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    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "\n",
    "# Example time series data\n",
    "np.random.seed(0)\n",
    "dates = pd.date_range('2023-01-01', periods=100)\n",
    "data = pd.Series(np.random.randn(100).cumsum(), index=dates)\n",
    "\n",
    "# Parameters\n",
    "window_size = 20\n",
    "\n",
    "# Function to calculate rolling window linear regression\n",
    "def rolling_linreg(series, window):\n",
    "    intercepts = []\n",
    "    slopes = []\n",
    "    for i in range(len(series) - window + 1):\n",
    "        y = series[i:i + window]\n",
    "        x = np.arange(window)\n",
    "        x = sm.add_constant(x)\n",
    "        model = sm.OLS(y, x).fit()\n",
    "        intercepts.append(model.params[0])\n",
    "        slopes.append(model.params[1])\n",
    "    return intercepts, slopes\n",
    "\n",
    "# Calculate rolling linear regression parameters\n",
    "intercepts, slopes = rolling_linreg(data, window_size)\n",
    "\n",
    "# Create a DataFrame for plotting\n",
    "rolling_dates = dates[window_size - 1:]\n",
    "rolling_intercepts = pd.Series(intercepts, index=rolling_dates)\n",
    "rolling_slopes = pd.Series(slopes, index=rolling_dates)\n",
    "\n",
    "# Plot the original data and the rolling linear regression\n",
    "plt.figure(figsize=(14, 7))\n",
    "plt.plot(data, label='Original Data')\n",
    "for i in range(len(rolling_intercepts)):\n",
    "    start_date = rolling_dates[i] - pd.DateOffset(days=window_size-1)\n",
    "    end_date = rolling_dates[i]\n",
    "    plt.plot([start_date, end_date],\n",
    "             [rolling_intercepts[i], rolling_intercepts[i] + rolling_slopes[i] * (window_size - 1)],\n",
    "             color='red', alpha=0.5)\n",
    "\n",
    "plt.legend()\n",
    "plt.title('Rolling Window Linear Regression')\n",
    "plt.xlabel('Date')\n",
    "plt.ylabel('Value')\n",
    "plt.show()\n"
   ]
  }
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