD"
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   ],
   "source": [
    "colors = ['blue', 'red', 'green', 'orange', 'purple', 'cyan', 'magenta', 'MidnightBlue', 'brown']\n",
    "\n",
    "fig = make_subplots(rows=2, cols=1, shared_xaxes=True, vertical_spacing=0)\n",
    "\n",
    "fig.update_layout(\n",
    "    height=800,\n",
    "    width=1000,\n",
    "    title='',\n",
    "    showlegend=False, \n",
    "    font=dict(family='Times New Roman', size=14),\n",
    "    plot_bgcolor='rgba(0,0,0,0)',\n",
    "    paper_bgcolor='rgba(0,0,0,0)',\n",
    ")\n",
    "\n",
    "for i, col in enumerate(df.columns[:-1]):\n",
    "    fig.add_trace(\n",
    "        go.Scatter(\n",
    "            y=df[(df.index >= '2022-01-01') & (df.index <= '2023-12-31')][col], \n",
    "            x=csad_df.index,\n",
    "            mode='lines',  \n",
    "            name=col, \n",
    "            line=dict(width=1, color=colors[i % len(colors)]), \n",
    "             opacity=.5,\n",
    "        ),\n",
    "        row=1, col=1 \n",
    "    )\n",
    "    \n",
    "fig.add_trace(go.Scatter(\n",
    "    y=csad_df['csad'], \n",
    "    x=csad_df.index,\n",
    "    line=dict(color='black', width=1),\n",
    "    ), row=2, col=1)\n",
    "\n",
    "# fig.add_trace(go.Scatter(\n",
    "    # y=avg_crix, \n",
    "    # x=avg_crix.index,\n",
    "    # line=dict(color='orange', width=1),\n",
    "    # ), row=1, col=1)\n",
    "\n",
    "\n",
    "fig.update_xaxes(\n",
    "    title='',\n",
    "    showticklabels=False,  \n",
    "    showline=True,\n",
    "    linewidth=1,\n",
    "    linecolor='black',\n",
    "    mirror=True,\n",
    "    showgrid=False,\n",
    "    row=1, col=1 \n",
    ")\n",
    "\n",
    "fig.update_xaxes(\n",
    "    title='',\n",
    "    tickformat='%Y-%m',  \n",
    "    dtick='M1',  \n",
    "    showline=True,\n",
    "    linewidth=1,\n",
    "    linecolor='black',\n",
    "    mirror=True,\n",
    "    showgrid=False,\n",
    "    row=2, col=1\n",
    ")\n",
    "\n",
    "fig.update_yaxes(\n",
    "    showticklabels=True,\n",
    "    title='Log return',\n",
    "    showline=True,\n",
    "    linewidth=1,\n",
    "    linecolor='black',\n",
    "    mirror=True,\n",
    "    showgrid=False,\n",
    "    row=1, col=1,  \n",
    ")\n",
    "\n",
    "fig.update_yaxes(\n",
    "    showticklabels=True,\n",
    "    title='CSAD',\n",
    "    showline=True,\n",
    "    linewidth=1,\n",
    "    linecolor='black',\n",
    "    mirror=True,\n",
    "    showgrid=False,\n",
    "    row=2, col=1 \n",
    ")\n",
    "\n",
    "fig.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "anime_df = pd.DataFrame()\n",
    "anime_df['csad'] = csad_df['csad']\n",
    "anime_df['avg_CRIX'] = avg_crix[(avg_crix.index >= '2022-01-01') & (avg_crix.index <= '2023-12-31')]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### static plot between csad and crix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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        },
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   "source": [
    "fig = make_subplots(rows=1, cols=1, shared_xaxes=True, vertical_spacing=0)\n",
    "\n",
    "fig.update_layout(\n",
    "    height=600,\n",
    "    width=600,\n",
    "    title='',\n",
    "    showlegend=False,  \n",
    "    font=dict(family='Times New Roman', size=14),\n",
    "    plot_bgcolor='rgba(0,0,0,0)',\n",
    "    paper_bgcolor='rgba(0,0,0,0)',\n",
    ")\n",
    "    \n",
    "fig.add_trace(go.Scatter(\n",
    "    y=anime_df['csad'], \n",
    "    x=anime_df['avg_CRIX'],\n",
    "    line=dict(color='black', width=1),\n",
    "    mode='markers', marker_size=10, \n",
    "    ), row=1, col=1)\n",
    "\n",
    "\n",
    "\n",
    "# Update x-axis for the first row\n",
    "fig.update_xaxes(\n",
    "    title='Expected market return',\n",
    "    showticklabels=True,  # Hide tick labels\n",
    "    showline=True,\n",
    "    linewidth=1,\n",
    "    linecolor='black',\n",
    "    mirror=True,\n",
    "    showgrid=False,\n",
    "    row=1, col=1,\n",
    "    range=[-0.2,0.2]\n",
    ")\n",
    "\n",
    "\n",
    "# Update y-axis for the first row\n",
    "fig.update_yaxes(\n",
    "    showticklabels=True,\n",
    "    title='CSAD',\n",
    "    showline=True,\n",
    "    linewidth=1,\n",
    "    linecolor='black',\n",
    "    mirror=True,\n",
    "    showgrid=False,\n",
    "    row=1, col=1,\n",
    "    range=[0, 0.15]\n",
    ")\n",
    "\n",
    "# Show the plot\n",
    "fig.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### anime without the marker of event dates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "anime_df = pd.DataFrame()\n",
    "anime_df['csad'] = csad_df['csad']\n",
    "anime_df['avg_CRIX'] = avg_crix[(avg_crix.index >= '2022-01-01') & (avg_crix.index <= '2023-12-31')]\n",
    "\n",
    "highlight_dates = pd.to_datetime(['2022-05-13', '2022-11-11', '2023-07-13'])\n",
    "\n",
    "fig = make_subplots(rows=1, cols=1)\n",
    "\n",
    "fig.update_layout(\n",
    "    height=600,\n",
    "    width=600,\n",
    "    showlegend=False,\n",
    "    font=dict(family='Times New Roman', size=14),\n",
    "    plot_bgcolor='rgba(0,0,0,0)',\n",
    "    paper_bgcolor='rgba(0,0,0,0)',\n",
    ")\n",
    "\n",
    "# Generate a colormap from dark to light using 'jet'\n",
    "cmap = cm.get_cmap('jet', len(anime_df))\n",
    "colors = [cmap(i) for i in range(len(anime_df))]\n",
    "colors = ['rgba({}, {}, {}, {})'.format(int(r*255), int(g*255), int(b*255), a) for r, g, b, a in colors]\n",
    "\n",
    "# Initial Trace\n",
    "fig.add_trace(\n",
    "    go.Scatter(\n",
    "        x=anime_df['avg_CRIX'],\n",
    "        y=anime_df['csad'],\n",
    "        mode='markers',\n",
    "        marker=dict(size=10, color=colors[0])\n",
    "    )\n",
    ")\n",
    "\n",
    "# Configure x and y axis\n",
    "fig.update_xaxes(title='Expected market return', range=[-0.2, 0.2])\n",
    "fig.update_yaxes(title='CSAD', range=[0, 0.15])\n",
    "\n",
    "# Create frames for animation\n",
    "frames = [\n",
    "    go.Frame(\n",
    "        data=[\n",
    "            go.Scatter(\n",
    "                x=anime_df.iloc[:i+1]['avg_CRIX'],\n",
    "                y=anime_df.iloc[:i+1]['csad'],\n",
    "                mode='markers',\n",
    "                marker=dict(\n",
    "                    size=[20 if anime_df.index[j] in highlight_dates else 10 for j in range(i+1)],\n",
    "                    color=[colors[j] if anime_df.index[j] not in highlight_dates else 'red' for j in range(i+1)],\n",
    "                    symbol=['circle' if anime_df.index[j] not in highlight_dates else 'star' for j in range(i+1)]\n",
    "                )\n",
    "            )\n",
    "        ],\n",
    "        name=f\"frame_{i}\"\n",
    "    )\n",
    "    for i in range(len(anime_df))\n",
    "]\n",
    "\n",
    "fig.frames = frames\n",
    "\n",
    "fig.update_layout(\n",
    "    updatemenus=[{\n",
    "        \"buttons\": [\n",
    "            {\"args\": [None, {\"frame\": {\"duration\": 20, \"redraw\": True}, \"fromcurrent\": True}], \"label\": \"Play\", \"method\": \"animate\"},\n",
    "            {\"args\": [[None], {\"frame\": {\"duration\": 0, \"redraw\": True}, \"mode\": \"immediate\", \"transition\": {\"duration\": 0}}], \"label\": \"Pause\", \"method\": \"animate\"}\n",
    "        ],\n",
    "        \"direction\": \"left\",\n",
    "        \"pad\": {\"r\": 10, \"t\": 87},\n",
    "        \"showactive\": False,\n",
    "        \"type\": \"buttons\",\n",
    "        \"x\": 0.1,\n",
    "        \"xanchor\": \"right\",\n",
    "        \"y\": 0,\n",
    "        \"yanchor\": \"top\"\n",
    "    }],\n",
    "    sliders=[{\n",
    "        \"active\": 0,\n",
    "        \"yanchor\": \"top\",\n",
    "        \"xanchor\": \"left\",\n",
    "        \"currentvalue\": {\n",
    "            \"font\": {\"size\": 20},\n",
    "            \"prefix\": \"Time:\",\n",
    "            \"visible\": True,\n",
    "            \"xanchor\": \"right\"\n",
    "        },\n",
    "        \"transition\": {\"duration\": 20, \"easing\": \"cubic-in-out\"},\n",
    "        \"pad\": {\"b\": 10, \"t\": 50},\n",
    "        \"len\": 0.9,\n",
    "        \"x\": 0.1,\n",
    "        \"y\": 0,\n",
    "        \"steps\": [{\n",
    "            \"args\": [[f'frame_{i}'], {\"frame\": {\"duration\": 20, \"redraw\": True}, \"mode\": \"immediate\", \"transition\": {\"duration\": 10}}],\n",
    "            \"label\": anime_df.index[i].strftime('%Y-%m-%d'),\n",
    "            \"method\": \"animate\"\n",
    "        } for i in range(len(anime_df))]\n",
    "    }]\n",
    ")\n",
    "\n",
    "fig.show()\n",
    "\n",
    "fig.write_html(\"animated_plot.html\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### anime with markers of the event dates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "anime_df = pd.DataFrame()\n",
    "anime_df['csad'] = csad_df['csad']\n",
    "anime_df['avg_CRIX'] = avg_crix[(avg_crix.index >= '2022-01-01') & (avg_crix.index <= '2023-12-31')]\n",
    "\n",
    "highlight_dates = pd.to_datetime(['2022-05-13', '2022-11-11', '2023-07-13'])\n",
    "highlight_labels = {\n",
    "    '2022-05-13': \"Terra's Crash\",\n",
    "    '2022-11-11': \"FTX’s Bankruptcy\",\n",
    "    '2023-07-13': \"Ripple's Win'\"\n",
    "}\n",
    "\n",
    "fig = make_subplots(rows=1, cols=1)\n",
    "\n",
    "fig.update_layout(\n",
    "    height=600,\n",
    "    width=600,\n",
    "    showlegend=False,\n",
    "    font=dict(family='Times New Roman', size=14),\n",
    "    plot_bgcolor='rgba(0,0,0,0)',\n",
    "    paper_bgcolor='rgba(0,0,0,0)',\n",
    ")\n",
    "\n",
    "# Generate a colormap from dark to light using 'jet'\n",
    "cmap = cm.get_cmap('jet', len(anime_df))\n",
    "colors = [cmap(i) for i in range(len(anime_df))]\n",
    "colors = ['rgba({}, {}, {}, {})'.format(int(r*255), int(g*255), int(b*255), a) for r, g, b, a in colors]\n",
    "\n",
    "# Initial Trace\n",
    "fig.add_trace(\n",
    "    go.Scatter(\n",
    "        x=anime_df['avg_CRIX'],\n",
    "        y=anime_df['csad'],\n",
    "        mode='markers',\n",
    "        marker=dict(size=10, color=colors[0])\n",
    "    )\n",
    ")\n",
    "\n",
    "# Configure x and y axis\n",
    "fig.update_xaxes(title='Expected market return', range=[-0.2, 0.2])\n",
    "fig.update_yaxes(title='CSAD', range=[0, 0.15])\n",
    "\n",
    "# Create frames for animation\n",
    "frames = [\n",
    "    go.Frame(\n",
    "        data=[\n",
    "            go.Scatter(\n",
    "                x=anime_df.iloc[:i+1]['avg_CRIX'],\n",
    "                y=anime_df.iloc[:i+1]['csad'],\n",
    "                mode='markers',\n",
    "                marker=dict(\n",
    "                    size=[20 if anime_df.index[j] in highlight_dates else 10 for j in range(i+1)],\n",
    "                    color=[colors[j] if anime_df.index[j] not in highlight_dates else 'red' for j in range(i+1)],\n",
    "                    symbol=['star' if anime_df.index[j] in highlight_dates else 'circle' for j in range(i+1)]\n",
    "                )\n",
    "            )\n",
    "        ],\n",
    "        name=f\"frame_{i}\",\n",
    "        layout=go.Layout(\n",
    "            annotations=[\n",
    "                dict(\n",
    "                    x=anime_df.loc[date]['avg_CRIX'],\n",
    "                    y=anime_df.loc[date]['csad'],\n",
    "                    text=label,\n",
    "                    showarrow=True,\n",
    "                    arrowhead=2,\n",
    "                    ax=20,\n",
    "                    ay=-30\n",
    "                ) for date, label in highlight_labels.items() if date in anime_df.index[:i+1]\n",
    "            ]\n",
    "        )\n",
    "    )\n",
    "    for i in range(len(anime_df))\n",
    "]\n",
    "\n",
    "fig.frames = frames\n",
    "\n",
    "fig.update_layout(\n",
    "    updatemenus=[{\n",
    "        \"buttons\": [\n",
    "            {\"args\": [None, {\"frame\": {\"duration\": 20, \"redraw\": True}, \"fromcurrent\": True}], \"label\": \"Play\", \"method\": \"animate\"},\n",
    "            {\"args\": [[None], {\"frame\": {\"duration\": 0, \"redraw\": True}, \"mode\": \"immediate\", \"transition\": {\"duration\": 0}}], \"label\": \"Pause\", \"method\": \"animate\"}\n",
    "        ],\n",
    "        \"direction\": \"left\",\n",
    "        \"pad\": {\"r\": 10, \"t\": 87},\n",
    "        \"showactive\": False,\n",
    "        \"type\": \"buttons\",\n",
    "        \"x\": 0.1,\n",
    "        \"xanchor\": \"right\",\n",
    "        \"y\": 0,\n",
    "        \"yanchor\": \"top\"\n",
    "    }],\n",
    "    sliders=[{\n",
    "        \"active\": 0,\n",
    "        \"yanchor\": \"top\",\n",
    "        \"xanchor\": \"left\",\n",
    "        \"currentvalue\": {\n",
    "            \"font\": {\"size\": 20},\n",
    "            \"prefix\": \"Time:\",\n",
    "            \"visible\": True,\n",
    "            \"xanchor\": \"right\"\n",
    "        },\n",
    "        \"transition\": {\"duration\": 20, \"easing\": \"cubic-in-out\"},\n",
    "        \"pad\": {\"b\": 10, \"t\": 50},\n",
    "        \"len\": 0.9,\n",
    "        \"x\": 0.1,\n",
    "        \"y\": 0,\n",
    "        \"steps\": [{\n",
    "            \"args\": [[f'frame_{i}'], {\"frame\": {\"duration\": 20, \"redraw\": True}, \"mode\": \"immediate\", \"transition\": {\"duration\": 10}}],\n",
    "            \"label\": anime_df.index[i].strftime('%Y-%m-%d'),\n",
    "            \"method\": \"animate\"\n",
    "        } for i in range(len(anime_df))]\n",
    "    }]\n",
    ")\n",
    "\n",
    "fig.show()\n",
    "\n",
    "fig.write_html(\"animated_plot.html\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   csad   R-squared:                       0.229\n",
      "Model:                            OLS   Adj. R-squared:                  0.227\n",
      "Method:                 Least Squares   F-statistic:                     108.1\n",
      "Date:                Fri, 28 Jun 2024   Prob (F-statistic):           7.77e-42\n",
      "Time:                        18:32:16   Log-Likelihood:                 2022.7\n",
      "No. Observations:                 730   AIC:                            -4039.\n",
      "Df Residuals:                     727   BIC:                            -4026.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0152      0.001     16.668      0.000       0.013       0.017\n",
      "abs_CRIX       0.4953      0.053      9.392      0.000       0.392       0.599\n",
      "sq_CRIX       -1.4105      0.466     -3.030      0.003      -2.324      -0.496\n",
      "==============================================================================\n",
      "Omnibus:                      286.470   Durbin-Watson:                   1.502\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1285.042\n",
      "Skew:                           1.770   Prob(JB):                    9.05e-280\n",
      "Kurtosis:                       8.451   Cond. No.                         833.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "Y = csad_df['csad']\n",
    "X = csad_df[['abs_CRIX', 'sq_CRIX']]\n",
    "\n",
    "# Add a constant to the independent variables (X) for the intercept\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "# Fit the OLS model\n",
    "model = sm.OLS(Y, X).fit()\n",
    "\n",
    "# Print the summary of the regression\n",
    "print(model.summary())"
   ]
  }
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