notebooks/Stochastic_Generators/Uniswap_Process_Modeling.ipynb

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    "# Exogenous Uniswap Process modeling \n",
    "\n",
    "\n",
    "## Liquidity demand stochastic process\n",
    "\n",
    "1. Acquire time series of order book for single collateral DAI 2017-2019; this is the proxy for the liquidity demand of RAI\n",
    "2. Fit a parametric distribution to the data, resulting in a distribution $F^D_{RAI}(t;\\mu_{RAI})$ and fitted parameters $\\mu_{RAI}$.\n",
    "\n",
    "\n",
    "To obtain this data, we ran a [Uniswap cadCAD model](https://github.com/cadCAD-org/demos/tree/master/demos/Multiscale/uniswap) twice, once to obtain Buy/Sell univariate time series data and once for obtaining univariate time series liquidity data. Shown below is the modification between runs. We then saved these runs as csv files and continue bring the data into this notebook for building stochastic generators.\n",
    "\n",
    "\n",
    "```\n",
    "# Mechanisms\n",
    "def mechanismHub_DAI(params, step, history, current_state, input_):\n",
    "    action = input_['action_id']\n",
    "    # 1 Buy/Sell\n",
    "    if action == 'TokenPurchase':\n",
    "        return ethToToken_DAI(params, step, history, current_state, input_)\n",
    "    elif action == 'EthPurchase':\n",
    "        return tokenToEth_DAI(params, step, history, current_state, input_)\n",
    "    # 2 Add/remove liquidity\n",
    "#     if action == 'AddLiquidity':\n",
    "#         return addLiquidity_DAI(params, step, history, current_state, input_)\n",
    "#     elif action == 'Transfer':\n",
    "#         return removeLiquidity_DAI(params, step, history, current_state, input_)\n",
    "    return('DAI_balance', abs(current_state['DAI_balance']))\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as st\n",
    "from sklearn.metrics import mean_squared_error\n",
    "import matplotlib.pyplot as plt\n",
    "from math import sqrt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://stackoverflow.com/questions/6620471/fitting-empirical-distribution-to-theoretical-ones-with-scipy-python?lq=1\n",
    "def get_best_distribution(data):\n",
    "    dist_names = [\"alpha\",\"gamma\",\"norm\", \"exponweib\", \"weibull_max\", \"weibull_min\", \"pareto\", \"genextreme\"]\n",
    "    dist_results = []\n",
    "    params = {}\n",
    "    for dist_name in dist_names:\n",
    "        dist = getattr(st, dist_name)\n",
    "        param = dist.fit(data)\n",
    "\n",
    "        params[dist_name] = param\n",
    "        # Applying the Kolmogorov-Smirnov test\n",
    "        D, p = st.kstest(data, dist_name, args=param)\n",
    "        print(\"p value for \"+dist_name+\" = \"+str(p))\n",
    "        dist_results.append((dist_name, p))\n",
    "\n",
    "    # select the best fitted distribution\n",
    "    best_dist, best_p = (max(dist_results, key=lambda item: item[1]))\n",
    "    # store the name of the best fit and its p value\n",
    "\n",
    "    print(\"Best fitting distribution: \"+str(best_dist))\n",
    "    print(\"Best p value: \"+ str(best_p))\n",
    "    print(\"Parameters for the best fit: \"+ str(params[best_dist]))\n",
    "\n",
    "    return best_dist, best_p, params[best_dist]\n",
    "\n",
    "\n",
    "def kl_divergence(p, q):\n",
    "    return sum(p[i] * np.log2(p[i]/q[i]) for i in range(len(p)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data preprocessing\n",
    "\n",
    "\n",
    "We examine the data two univariate time series,buy/sell and liquidity, make changes absolute, and remove all zero values."
   ]
  },
  {
   "cell_type": "code",
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       "   Unnamed: 0             DAI_balance           ETH_balance  \\\n",
       "0           1  5905000000000000000000  29974673940746674209   \n",
       "1           2  5907000000000000000000  29964555511671268196   \n",
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       "4           5  5901109640216828255225  29994555511671268196   \n",
       "\n",
       "             UNI_supply  simulation  subset  run  substep  timestep  \n",
       "0  30000000000000000000           0       0    1        1         1  \n",
       "1  30000000000000000000           0       0    1        1         2  \n",
       "2  30000000000000000000           0       0    1        1         3  \n",
       "3  30000000000000000000           0       0    1        1         4  \n",
       "4  30000000000000000000           0       0    1        1         5  "
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     "execution_count": 3,
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   ],
   "source": [
    "# import data\n",
    "buy_sell_uniswap_events = pd.read_csv('data/uniswap_data_buy_sell.csv')\n",
    "liquidity_uniswap_events = pd.read_csv('data/uniswap_liquidity_data.csv')\n",
    "\n",
    "buy_sell_uniswap_events.head()"
   ]
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   "cell_type": "code",
   "execution_count": 4,
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       "   Unnamed: 0             DAI_balance           ETH_balance  \\\n",
       "0           1  5900000000000000000000  29974673940746674209   \n",
       "1           2  5900000000000000000000  29964546939628433685   \n",
       "2           3  5900000000000000000000  29974546939628433685   \n",
       "3           4  5900000000000000000000  29984546939628433685   \n",
       "4           5  5900000000000000000000  29994546939628433685   \n",
       "\n",
       "             UNI_supply  simulation  subset  run  substep  timestep  \n",
       "0  30000000000000000000           0       0    1        1         1  \n",
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       "3  30000000000000000000           0       0    1        1         4  \n",
       "4  30000000000000000000           0       0    1        1         5  "
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     "execution_count": 4,
     "metadata": {},
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   "source": [
    "liquidity_uniswap_events.head()"
   ]
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       "<AxesSubplot:title={'center':'Dai liquidity univariate series'}, xlabel='timestep'>"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# liquidity series\n",
    "liquidity_uniswap_events['DAI_balance'] = liquidity_uniswap_events['DAI_balance'].astype(float)\n",
    "liquidity_uniswap_events['DAI_diff'] = abs(liquidity_uniswap_events['DAI_balance'].diff())\n",
    "liquidity_uniswap_events['DAI_diff'].fillna(0,inplace=True)\n",
    "liquidity_uniswap_events = liquidity_uniswap_events.query('DAI_diff > 0') \n",
    "liquidity_uniswap_events.plot(x='timestep',y='DAI_diff',title='Dai liquidity univariate series')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Liquidity IID Samples')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(liquidity_uniswap_events['DAI_diff'].apply(np.log))\n",
    "plt.title('Histogram of Liquidity IID Samples')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'Dai Buy/Sell Univariate Series'}, xlabel='timestep'>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# buy/sell series\n",
    "buy_sell_uniswap_events['DAI_balance'] = buy_sell_uniswap_events['DAI_balance'].astype(float)\n",
    "buy_sell_uniswap_events['DAI_diff'] = abs(buy_sell_uniswap_events['DAI_balance'].diff())\n",
    "buy_sell_uniswap_events['DAI_diff'].fillna(0,inplace=True)\n",
    "buy_sell_uniswap_events = buy_sell_uniswap_events.query('DAI_diff > 0') \n",
    "buy_sell_uniswap_events.plot(x='timestep',y='DAI_diff',title='Dai Buy/Sell Univariate Series')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Buy/Sell IID Samples')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAEICAYAAAC9E5gJAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy86wFpkAAAACXBIWXMAAAsTAAALEwEAmpwYAAAeXklEQVR4nO3df5QddZnn8ffHhAiKkATaTEyyJiMZ2YiHCD0QFtdVoiEBNfGsMmF10nIyZGYJrrruSnBnFgWZA7sqwhHwRMmQiBIyKIccicZswPXHmJhGIpggm+aX6RhIS36BjGDg2T/quVjc3O6+nXTuvaE/r3Pu6aqnvlX1VHX3faq+VfeWIgIzMxvaXtXsBMzMrPlcDMzMzMXAzMxcDMzMDBcDMzPDxcDMzHAxeMWTtEnSO5udRzNJ+oCkrZKekfS2ZudzICRNlBSShuf4DyX9TbPzarTcByc0O49XIheDw5ikxyS9uyr2UUk/qYxHxFsi4of9LOdlbzSvQF8ALo6IoyPivuqJue2/z2LxO0m3Sho5WCuXdIakf8nh2ZI2Stqb67pb0qTBWleu47OSbimNv/QGmtP+KOnpfP0/SV+RNLaP5Y2Q9EVJ3bmPHpP05cHM2ZrPxcAOuRYoMm8ENvXT5uSIOBr4c2AU8NlBXP+5wKp8Q14GfAo4FpgEXA+8MIjrqsdtEfE6YDTwAeDPgHv7KAiXAu3AacDrgHcCv2hAntZALgavcOWzB0mnSerMo9InJX0pm/0of+7OI78zJL1K0t9LelzSDknLJB1bWu68nPaUpH+oWs9nJd0u6RZJe4GP5rp/Jmm3pO15NDqitLyQdJGkLXnEeoWkN0n6l8x3Rbl91TbWzFXSqyU9AwwDfinp4f72V0TsBVYCU2rtw9L23ZLDd0n6WFU+90v6QCl0DrAKmAo8GhFro/B0RHw7In5T2o5Fkh7O/bpC0uj+cj5QEfHHiNgE/BXQQ1GkavlL4I6I+G3m/VhELKtMLOX8tKTN5W3PM9WfSromf/ePSPp3Gd+av6+OUvubJX1V0ppc3v+V9MZaSeXv9wuSfpN/z1+VdFROO17Sd3OdOyX9WJLf7/rgnTO0XAtcGxHHAG8CVmT8HflzZHal/Az4aL7eRXG0fDTwFQBJU4AbgA8DYymOcsdVrWs2cDswEvgmxdHvJ4HjgTOA6cBFVfOcDZwKTAM+DSwGPgJMAE4Czu9lu2rmGhHP5dE+FEf+b+p1zyRJo4A5wLr+2qalmWNl/pMp9sVdOT4WGAPcR3E0fWK+Mb5L0tFVy/pYrvs/AG8AdlGcORxSEfECcCfw73tpsg74r1ms3ypJVdMfznmPBT4H3FJ1lnE6cD9wHPAtYDlFgTmBYt99pWpffBi4guJvZSPF308tVwF/QVFkT6DY7/8zp30K6AbaKPb/ZwB/905fIsKvw/QFPAY8A+wuvZ4FflLV5t05/COKf9bjq5YzkeIfZXgptha4qDT+ZuCPwHCKf7hbS9NeAzxfWs9ngR/1k/snKI42K+MBnFkavxe4pDT+ReDLvSyr11xLyz6hj1wC2Jv77wXg18C4WvuwtH235PCRFG/ak3P8C8ANpbbzgZtK49MoinAP8AfgZuDonPYgML3Udmxpn7/sdwT8EPibXrbnpfyqt796WqnN3wFbelneMGAh8FPgOeC3QEcf+3MjMDuHP1peLvDWzGdMKfYUMDWHbwaWl6Ydnb+TCeVtAQT8HnhTqe0ZFGdeAJdTFLhef+9+vfzlM4PD35yIGFl5sf/Rdtl8iiOpX0vaIOm9fbR9A/B4afxxijelMTlta2VCRDxL8Q9dtrU8Iukv8rT9iew6+keKI7+yJ0vD/1pjvPpIup5c63VK7r8jgRuBH0s6sr+ZIuIPwG3AR7Ib4nzgG6UmlS6iSvt1EXFeRLRRHE2/A/gfOfmNwB3ZtbGboji8MMDtOFDjgJ21JkTECxFxfUScSXGmdyWwRNK/hZe6DDeW8j6Jl/9uq3+PRERfv9vy39YzmdcbqtJqozgIube03u9nHOB/A13AD7JralHfm28uBkNIRGyJiPOB1wNXA7dLei21T59/S/HmVPFvgH0U/9jbgfGVCdlPe1z16qrGb6Q44p4cRTfVZyiO7gZDX7kOSET8Efg6xcXdkzL8e4o3noo/q5ptKUXXxnTg2Si62ZB0BEWXz5pe1rUB+E5pPVuBWeXiHhFHRsS2gW7HQGQRex/w4/7aRsS/RsT1FGdDU7I//2vAxcBxWVB/xcH9bieUcjua4kL3b6va/I6iiLyltK+OjewWjOJ6zKci4s+B91N0c00/iJxe8VwMhhBJH5HUFhEvUnSJALxI0WXxIkV/e8WtwCclTcp/yH+kuAtlH8W1gPflhcARFF0P/f3zv46iK+YZSScC/3mQNqu/XAdE0jDgAoo3mkcyvBGYK+kISe3AB8vz5Jv/ixRdWeWzgrcD90dxURpJb5d0oaTX5/iJFG9UlesTXwWurFwwldQmafZAt6Fekobn0f2tFAXuS720+4Skd0o6KufpoPh93gdUDiZ6su0F/Km4Hahzcl+NoLh2sC4iXnammX/DXwOuKe3PcZLOzuH3Sjohr2/soTjDevEg83pFczEYWmYCm1TcYXMtMDeP9J6lOPX/aZ5yTwOWULyx/Qh4lKJ/+2MAUdyB8jGKC4HbKa5b7KDoT+7NfwP+E/A0xT/xbYO4Xb3mOgC/zP2yC+gAPhARlW6Tf6C44L6L4prLt2rMv4yiP/yWUuxcSl1EFAX4/cADua7vA3cA/yunX0txJ9MPJD1NUSROH+B21OOvcv17cn1PAadGRPXRd8WzFIXuCYoj8oXAf4yIRyJic077GcWZ2Fspri0cjG8Bl1F0D51K6QJ9lUsouoLWZdfj/6G4XgQwOcefydxuiIh7DjKvVzTlxRazA5ZH47spuoAebXI6TSFpHrAgIt5eim0GPphvmFYHSTcD3RHx983OZajxmYEdEEnvk/SavObwBeABirtuhhxJr6G4cL+4FBsBLHMhsMOFi4EdqNkUF/V+S3FKPjeG4Glm9lH3UHSRvNR9FBHPR8RVTUvMbIDcTWRmZj4zMDOz4oM5h6Xjjz8+Jk6c2Ow0zMwOG/fee+/v8gOP+zlsi8HEiRPp7OxsdhpmZocNSY/3Ns3dRGZm5mJgZmYuBmZmhouBmZnhYmBmZtRZDCR9UtImSb9S8bDwI/MbItdL6pJ0W378vvIoutsyvl7SxNJyLs34Q5VvF8z4zIx1+XvHzcwar99iIGkc8F+A9og4ieKpR3Mpvg//mog4geLbHOfnLPOBXRm/JttVHpU4F3gLxbdn3iBpWH5l8PXALIrnzp6fbc3MrEHq7SYaDhwlaTjFQz62A2dRfK89FA/3mJPDs3OcnD49v1N8NsXj7J7Lb7bsAk7LV1d+He7zFF+LfMi+w93MzPbXbzHIpyx9AfgNRRHYQ/F82t2lh4d086cHoo8jH1uX0/dQPAXrpXjVPL3F9yNpgaROSZ09PT31bJ+ZmdWh308gSxpFcaQ+ieI76/+Zopun4SJiMfk1we3t7f6GPbMhbuKiu5q27seuOrdp6z4U6ukmejfwaET05PNhvwOcCYzMbiMonodbeU7rNvIZpjn9WIonKb0Ur5qnt7iZmTVIPcXgN8C0fJCJKB76vRm4hz89C7YDuDOHV+Y4Of3u/J77lRTPkX21pEkU34H/c2ADMDnvThpBcZF55cFvmpmZ1avfbqKIWC/pduAXwD6Kh2AvBu4Clkv6fMZuylluAr4hqYviGaZzczmbJK2gKCT7gIUR8QKApIuB1RR3Ki3JZ+yamVmD1PWtpRFxGcUDqsseobgTqLrtH4AP9bKcKykevF4dX8XLHxxuZmYN5E8gm5mZi4GZmbkYmJkZLgZmZoaLgZmZ4WJgZma4GJiZGS4GZmaGi4GZmeFiYGZmuBiYmRkuBmZmhouBmZnhYmBmZrgYmJkZLgZmZoaLgZmZUUcxkPRmSRtLr72SPiFptKQ1krbkz1HZXpKuk9Ql6X5Jp5SW1ZHtt0jqKMVPlfRAznNdPmvZzMwapN9iEBEPRcTUiJgKnAo8C9wBLALWRsRkYG2OA8yieNj9ZGABcCOApNEUj848neJxmZdVCki2ubA038zB2DgzM6vPQLuJpgMPR8TjwGxgacaXAnNyeDawLArrgJGSxgJnA2siYmdE7ALWADNz2jERsS4iAlhWWpaZmTXAQIvBXODWHB4TEdtz+AlgTA6PA7aW5unOWF/x7hrx/UhaIKlTUmdPT88AUzczs97UXQwkjQDeD/xz9bQ8oo9BzKumiFgcEe0R0d7W1naoV2dmNmQM5MxgFvCLiHgyx5/MLh7y546MbwMmlOYbn7G+4uNrxM3MrEEGUgzO509dRAArgcodQR3AnaX4vLyraBqwJ7uTVgMzJI3KC8czgNU5ba+kaXkX0bzSsszMrAGG19NI0muB9wB/WwpfBayQNB94HDgv46uAc4AuijuPLgCIiJ2SrgA2ZLvLI2JnDl8E3AwcBXwvX2Zm1iB1FYOI+D1wXFXsKYq7i6rbBrCwl+UsAZbUiHcCJ9WTi5mZDT5/AtnMzFwMzMzMxcDMzHAxMDMzXAzMzAwXAzMzw8XAzMxwMTAzM1wMzMwMFwMzM8PFwMzMcDEwMzNcDMzMDBcDMzPDxcDMzHAxMDMzXAzMzIw6i4GkkZJul/RrSQ9KOkPSaElrJG3Jn6OyrSRdJ6lL0v2STiktpyPbb5HUUYqfKumBnOe6fBaymZk1SL1nBtcC34+IE4GTgQeBRcDaiJgMrM1xgFnA5HwtAG4EkDQauAw4HTgNuKxSQLLNhaX5Zh7cZpmZ2UD0WwwkHQu8A7gJICKej4jdwGxgaTZbCszJ4dnAsiisA0ZKGgucDayJiJ0RsQtYA8zMacdExLp8fvKy0rLMzKwB6jkzmAT0AP8k6T5JX5f0WmBMRGzPNk8AY3J4HLC1NH93xvqKd9eI70fSAkmdkjp7enrqSN3MzOpRTzEYDpwC3BgRbwN+z5+6hADII/oY/PReLiIWR0R7RLS3tbUd6tWZmQ0Z9RSDbqA7Itbn+O0UxeHJ7OIhf+7I6duACaX5x2esr/j4GnEzM2uQfotBRDwBbJX05gxNBzYDK4HKHUEdwJ05vBKYl3cVTQP2ZHfSamCGpFF54XgGsDqn7ZU0Le8imldalpmZNcDwOtt9DPimpBHAI8AFFIVkhaT5wOPAedl2FXAO0AU8m22JiJ2SrgA2ZLvLI2JnDl8E3AwcBXwvX2Zm1iB1FYOI2Ai015g0vUbbABb2spwlwJIa8U7gpHpyMTOzwedPIJuZmYuBmZm5GJiZGS4GZmaGi4GZmeFiYGZmuBiYmRkuBmZmhouBmZnhYmBmZrgYmJkZLgZmZoaLgZmZ4WJgZma4GJiZGS4GZmaGi4GZmVFnMZD0mKQHJG2U1Jmx0ZLWSNqSP0dlXJKuk9Ql6X5Jp5SW05Htt0jqKMVPzeV35bwa7A01M7PeDeTM4F0RMTUiKo+/XASsjYjJwNocB5gFTM7XAuBGKIoHcBlwOnAacFmlgGSbC0vzzTzgLTIzswE7mG6i2cDSHF4KzCnFl0VhHTBS0ljgbGBNROyMiF3AGmBmTjsmItbl85OXlZZlZmYNUG8xCOAHku6VtCBjYyJiew4/AYzJ4XHA1tK83RnrK95dI74fSQskdUrq7OnpqTN1MzPrz/A62709IrZJej2wRtKvyxMjIiTF4Kf3chGxGFgM0N7efsjXZ2Y2VNR1ZhAR2/LnDuAOij7/J7OLh/y5I5tvAyaUZh+fsb7i42vEzcysQfotBpJeK+l1lWFgBvArYCVQuSOoA7gzh1cC8/KuomnAnuxOWg3MkDQqLxzPAFbntL2SpuVdRPNKyzIzswaop5toDHBH3u05HPhWRHxf0gZghaT5wOPAedl+FXAO0AU8C1wAEBE7JV0BbMh2l0fEzhy+CLgZOAr4Xr7MzKxB+i0GEfEIcHKN+FPA9BrxABb2sqwlwJIa8U7gpDryNTOzQ8CfQDYzMxcDMzNzMTAzM1wMzMwMFwMzM8PFwMzMcDEwMzNcDMzMDBcDMzPDxcDMzHAxMDMzXAzMzAwXAzMzw8XAzMxwMTAzM1wMzMwMFwMzM2MAxUDSMEn3Sfpujk+StF5Sl6TbJI3I+KtzvCunTywt49KMPyTp7FJ8Zsa6JC0axO0zM7M6DOTM4OPAg6Xxq4FrIuIEYBcwP+PzgV0ZvybbIWkKMBd4CzATuCELzDDgemAWMAU4P9uamVmD1FUMJI0HzgW+nuMCzgJuzyZLgTk5PDvHyenTs/1sYHlEPBcRjwJdwGn56oqIRyLieWB5tjUzswap98zgy8CngRdz/Dhgd0Tsy/FuYFwOjwO2AuT0Pdn+pXjVPL3F9yNpgaROSZ09PT11pm5mZv3ptxhIei+wIyLubUA+fYqIxRHRHhHtbW1tzU7HzOwVY3gdbc4E3i/pHOBI4BjgWmCkpOF59D8e2JbttwETgG5Jw4FjgadK8YryPL3FzcysAfo9M4iISyNifERMpLgAfHdEfBi4B/hgNusA7szhlTlOTr87IiLjc/Nuo0nAZODnwAZgct6dNCLXsXJQts7MzOpSz5lBby4Blkv6PHAfcFPGbwK+IakL2Enx5k5EbJK0AtgM7AMWRsQLAJIuBlYDw4AlEbHpIPIyM7MBGlAxiIgfAj/M4Uco7gSqbvMH4EO9zH8lcGWN+Cpg1UByMTOzweNPIJuZmYuBmZm5GJiZGS4GZmaGi4GZmeFiYGZmHNznDMzMAJi46K5mp2AHyWcGZmbmYmBmZi4GZmaGi4GZmeFiYGZmuBiYmRkuBmZmhouBmZnhYmBmZrgYmJkZdRQDSUdK+rmkX0raJOlzGZ8kab2kLkm35fOLyWcc35bx9ZImlpZ1acYfknR2KT4zY12SFh2C7TQzsz7Uc2bwHHBWRJwMTAVmSpoGXA1cExEnALuA+dl+PrAr49dkOyRNoXge8luAmcANkoZJGgZcD8wCpgDnZ1szM2uQfotBFJ7J0SPyFcBZwO0ZXwrMyeHZOU5Ony5JGV8eEc9FxKNAF8UzlE8DuiLikYh4Hliebc3MrEHqumaQR/AbgR3AGuBhYHdE7Msm3cC4HB4HbAXI6XuA48rxqnl6i9fKY4GkTkmdPT099aRuZmZ1qKsYRMQLETEVGE9xJH/ioUyqjzwWR0R7RLS3tbU1IwUzs1ekAd1NFBG7gXuAM4CRkirPQxgPbMvhbcAEgJx+LPBUOV41T29xMzNrkHruJmqTNDKHjwLeAzxIURQ+mM06gDtzeGWOk9PvjojI+Ny822gSMBn4ObABmJx3J42guMi8chC2zczM6lTPk87GAkvzrp9XASsi4ruSNgPLJX0euA+4KdvfBHxDUhewk+LNnYjYJGkFsBnYByyMiBcAJF0MrAaGAUsiYtOgbaGZmfWr32IQEfcDb6sRf4Ti+kF1/A/Ah3pZ1pXAlTXiq4BVdeRrZmaHgD+BbGZmLgZmZuZiYGZmuBiYmRkuBmZmhouBmZnhYmBmZrgYmJkZLgZmZoaLgZmZ4WJgZma4GJiZGS4GZmaGi4GZmeFiYGZmuBiYmRkuBmZmRn3PQJ4g6R5JmyVtkvTxjI+WtEbSlvw5KuOSdJ2kLkn3SzqltKyObL9FUkcpfqqkB3Ke6yTpUGysmZnVVs+ZwT7gUxExBZgGLJQ0BVgErI2IycDaHAeYRfGw+8nAAuBGKIoHcBlwOsXjMi+rFJBsc2FpvpkHv2lmZlavfotBRGyPiF/k8NPAg8A4YDawNJstBebk8GxgWRTWASMljQXOBtZExM6I2AWsAWbmtGMiYl1EBLCstCwzM2uAAV0zkDQReBuwHhgTEdtz0hPAmBweB2wtzdadsb7i3TXitda/QFKnpM6enp6BpG5mZn2ouxhIOhr4NvCJiNhbnpZH9DHIue0nIhZHRHtEtLe1tR3q1ZmZDRl1FQNJR1AUgm9GxHcy/GR28ZA/d2R8GzChNPv4jPUVH18jbmZmDVLP3UQCbgIejIgvlSatBCp3BHUAd5bi8/KuomnAnuxOWg3MkDQqLxzPAFbntL2SpuW65pWWZWZmDTC8jjZnAn8NPCBpY8Y+A1wFrJA0H3gcOC+nrQLOAbqAZ4ELACJip6QrgA3Z7vKI2JnDFwE3A0cB38uXmZk1SL/FICJ+AvR23//0Gu0DWNjLspYAS2rEO4GT+svFzMwODX8C2czMXAzMzMzFwMzMcDEwMzNcDMzMDBcDMzPDxcDMzHAxMDMzXAzMzAwXAzMzw8XAzMxwMTAzM1wMzMwMFwMzM8PFwMzMcDEwMzNcDMzMjPqegbxE0g5JvyrFRktaI2lL/hyVcUm6TlKXpPslnVKapyPbb5HUUYqfKumBnOe6fA6ymZk1UD3PQL4Z+AqwrBRbBKyNiKskLcrxS4BZwOR8nQ7cCJwuaTRwGdAOBHCvpJURsSvbXAisp3h+8kz8DGSzAZu46K5mp2CHsX7PDCLiR8DOqvBsYGkOLwXmlOLLorAOGClpLHA2sCYidmYBWAPMzGnHRMS6fHbystKyzMysQQ70msGYiNiew08AY3J4HLC11K47Y33Fu2vEa5K0QFKnpM6enp4DTN3MzKod9AXkPKKPQcilnnUtjoj2iGhva2trxCrNzIaEAy0GT2YXD/lzR8a3ARNK7cZnrK/4+BpxMzNroAMtBiuByh1BHcCdpfi8vKtoGrAnu5NWAzMkjco7j2YAq3PaXknT8i6ieaVlmZlZg/R7N5GkW4F3AsdL6qa4K+gqYIWk+cDjwHnZfBVwDtAFPAtcABAROyVdAWzIdpdHROWi9EUUdywdRXEXke8kMjNrsH6LQUSc38uk6TXaBrCwl+UsAZbUiHcCJ/WXh5mZHTr+BLKZmbkYmJmZi4GZmeFiYGZmuBiYmRkuBmZmRn3fWmpmZlWa9S2xj1117iFZrs8MzMzMxcDMzFwMzMwMFwMzM8PFwMzMcDEwMzN8a6nZoPOD6e1w5DMDMzNzMTAzMxcDMzOjhYqBpJmSHpLUJWlRs/MxMxtKWuICsqRhwPXAe4BuYIOklRGxubmZ2cHyxVSzw0NLFAPgNKArIh4BkLQcmA24GAwSvymbWV9apRiMA7aWxruB06sbSVoALMjRZyQ9NIg5HA/8bhCX1wjOuTGcc2M45zro6oOa/Y29TWiVYlCXiFgMLD4Uy5bUGRHth2LZh4pzbgzn3BjOubla5QLyNmBCaXx8xszMrAFapRhsACZLmiRpBDAXWNnknMzMhoyW6CaKiH2SLgZWA8OAJRGxqcFpHJLup0PMOTeGc24M59xEiohm52BmZk3WKt1EZmbWRC4GZmY2NIuBpAmS7pG0WdImSR/P+GhJayRtyZ+jmp0r9JnvZyVtk7QxX+c0O9cKSUdK+rmkX2bOn8v4JEnr82tHbssbBlpCHznfLOnR0n6e2uRU9yNpmKT7JH03x1t2P1fUyLml97OkxyQ9kLl1Zqwl3zMOxJAsBsA+4FMRMQWYBiyUNAVYBKyNiMnA2hxvBb3lC3BNREzN16rmpbif54CzIuJkYCowU9I04GqKnE8AdgHzm5fifnrLGeC/l/bzxmYl2IePAw+Wxlt5P1dU5wytv5/flblVPlvQqu8ZAzYki0FEbI+IX+Tw0xR/kOMovgJjaTZbCsxpSoJV+si3ZUXhmRw9Il8BnAXcnvGW2cfQZ84tTdJ44Fzg6zkuWng/w/45H8Za8j3jQAzJYlAmaSLwNmA9MCYituekJ4AxzcqrN1X5Alws6X5JS1rtFDW7ATYCO4A1wMPA7ojYl026abGiVp1zRFT285W5n6+R9OrmZVjTl4FPAy/m+HG0+H5m/5wrWnk/B/ADSffmV+PAYfCeUa8hXQwkHQ18G/hEROwtT4vintuWOiqske+NwJsoujS2A19sXnb7i4gXImIqxSfKTwNObG5G/avOWdJJwKUUuf8lMBq4pHkZvpyk9wI7IuLeZudSrz5ybtn9nN4eEacAsyi6at9RntiK7xkDMWSLgaQjKN5YvxkR38nwk5LG5vSxFEeHLaFWvhHxZL55vQh8jeINt+VExG7gHuAMYKSkyocdW/ZrR0o5z8xuuoiI54B/orX285nA+yU9Biyn6B66ltbez/vlLOmWFt/PRMS2/LkDuIMiv5Z9zxioIVkMsk/1JuDBiPhSadJKoCOHO4A7G51bLb3lW/kjTB8AftXo3HojqU3SyBw+iuJZFQ9SvMF+MJu1zD6GXnP+demfXRR9wi2znyPi0ogYHxETKb7G5e6I+DAtvJ97yfkjrbyfJb1W0usqw8AMivxa8j3jQLTE11E0wZnAXwMPZP8wwGeAq4AVkuYDjwPnNSe9/fSW7/l5+10AjwF/24zkejEWWKriwUWvAlZExHclbQaWS/o8cB9FkWsVveV8t6Q2QMBG4O+amGO9LqF193NvvtnC+3kMcEdRpxgOfCsivi9pA635njFg/joKMzMbmt1EZmb2ci4GZmbmYmBmZi4GZmaGi4GZmeFiYGZmuBiYmRnw/wGlvJbCokhhUAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(buy_sell_uniswap_events['DAI_diff'].apply(np.log))\n",
    "plt.title('Histogram of Buy/Sell IID Samples')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribution fitting\n",
    "\n",
    "We take the log of liquidity data prior to fitting to make the trend more discernible. We fit both the liquidity and buy/sell univariate series to an alpha distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We take the log of liquidity data prior to fitting to make the trend more discernible \n",
    "#distribution, pvalue, params = get_best_distribution(liquidity_uniswap_events['DAI_diff'].apply(np.log).values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/georgekellerman/github/geb-sims/venv/lib/python3.8/site-packages/scipy/stats/_distn_infrastructure.py:2429: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  Lhat = muhat - Shat*mu\n"
     ]
    }
   ],
   "source": [
    "# fit liquidity to the alpha distribution.\n",
    "fit_shape_liquidity, fit_loc_liquidity, fit_scale_liquidity =st.alpha.fit(liquidity_uniswap_events['DAI_diff'].apply(np.log).values)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8760"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timesteps = 24 * 365 # 24 hours a day * 365 days a year \n",
    "timesteps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Liquidity IID Samples')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 8760 timestamp sample histogram\n",
    "liquidity = st.alpha.rvs(fit_shape_liquidity, loc=fit_loc_liquidity, scale=fit_scale_liquidity, size=timesteps)\n",
    "plt.hist(liquidity)\n",
    "plt.title('Histogram of Liquidity IID Samples')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Liquidity IID Samples against original data')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ek36550eSlkp6TNKoXNmJkpakv232p9zMbOuz0047MW/ePKZPn05NTQ2f+MQnmDFjBvfddx+jR49mv/32495772XhwoXvLHP88ccDsN9++7HvvvsyYMAAevbsyXve8x6WLct+jnjw4MGMGTMGgNNOO40HHnhgk+0+9NBDLFq0iDFjxnDAAQdw3XXX8eyzz/LEE08wZMgQhg4diiROO+20Tt3f9vTxzwB+TPZDze+QNBgYDzyXm/xhsh/pHgqMBn4CjM79Cn0d2c/pzZM0KyJeKncHzMw6Q7du3Rg7dixjx45lv/324+qrr+axxx5j7ty5DB48mIsuumiTe+Ybu4W22267d4Ybxzdu3Ahsfrtl0/GI4KijjuLmm2/eZPr8+fM7c9c202aLPyL+CLzYzKzLgfPIEnmjCcD1kXkI6CNpAPAhYHZEvJiS/Wzg6LKjNzPrBE8++SRLlix5Z3z+/Pnss88+QNbfv27dOmbOnNnh9T733HM8+OCDANx000184AMf2GT+IYccwp/+9CeWLl0KwN///neeeuophg0bRn19PU8//TTAZh8M5Srprh5JE4DlEfFok0+wgcCy3HhDmtbS9ObWPQmYBLDnnnuWEp6ZbeXac/tlZ1q3bh1f+MIXWLt2Ld27d2evvfZi+vTp9OnTh5EjR7L77rtz0EEHdXi9++yzD1dddRWf+cxnGDFiBJ///Oc3mV9TU8OMGTM49dRTeeONNwCYOnUqe++9N9OnT+fYY49lhx124LDDDuPVV1/tlH2Fdv7mrqRa4I6IGClpB+A+YHxEvCypHqiLiNWS7gAujYgH0nL3AOcDY4FeETE1Tf934LWIuKy17dbV1YV/iMWsC1T4ds7FixczfPjwLb6drlRfX89xxx3HggWbXR7tVM3VnaR5EdHilwRKuavnvcAQ4NGU9AcBj0jaHVgODM6VHZSmtTTdzMy6WIcTf0Q8HhH/FBG1EVFL1m0zKiJWArOAT6e7ew4BXo6IFcDvgPGS+krqS3ZR+HedtxtmZtWltrZ2i7f2S9We2zlvBh4E9pHUIOnMVorfCTwDLAV+CkwGiIgXgYuBOenv22mamZl1sTYv7kbEqW3Mr80NB3B2C+WuBa7tYHxmZtbJ/M1dM7OCceI3MysYP53TzKpPa7eXlqIdt6Q2NDRw9tlns2jRIt5++22OO+44vv/979OjR49Nyv3tb3/ji1/8Yptf6DrmmGO46aab6NOnT4fDveiii9hpp5346le/2uFl28MtfjMrvIjgxBNP5IQTTmDJkiU89dRTrFu3jq9//eublNu4cSN77LFHu77Fe+edd5aU9LuCE7+ZFd69995Lr169OOOMM4DsuT2XX3451157LdOmTeP444/niCOOYNy4cdTX1zNy5EgA1q9fz8knn8yIESP46Ec/yujRo2n80mltbS2rV6+mvr6e4cOHc9ZZZ7Hvvvsyfvx4XnvtNQB++tOfctBBB7H//vvzsY99rNnHNm8JTvxmVngLFy7kwAMP3GTazjvvzJ577snGjRt55JFHmDlz5juPa240bdo0+vbty6JFi7j44ouZN29es+tfsmQJZ599NgsXLqRPnz786le/AuDEE09kzpw5PProowwfPpxrrrlmy+xgE078ZmZtOOqoo9h11103m/7AAw9wyimnADBy5Eje9773Nbv8kCFDOOCAAwA48MADqa+vB2DBggUcdthh7Lffftx4442bPPZ5S3LiN7PCGzFixGat9VdeeYXnnnuO7t27s+OOO5a1/vxjm7t16/bOY5tPP/10fvzjH/P4449z4YUXbvLY5y3Jid/MCm/cuHGsX7+e66/Pfnbkrbfe4itf+Qqnn346O+ywQ4vLjRkzhltvvRWARYsW8fjjj3dou6+++ioDBgxgw4YN3HjjjaXvQAf5dk4zqz5d/APvkrjtttuYPHkyF198MW+//TbHHHMM3/nOd1p9Fv7kyZOZOHEiI0aMYNiwYey7777ssssu7d7uxRdfzOjRo6mpqWH06NGd+ujl1rTrscyV4scym3URP5a5JG+99RYbNmygV69ePP300xx55JE8+eSTm937vyWV8lhmt/jNzEq0fv16Dj/8cDZs2EBEMG3atC5N+qVy4jczK1Hv3r3ZGnslfHHXzKpCNXc7V6tS68yJ38wqrlevXqxZs8bJvwMigjVr1tCrV68OL+uuHjOruEGDBtHQ0MCqVasqHcpWpVevXgwaNKjDyznxm1nFbb/99gwZMqTSYRSGu3rMzArGid/MrGCc+M3MCqbNxC/pWkkvSFqQm/Z9SU9IekzSbZL65OZdIGmppCclfSg3/eg0bamkKZ2+J2Zm1i7tafHPAI5uMm02MDIi3gc8BVwAIGkEcAqwb1pmmqRukroBVwEfBkYAp6ayZmbWxdpM/BHxR+DFJtPujoiNafQhoPF+ognALRHxRkT8FVgKHJz+lkbEMxHxJnBLKmtmZl2sM/r4PwP8dxoeCCzLzWtI01qavhlJkyTNlTTX9/SamXW+shK/pK8DG4FOe5B0REyPiLqIqKupqems1ZqZWVLyF7gknQ4cB4yLf3zPejkwOFdsUJpGK9PNzKwLldTil3Q0cB5wfETkfxZ+FnCKpJ6ShgBDgT8Dc4ChkoZI6kF2AXhWeaGbmVkp2mzxS7oZGAv0l9QAXEh2F09PYLYkgIci4nMRsVDSrcAisi6gsyPirbSec4DfAd2AayOia35V2MzMNtFm4o+IU5uZfE0r5S8BLmlm+p3AnR2KzszMOp2/uWtmVjBO/GZmBePEb2ZWME78ZmYF48RvZlYw/gUuswKonfLbVufXf6jV2baNcYvfzKxgnPjNzArGid/MrGCc+M3MCsaJ38ysYJz4zcwKxonfzKxgfB+/mXHFPU+1OO/cw7swEOsSbvGbmRWME7+ZWcE48ZuZFYwTv5lZwTjxm5kVjBO/mVnBtJn4JV0r6QVJC3LTdpU0W9KS9L9vmi5JP5K0VNJjkkbllpmYyi+RNHHL7I6ZmbWlPS3+GcDRTaZNAe6JiKHAPWkc4MPA0PQ3CfgJZB8UwIXAaOBg4MLGDwszM+tabX6BKyL+KKm2yeQJwNg0fB1wP3B+mn59RATwkKQ+kgaksrMj4kUASbPJPkxuLn8XzKytH1oxyyu1j3+3iFiRhlcCu6XhgcCyXLmGNK2l6ZuRNEnSXElzV61aVWJ4ZmbWkrIf2RARISk6I5i0vunAdIC6urpOW6+ZlabNn2289NguisQ6S6kt/udTFw7p/wtp+nJgcK7coDStpelmZtbFSk38s4DGO3MmArfnpn863d1zCPBy6hL6HTBeUt90UXd8mmZmZl2sza4eSTeTXZztL6mB7O6cS4FbJZ0JPAucnIrfCRwDLAXWA2cARMSLki4G5qRy32680GtmZl2rPXf1nNrCrHHNlA3g7BbWcy1wbYeiMzOzTudv7pqZFYwTv5lZwTjxm5kVjBO/mVnBOPGbmRWME7+ZWcE48ZuZFYwTv5lZwTjxm5kVjBO/mVnBOPGbmRWME7+ZWcE48ZuZFYwTv5lZwTjxm5kVjBO/mVnBOPGbmRWME7+ZWcE48ZuZFUxZiV/SlyUtlLRA0s2SekkaIulhSUsl/VJSj1S2ZxpfmubXdsoemJlZh5Sc+CUNBL4I1EXESKAbcArwPeDyiNgLeAk4My1yJvBSmn55KmdmZl2s3K6e7sC7JHUHdgBWAEcAM9P864AT0vCENE6aP06Syty+mZl1UMmJPyKWA5cBz5El/JeBecDaiNiYijUAA9PwQGBZWnZjKt+v6XolTZI0V9LcVatWlRqemZm1oJyunr5krfghwB7AjsDR5QYUEdMjoi4i6mpqaspdnZmZNVFOV8+RwF8jYlVEbAB+DYwB+qSuH4BBwPI0vBwYDJDm7wKsKWP7ZmZWgu5tF2nRc8AhknYAXgPGAXOB+4CTgFuAicDtqfysNP5gmn9vREQZ2zcrjNopvy1r+XO7z2y7kBVGOX38D5NdpH0EeDytazpwPvBvkpaS9eFfkxa5BuiXpv8bMKWMuM3MrETltPiJiAuBC5tMfgY4uJmyrwMfL2d7ZmZWPn9z18ysYMpq8ZuZtXX9of7SY7soEmsvt/jNzArGid/MrGCc+M3MCsaJ38ysYJz4zcwKxonfzKxgnPjNzArGid/MrGCc+M3MCsaJ38ysYJz4zcwKxonfzKxgnPjNzArGid/MrGCc+M3MCsaJ38ysYJz4zcwKxonfzKxgykr8kvpIminpCUmLJR0qaVdJsyUtSf/7prKS9CNJSyU9JmlU5+yCmZl1RLkt/iuBuyJiGLA/sBiYAtwTEUOBe9I4wIeBoelvEvCTMrdtZmYlKDnxS9oF+CBwDUBEvBkRa4EJwHWp2HXACWl4AnB9ZB4C+kgaUOr2zcysNOW0+IcAq4CfS/qLpJ9J2hHYLSJWpDIrgd3S8EBgWW75hjRtE5ImSZorae6qVavKCM/MzJrTvcxlRwFfiIiHJV3JP7p1AIiIkBQdWWlETAemA9TV1XVoWbOtVe2U31Y6hBad231mq/Ov2HhSF0VinaWcxN8ANETEw2l8Jlnif17SgIhYkbpyXkjzlwODc8sPStPMbBvW1oda/aXHdlEk1qjkrp6IWAksk7RPmjQOWATMAiamaROB29PwLODT6e6eQ4CXc11CZmbWRcpp8QN8AbhRUg/gGeAMsg+TWyWdCTwLnJzK3gkcAywF1qeyZmbWxcpK/BExH6hrZta4ZsoGcHY52zMzs/L5m7tmZgXjxG9mVjBO/GZmBePEb2ZWME78ZmYF48RvZlYwTvxmZgVT7he4zKzg/CyfrY9b/GZmBePEb2ZWME78ZmYF48RvZlYwTvxmZgXjxG9mVjBO/GZmBePEb2ZWMP4Cl9k2oK0vUZnlucVvZlYwTvxmZgVTdlePpG7AXGB5RBwnaQhwC9APmAd8KiLelNQTuB44EFgDfCIi6svdvtnWonbKbysdghnQOS3+LwGLc+PfAy6PiL2Al4Az0/QzgZfS9MtTOTMz62JlJX5Jg4BjgZ+lcQFHAI1Xmq4DTkjDE9I4af64VN7MzLpQuV09VwDnAb3TeD9gbURsTOMNwMA0PBBYBhARGyW9nMqvLjMGM9uKtdUFVn/psV0USXGU3OKXdBzwQkTM68R4kDRJ0lxJc1etWtWZqzYzM8rr6hkDHC+pnuxi7hHAlUAfSY1nEoOA5Wl4OTAYIM3fhewi7yYiYnpE1EVEXU1NTRnhmZlZc0pO/BFxQUQMioha4BTg3oj4JHAf0PiTOxOB29PwrDROmn9vRESp2zczs9Jsifv4zwf+TdJSsj78a9L0a4B+afq/AVO2wLbNzKwNnfLIhoi4H7g/DT8DHNxMmdeBj3fG9szMrHT+5q6ZWcH4IW1mtkW19QC5Kzae1Op863xu8ZuZFYwTv5lZwTjxm5kVjBO/mVnB+OKu2VbAv7BlncktfjOzgnHiNzMrGCd+M7OCceI3MysYJ34zs4Jx4jczKxgnfjOzgvF9/GZVwPfpW1dy4jezqtbaj7H7h9hL464eM7OCceI3MysYd/WYdZLWuiSsZf6hlq7nFr+ZWcGUnPglDZZ0n6RFkhZK+lKavquk2ZKWpP9903RJ+pGkpZIekzSqs3bCzMzar5wW/0bgKxExAjgEOFvSCGAKcE9EDAXuSeMAHwaGpr9JwE/K2LaZmZWo5MQfESsi4pE0/CqwGBgITACuS8WuA05IwxOA6yPzENBH0oBSt29mZqXplIu7kmqB9wMPA7tFxIo0ayWwWxoeCCzLLdaQpq3ITUPSJLIzAvbcc8/OCM+sKvhLWlYtyr64K2kn4FfAuRHxSn5eRAQQHVlfREyPiLqIqKupqSk3PDMza6KsxC9pe7Kkf2NE/DpNfr6xCyf9fyFNXw4Mzi0+KE0zM7MuVM5dPQKuARZHxA9zs2YBE9PwROD23PRPp7t7DgFeznUJmZlZFymnj38M8CngcUnz07SvAZcCt0o6E3gWODnNuxM4BlgKrAfOKGPbZmZWopITf0Q8AKiF2eOaKR/A2aVuz8zMOocf2WBmW622HpPhp3c2z49sMDMrGLf4zayqtfb9Bz/ArTRu8ZuZFYxb/Gbt5Mcu27bCLX4zs4Jx4jczKxgnfjOzgnHiNzMrGCd+M7OC8V09ZrbN8jd7m+cWv5lZwTjxm5kVjLt6zNqprZ9O9OMDbGvhFr+ZWcG4xW/WSfxj6lufol78dYvfzKxg3OI3S9pq/Z3ro6Xq+LpLadziNzMrGLdhzMxasK1eA+jyxC/paOBKoBvws4i4tKtjsIK677ttFHhfl4RhXcddQc3r0sQvqRtwFXAU0ADMkTQrIhZ1ZRxbvbYS2OEXdE0c1aiVurninqdaXfTc7q3PN9tWdHWL/2BgaUQ8AyDpFmACULzE32brs4Kq+YOlmuvNCqe1rqBq7gZSRHTdxqSTgKMj4rNp/FPA6Ig4J1dmEjApje4DPFnGJvsDq8tYfktybKVxbKVxbKXZWmN7d0TUtLRg1V3cjYjpwPTOWJekuRFR1xnr6myOrTSOrTSOrTTbamxdfTvncmBwbnxQmmZmZl2kqxP/HGCopCGSegCnALO6OAYzs0Lr0q6eiNgo6Rzgd2S3c14bEQu34CY7pctoC3FspXFspXFspdkmY+vSi7tmZlZ5fmSDmVnBOPGbmRXMNpH4JQ2WdJ+kRZIWSvpSmr6rpNmSlqT/fasotoskLZc0P/0dU4HYekn6s6RHU2zfStOHSHpY0lJJv0wX4qslthmS/pqrtwO6OrZcjN0k/UXSHWm84vXWSmxVUW+S6iU9nmKYm6ZV/DhtJbaKH6cpjj6SZkp6QtJiSYeWU2/bROIHNgJfiYgRwCHA2ZJGAFOAeyJiKHBPGq+W2AAuj4gD0t+dFYjtDeCIiNgfOAA4WtIhwPdSbHsBLwFnVlFsAP87V2/zKxBboy8Bi3Pj1VBvjZrGBtVTb4enGBrvQa+G47RR09ig8scpZM83uysihgH7k722JdfbNpH4I2JFRDyShl8lq5SBZI+DuC4Vuw44oYpiq7jIrEuj26e/AI4AGp9uVal6aym2qiBpEHAs8LM0Lqqg3pqLbStQ8eO0mknaBfggcA1ARLwZEWspo962icSfJ6kWeD/wMLBbRKxIs1YCu1UqLtgsNoBzJD0m6doKnt52kzQfeAGYDTwNrI2IjalIAxX6oGoaW0Q01tslqd4ul9SzErEBVwDnAW+n8X5USb2xeWyNqqHeArhb0rz0eBaonuO0udig8sfpEGAV8PPUffczSTtSRr1tU4lf0k7Ar4BzI+KV/LzI7lutWIuxmdh+AryXrBtjBfCDSsQVEW9FxAFk36I+GBhWiTia0zQ2SSOBC8hiPAjYFTi/q+OSdBzwQkTM6+ptt6WV2Cpeb8kHImIU8GGybs8P5mdW+DhtLrZqOE67A6OAn0TE+4G/06Rbp6P1ts0kfknbkyXWGyPi12ny85IGpPkDyFqOVRFbRDyfEtvbwE/Jkm7FpFPH+4BDgT6SGr/cV/HHauRiOzp1nUVEvAH8nMrU2xjgeEn1wC1kXTxXUh31tllskm6oknojIpan/y8At6U4quI4bS62KjlOG4CG3BnvTLIPgpLrbZtI/Kl/9RpgcUT8MDdrFjAxDU8Ebq+W2BpfsOSjwIIKxFYjqU8afhfZ7yQsJkuyjb9QUal6ay62J3JvdJH1aXZ5vUXEBRExKCJqyR47cm9EfJIqqLcWYjutGupN0o6SejcOA+NTHNVwnDYbWzUcpxGxElgmaZ80aRzZo+xLrreqezpnicYAnwIeT33CAF8DLgVulXQm8CxwchXFdmq6pS6AeuBfKxDbAOA6ZT+Qsx1wa0TcIWkRcIukqcBfSBeVqiS2eyXVAALmA5+rQGwtOZ/K11tLbqyCetsNuC377KE7cFNE3CVpDpU/TluK7RdVcJwCfIHsNewBPAOcQTouSqk3P7LBzKxgtomuHjMzaz8nfjOzgnHiNzMrGCd+M7OCceI3MysYJ34zs4Jx4jczK5j/D/4q6hX2tVylAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(liquidity,bins=np.arange(20, 60),label='Sampled')\n",
    "plt.hist(liquidity_uniswap_events['DAI_diff'].apply(np.log),alpha=0.5,bins=np.arange(20, 60),label='Original')\n",
    "plt.legend()\n",
    "plt.title('Histogram of Liquidity IID Samples against original data')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# hist,bins = np.histogram(liquidity,bins=50)\n",
    "# hist_original, bins = np.histogram(liquidity_uniswap_events['DAI_diff'].apply(np.log),bins=50) \n",
    "# kl_divergence(hist,hist_original)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Time Series of Liquidity IID Samples')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(liquidity)\n",
    "plt.title('Time Series of Liquidity IID Samples')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# export liquidity series\n",
    "liquidity_samples = pd.DataFrame(np.exp(liquidity),columns=['Liquidity_Samples'])\n",
    "liquidity_samples.to_csv('data/liquidity_samples.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fit buy/sell series distribution\n",
    "#distribution, pvalue, params = get_best_distribution(buy_sell_uniswap_events['DAI_diff'].apply(np.log).values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/georgekellerman/github/geb-sims/venv/lib/python3.8/site-packages/scipy/stats/_distn_infrastructure.py:2429: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  Lhat = muhat - Shat*mu\n"
     ]
    }
   ],
   "source": [
    "# Fit buy/sell series\n",
    "fit_shape_buy_sell, fit_loc_buy_sell, fit_scale_buy_sell = st.alpha.fit(buy_sell_uniswap_events['DAI_diff'].apply(np.log).values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Buy Sell IID Samples')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "buy_sell = st.alpha.rvs(fit_shape_buy_sell, loc=fit_loc_buy_sell, scale=fit_scale_buy_sell, size=timesteps)\n",
    "\n",
    "plt.hist(buy_sell)\n",
    "plt.title('Histogram of Buy Sell IID Samples')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Time Series of Buy Sell IID Samples')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(buy_sell)\n",
    "plt.title('Time Series of Buy Sell IID Samples')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Buy/Sell IID Samples against original data')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(buy_sell,bins=np.arange(25, 60),label='Sampled')\n",
    "plt.hist(buy_sell_uniswap_events['DAI_diff'].apply(np.log),alpha=0.3,bins=np.arange(25, 60),label='Original')\n",
    "plt.legend()\n",
    "plt.title('Histogram of Buy/Sell IID Samples against original data')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Export buy/sell time series\n",
    "buy_sell_samples = pd.DataFrame(np.exp(buy_sell),columns=['Buy_Sell_Samples'])\n",
    "buy_sell_samples.to_csv('data/buy_sell.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate Monte Carlo runs\n",
    "### Buy/Sell Events"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.163837e+20</td>\n",
       "      <td>7.570096e+19</td>\n",
       "      <td>8.813644e+19</td>\n",
       "      <td>2.198650e+20</td>\n",
       "      <td>6.232496e+22</td>\n",
       "      <td>1.347115e+19</td>\n",
       "      <td>8.298759e+21</td>\n",
       "      <td>1.797504e+18</td>\n",
       "      <td>5.966618e+21</td>\n",
       "      <td>1.346515e+17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.066745e+20</td>\n",
       "      <td>9.524847e+20</td>\n",
       "      <td>3.927835e+17</td>\n",
       "      <td>8.480389e+20</td>\n",
       "      <td>2.136511e+20</td>\n",
       "      <td>5.716574e+21</td>\n",
       "      <td>3.747493e+19</td>\n",
       "      <td>1.757802e+21</td>\n",
       "      <td>6.695430e+22</td>\n",
       "      <td>1.487759e+20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.359949e+20</td>\n",
       "      <td>2.842199e+15</td>\n",
       "      <td>2.178659e+20</td>\n",
       "      <td>2.611943e+19</td>\n",
       "      <td>8.281983e+22</td>\n",
       "      <td>1.147204e+19</td>\n",
       "      <td>2.857650e+21</td>\n",
       "      <td>8.985252e+19</td>\n",
       "      <td>5.580330e+21</td>\n",
       "      <td>1.417418e+20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.096584e+20</td>\n",
       "      <td>2.893552e+19</td>\n",
       "      <td>8.766407e+19</td>\n",
       "      <td>1.597450e+20</td>\n",
       "      <td>9.034470e+20</td>\n",
       "      <td>1.388867e+22</td>\n",
       "      <td>7.349695e+17</td>\n",
       "      <td>9.818634e+20</td>\n",
       "      <td>1.873847e+20</td>\n",
       "      <td>4.734081e+18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7.984484e+19</td>\n",
       "      <td>5.644476e+18</td>\n",
       "      <td>7.776507e+19</td>\n",
       "      <td>8.311794e+21</td>\n",
       "      <td>7.692858e+20</td>\n",
       "      <td>1.336992e+20</td>\n",
       "      <td>3.190944e+18</td>\n",
       "      <td>1.136845e+23</td>\n",
       "      <td>1.502757e+19</td>\n",
       "      <td>5.305190e+18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8756</th>\n",
       "      <td>4.679528e+20</td>\n",
       "      <td>2.584568e+20</td>\n",
       "      <td>1.725249e+19</td>\n",
       "      <td>1.489461e+19</td>\n",
       "      <td>2.078494e+17</td>\n",
       "      <td>4.467655e+21</td>\n",
       "      <td>1.613780e+21</td>\n",
       "      <td>1.910166e+21</td>\n",
       "      <td>1.761497e+20</td>\n",
       "      <td>2.635811e+18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8757</th>\n",
       "      <td>2.657090e+19</td>\n",
       "      <td>1.841770e+22</td>\n",
       "      <td>2.962791e+18</td>\n",
       "      <td>3.157576e+21</td>\n",
       "      <td>4.562168e+21</td>\n",
       "      <td>6.210070e+20</td>\n",
       "      <td>5.399060e+21</td>\n",
       "      <td>2.281226e+19</td>\n",
       "      <td>2.342377e+20</td>\n",
       "      <td>2.255422e+21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8758</th>\n",
       "      <td>8.502123e+20</td>\n",
       "      <td>1.871972e+19</td>\n",
       "      <td>1.428931e+18</td>\n",
       "      <td>7.997419e+18</td>\n",
       "      <td>1.032074e+19</td>\n",
       "      <td>3.389267e+20</td>\n",
       "      <td>9.127109e+19</td>\n",
       "      <td>1.402440e+17</td>\n",
       "      <td>1.079209e+21</td>\n",
       "      <td>3.437831e+21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8759</th>\n",
       "      <td>1.287900e+22</td>\n",
       "      <td>5.300630e+20</td>\n",
       "      <td>8.547005e+19</td>\n",
       "      <td>5.302657e+21</td>\n",
       "      <td>1.488332e+19</td>\n",
       "      <td>4.456376e+18</td>\n",
       "      <td>2.894623e+21</td>\n",
       "      <td>4.479710e+19</td>\n",
       "      <td>5.516330e+20</td>\n",
       "      <td>2.382547e+20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8760</th>\n",
       "      <td>8.526412e+17</td>\n",
       "      <td>1.783823e+21</td>\n",
       "      <td>4.998620e+20</td>\n",
       "      <td>5.859993e+21</td>\n",
       "      <td>9.114547e+20</td>\n",
       "      <td>5.907238e+20</td>\n",
       "      <td>7.437359e+20</td>\n",
       "      <td>1.413708e+21</td>\n",
       "      <td>4.892763e+19</td>\n",
       "      <td>1.392639e+21</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8761 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0             1             2             3             4  \\\n",
       "0     2.163837e+20  7.570096e+19  8.813644e+19  2.198650e+20  6.232496e+22   \n",
       "1     9.066745e+20  9.524847e+20  3.927835e+17  8.480389e+20  2.136511e+20   \n",
       "2     3.359949e+20  2.842199e+15  2.178659e+20  2.611943e+19  8.281983e+22   \n",
       "3     2.096584e+20  2.893552e+19  8.766407e+19  1.597450e+20  9.034470e+20   \n",
       "4     7.984484e+19  5.644476e+18  7.776507e+19  8.311794e+21  7.692858e+20   \n",
       "...            ...           ...           ...           ...           ...   \n",
       "8756  4.679528e+20  2.584568e+20  1.725249e+19  1.489461e+19  2.078494e+17   \n",
       "8757  2.657090e+19  1.841770e+22  2.962791e+18  3.157576e+21  4.562168e+21   \n",
       "8758  8.502123e+20  1.871972e+19  1.428931e+18  7.997419e+18  1.032074e+19   \n",
       "8759  1.287900e+22  5.300630e+20  8.547005e+19  5.302657e+21  1.488332e+19   \n",
       "8760  8.526412e+17  1.783823e+21  4.998620e+20  5.859993e+21  9.114547e+20   \n",
       "\n",
       "                 5             6             7             8             9  \n",
       "0     1.347115e+19  8.298759e+21  1.797504e+18  5.966618e+21  1.346515e+17  \n",
       "1     5.716574e+21  3.747493e+19  1.757802e+21  6.695430e+22  1.487759e+20  \n",
       "2     1.147204e+19  2.857650e+21  8.985252e+19  5.580330e+21  1.417418e+20  \n",
       "3     1.388867e+22  7.349695e+17  9.818634e+20  1.873847e+20  4.734081e+18  \n",
       "4     1.336992e+20  3.190944e+18  1.136845e+23  1.502757e+19  5.305190e+18  \n",
       "...            ...           ...           ...           ...           ...  \n",
       "8756  4.467655e+21  1.613780e+21  1.910166e+21  1.761497e+20  2.635811e+18  \n",
       "8757  6.210070e+20  5.399060e+21  2.281226e+19  2.342377e+20  2.255422e+21  \n",
       "8758  3.389267e+20  9.127109e+19  1.402440e+17  1.079209e+21  3.437831e+21  \n",
       "8759  4.456376e+18  2.894623e+21  4.479710e+19  5.516330e+20  2.382547e+20  \n",
       "8760  5.907238e+20  7.437359e+20  1.413708e+21  4.892763e+19  1.392639e+21  \n",
       "\n",
       "[8761 rows x 10 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monte_carlo_runs = 10\n",
    "\n",
    "buy_sell_mc = {}\n",
    "for run in range(0, monte_carlo_runs):\n",
    "    np.random.seed(seed=run)\n",
    "    \n",
    "    buy_sell = st.alpha.rvs(fit_shape_buy_sell, loc=fit_loc_buy_sell, scale=fit_scale_buy_sell, size=timesteps + 1)\n",
    "    buy_sell_mc[run] = np.exp(buy_sell)\n",
    "\n",
    "buy_sell_mc_df = pd.DataFrame(buy_sell_mc)\n",
    "buy_sell_mc_df.to_csv('data/buy_sell_mc.csv')\n",
    "buy_sell_mc_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Liquidity Demand Events"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.446570e+20</td>\n",
       "      <td>5.060642e+19</td>\n",
       "      <td>5.890844e+19</td>\n",
       "      <td>1.469880e+20</td>\n",
       "      <td>4.399110e+22</td>\n",
       "      <td>9.066131e+18</td>\n",
       "      <td>5.685084e+21</td>\n",
       "      <td>1.232147e+18</td>\n",
       "      <td>4.072046e+21</td>\n",
       "      <td>9.608383e+16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6.092140e+20</td>\n",
       "      <td>6.401730e+20</td>\n",
       "      <td>2.750487e+17</td>\n",
       "      <td>5.696066e+20</td>\n",
       "      <td>1.428276e+20</td>\n",
       "      <td>3.899577e+21</td>\n",
       "      <td>2.509532e+19</td>\n",
       "      <td>1.186215e+21</td>\n",
       "      <td>4.731910e+22</td>\n",
       "      <td>9.942340e+19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.248305e+20</td>\n",
       "      <td>2.227779e+15</td>\n",
       "      <td>1.456495e+20</td>\n",
       "      <td>1.751596e+19</td>\n",
       "      <td>5.875952e+22</td>\n",
       "      <td>7.728828e+18</td>\n",
       "      <td>1.936087e+21</td>\n",
       "      <td>6.005428e+19</td>\n",
       "      <td>3.805645e+21</td>\n",
       "      <td>9.472088e+19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.401546e+20</td>\n",
       "      <td>1.939591e+19</td>\n",
       "      <td>5.859305e+19</td>\n",
       "      <td>1.067579e+20</td>\n",
       "      <td>6.070333e+20</td>\n",
       "      <td>9.576679e+21</td>\n",
       "      <td>5.097682e+17</td>\n",
       "      <td>6.600342e+20</td>\n",
       "      <td>1.252471e+20</td>\n",
       "      <td>3.212041e+18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.337269e+19</td>\n",
       "      <td>3.823693e+18</td>\n",
       "      <td>5.198430e+19</td>\n",
       "      <td>5.694120e+21</td>\n",
       "      <td>5.164459e+20</td>\n",
       "      <td>8.934512e+19</td>\n",
       "      <td>2.173399e+18</td>\n",
       "      <td>8.114506e+22</td>\n",
       "      <td>1.010680e+19</td>\n",
       "      <td>3.595819e+18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8756</th>\n",
       "      <td>3.134647e+20</td>\n",
       "      <td>1.728379e+20</td>\n",
       "      <td>1.159388e+19</td>\n",
       "      <td>1.001792e+19</td>\n",
       "      <td>1.471312e+17</td>\n",
       "      <td>3.039753e+21</td>\n",
       "      <td>1.088342e+21</td>\n",
       "      <td>1.289848e+21</td>\n",
       "      <td>1.177303e+20</td>\n",
       "      <td>1.798927e+18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8757</th>\n",
       "      <td>1.781737e+19</td>\n",
       "      <td>1.274916e+22</td>\n",
       "      <td>2.019563e+18</td>\n",
       "      <td>2.141212e+21</td>\n",
       "      <td>3.104720e+21</td>\n",
       "      <td>4.164730e+20</td>\n",
       "      <td>3.680720e+21</td>\n",
       "      <td>1.530776e+19</td>\n",
       "      <td>1.566129e+20</td>\n",
       "      <td>1.524994e+21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8758</th>\n",
       "      <td>5.710743e+20</td>\n",
       "      <td>1.257423e+19</td>\n",
       "      <td>9.822530e+17</td>\n",
       "      <td>5.402075e+18</td>\n",
       "      <td>6.958269e+18</td>\n",
       "      <td>2.267978e+20</td>\n",
       "      <td>6.100148e+19</td>\n",
       "      <td>9.999709e+16</td>\n",
       "      <td>7.258801e+20</td>\n",
       "      <td>2.333095e+21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8759</th>\n",
       "      <td>8.871576e+21</td>\n",
       "      <td>3.552415e+20</td>\n",
       "      <td>5.712817e+19</td>\n",
       "      <td>3.614305e+21</td>\n",
       "      <td>1.001037e+19</td>\n",
       "      <td>3.025323e+18</td>\n",
       "      <td>1.961360e+21</td>\n",
       "      <td>2.998160e+19</td>\n",
       "      <td>3.697581e+20</td>\n",
       "      <td>1.593035e+20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8760</th>\n",
       "      <td>5.901392e+17</td>\n",
       "      <td>1.203907e+21</td>\n",
       "      <td>3.349233e+20</td>\n",
       "      <td>3.998489e+21</td>\n",
       "      <td>6.124439e+20</td>\n",
       "      <td>3.960761e+20</td>\n",
       "      <td>4.992081e+20</td>\n",
       "      <td>9.525248e+20</td>\n",
       "      <td>3.273795e+19</td>\n",
       "      <td>9.382326e+20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8761 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0             1             2             3             4  \\\n",
       "0     1.446570e+20  5.060642e+19  5.890844e+19  1.469880e+20  4.399110e+22   \n",
       "1     6.092140e+20  6.401730e+20  2.750487e+17  5.696066e+20  1.428276e+20   \n",
       "2     2.248305e+20  2.227779e+15  1.456495e+20  1.751596e+19  5.875952e+22   \n",
       "3     1.401546e+20  1.939591e+19  5.859305e+19  1.067579e+20  6.070333e+20   \n",
       "4     5.337269e+19  3.823693e+18  5.198430e+19  5.694120e+21  5.164459e+20   \n",
       "...            ...           ...           ...           ...           ...   \n",
       "8756  3.134647e+20  1.728379e+20  1.159388e+19  1.001792e+19  1.471312e+17   \n",
       "8757  1.781737e+19  1.274916e+22  2.019563e+18  2.141212e+21  3.104720e+21   \n",
       "8758  5.710743e+20  1.257423e+19  9.822530e+17  5.402075e+18  6.958269e+18   \n",
       "8759  8.871576e+21  3.552415e+20  5.712817e+19  3.614305e+21  1.001037e+19   \n",
       "8760  5.901392e+17  1.203907e+21  3.349233e+20  3.998489e+21  6.124439e+20   \n",
       "\n",
       "                 5             6             7             8             9  \n",
       "0     9.066131e+18  5.685084e+21  1.232147e+18  4.072046e+21  9.608383e+16  \n",
       "1     3.899577e+21  2.509532e+19  1.186215e+21  4.731910e+22  9.942340e+19  \n",
       "2     7.728828e+18  1.936087e+21  6.005428e+19  3.805645e+21  9.472088e+19  \n",
       "3     9.576679e+21  5.097682e+17  6.600342e+20  1.252471e+20  3.212041e+18  \n",
       "4     8.934512e+19  2.173399e+18  8.114506e+22  1.010680e+19  3.595819e+18  \n",
       "...            ...           ...           ...           ...           ...  \n",
       "8756  3.039753e+21  1.088342e+21  1.289848e+21  1.177303e+20  1.798927e+18  \n",
       "8757  4.164730e+20  3.680720e+21  1.530776e+19  1.566129e+20  1.524994e+21  \n",
       "8758  2.267978e+20  6.100148e+19  9.999709e+16  7.258801e+20  2.333095e+21  \n",
       "8759  3.025323e+18  1.961360e+21  2.998160e+19  3.697581e+20  1.593035e+20  \n",
       "8760  3.960761e+20  4.992081e+20  9.525248e+20  3.273795e+19  9.382326e+20  \n",
       "\n",
       "[8761 rows x 10 columns]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monte_carlo_runs = 10\n",
    "\n",
    "liquidity_mc = {}\n",
    "for run in range(0, monte_carlo_runs):\n",
    "    np.random.seed(seed=run)\n",
    "    \n",
    "    liquidity = st.alpha.rvs(fit_shape_liquidity, loc=fit_loc_liquidity, scale=fit_scale_liquidity, size=timesteps + 1)\n",
    "    liquidity_mc[run] = np.exp(liquidity)\n",
    "\n",
    "liquidity_mc_df = pd.DataFrame(liquidity_mc)\n",
    "liquidity_mc_df.to_csv('data/liquidity_mc.csv')\n",
    "liquidity_mc_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation information\n",
    "Below is an example of how to integrate these univariate time series datasets into the exogenous process section of a cadCAD model, assuming each timestep is an hour."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "# exogenousProcesses.py\n",
    "\n",
    "# import libraries\n",
    "import pandas as pd\n",
    "\n",
    "# import data\n",
    "liquidity_samples = pd.read_csv('data/liquidity_samples.csv')\n",
    "buy_sell_samples = pd.read_csv('data/buy_sell.csv')\n",
    "\n",
    "# mechanisms\n",
    "def liquidity_exogenous_process(params, step, sL, s, _input):\n",
    "    y = 'liquidity'\n",
    "    timestep = s['timestep'] \n",
    "    x = liquidity_samples.Liquidity_Samples.values[timestep]\n",
    "    return (y, x)\n",
    "    \n",
    "def buy_sell_exogenous_process(params, step, sL, s, _input):\n",
    "    y = 'buy_sell'\n",
    "    timestep = s['timestep'] \n",
    "    x = buy_sell_samples.Buy_Sell_Samples.values[timestep]\n",
    "    return (y, x)\n",
    "    \n",
    "```"
   ]
  }
 ],
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}