Linear Extrapolation within Pandas

linear-extrapolation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear extrapolation within Pandas\n",
    "Pandas currently has the insufficiency to not be able to extrapolate. This notebook gives a simple implementation of linear extrapolation with exemplary usage.\n",
    "\n",
    "For more information, please see [this issue](https://github.com/pandas-dev/pandas/issues/31949)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import pylab as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_style('whitegrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "figsize = (18, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_min = pd.Timestamp('2021-03-01 23:00:00.007893084')\n",
    "t_max = pd.Timestamp('2021-03-08 06:59:59.970214128')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "idx1 = pd.date_range(t_min, t_max, freq='1d')\n",
    "idx2 = pd.date_range(t_min, t_max, freq='1h')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "s1 = pd.Series(index=idx1, dtype=float)\n",
    "s1[1] = 1\n",
    "s1[-3] = 4.75\n",
    "s1[-2] = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "s2 = pd.Series(index=idx2, dtype=float)\n",
    "s2[24] = 1\n",
    "s2[96] = 4.75\n",
    "s2[-32] = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_interpolation(i1, i2, title=None):\n",
    "    fig, ax = plt.subplots(2, 1, figsize=figsize, sharex=True)\n",
    "    s1.plot(style='o', ms=10, ax=ax[0], label='original')\n",
    "    i1.plot(style='o-', color='C0', ax=ax[0], label='daily')\n",
    "    s2.plot(style='o', color='C1', ms=10, ax=ax[1], label='original')\n",
    "    i2.plot(style='o-', color='C1', ax=ax[1], label='hourly')\n",
    "    if title is not None:\n",
    "        plt.suptitle(title)\n",
    "    plt.tight_layout()\n",
    "    ax[0].legend()\n",
    "    ax[1].legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1296x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Forward-, backward-fill\n",
    "i1 = s1.ffill().bfill()\n",
    "i2 = s2.ffill().bfill()\n",
    "\n",
    "plot_interpolation(i1, i2, title=\"Forward-, backward-fill\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Interpolation, forward-, backward-fill\n",
    "i1 = s1.interpolate(limit_area='inside').ffill().bfill()\n",
    "i2 = s2.interpolate(limit_area='inside').ffill().bfill()\n",
    "\n",
    "plot_interpolation(i1, i2, title=\"Interpolation, forward-, backward-fill\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def extrapolate_linear(s):\n",
    "    s = s.copy()\n",
    "    # Indices of not-nan values\n",
    "    idx_nn = s.index[~s.isna()]\n",
    "    \n",
    "    # At least two data points needed for trend analysis\n",
    "    assert len(idx_nn) >= 2\n",
    "    \n",
    "    # Outermost indices\n",
    "    idx_l = idx_nn[0]\n",
    "    idx_r = idx_nn[-1]\n",
    "    \n",
    "    # Indices left and right of outermost values\n",
    "    idx_ll = s.index[s.index < idx_l]\n",
    "    idx_rr = s.index[s.index > idx_r]\n",
    "    \n",
    "    # Derivative of not-nan indices / values\n",
    "    v = s[idx_nn].diff()\n",
    "    \n",
    "    # Left- and right-most derivative values\n",
    "    v_l = v[1]\n",
    "    v_r = v[-1]\n",
    "    f_l = idx_l - idx_nn[1]\n",
    "    f_r = idx_nn[-2] - idx_r\n",
    "    \n",
    "    # Set values left / right of boundaries\n",
    "    l_l = lambda idx: (idx_l - idx) / f_l * v_l + s[idx_l]\n",
    "    l_r = lambda idx: (idx_r - idx) / f_r * v_r + s[idx_r]\n",
    "    x_l = pd.Series(idx_ll).apply(l_l)\n",
    "    x_l.index = idx_ll\n",
    "    x_r = pd.Series(idx_rr).apply(l_r)\n",
    "    x_r.index = idx_rr\n",
    "    s[idx_ll] = x_l\n",
    "    s[idx_rr] = x_r\n",
    "    \n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "i1 = extrapolate_linear(s1)\n",
    "i2 = extrapolate_linear(s2)\n",
    "\n",
    "plot_interpolation(i1, i2, title=\"Extrapolation only\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "i1 = extrapolate_linear(s1).interpolate()\n",
    "i2 = extrapolate_linear(s2).interpolate()\n",
    "\n",
    "plot_interpolation(i1, i2, title=\"Extrapolation and interpolation\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}