notebooks/Stochastic_Generators/Eth_Exogenous_Process_Modeling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exogenous Process modeling \n",
    "\n",
    "## ETH price stochastic process\n",
    "\n",
    "1. Acquire time series of tick-by-tick (or as-close-as) data for ETH price e.g. 2017-2020, e.g. [Kaggle Hourly Dataset](https://www.kaggle.com/prasoonkottarathil/ethereum-historical-dataset)\n",
    "2. Fit a parametric distribution to the price of ETH, gamma + Kalman fit (prediction) resulting in a distribution $F^p_{ETH}(t; \\mu_{ETH})$ and fitted parameters $\\mu_{ETH}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy.stats import gamma\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": "markdown",
   "metadata": {},
   "source": [
    "## Data preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unix Timestamp</th>\n",
       "      <th>Date</th>\n",
       "      <th>Symbol</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1586995200000</td>\n",
       "      <td>2020-04-16 00:00:00</td>\n",
       "      <td>ETHUSD</td>\n",
       "      <td>152.94</td>\n",
       "      <td>152.94</td>\n",
       "      <td>150.39</td>\n",
       "      <td>150.39</td>\n",
       "      <td>650.188125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1586991600000</td>\n",
       "      <td>2020-04-15 23:00:00</td>\n",
       "      <td>ETHUSD</td>\n",
       "      <td>155.81</td>\n",
       "      <td>155.81</td>\n",
       "      <td>151.39</td>\n",
       "      <td>152.94</td>\n",
       "      <td>4277.567299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1586988000000</td>\n",
       "      <td>2020-04-15 22:00:00</td>\n",
       "      <td>ETHUSD</td>\n",
       "      <td>157.18</td>\n",
       "      <td>157.30</td>\n",
       "      <td>155.32</td>\n",
       "      <td>155.81</td>\n",
       "      <td>106.337279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1586984400000</td>\n",
       "      <td>2020-04-15 21:00:00</td>\n",
       "      <td>ETHUSD</td>\n",
       "      <td>158.04</td>\n",
       "      <td>158.31</td>\n",
       "      <td>157.16</td>\n",
       "      <td>157.18</td>\n",
       "      <td>55.244131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1586980800000</td>\n",
       "      <td>2020-04-15 20:00:00</td>\n",
       "      <td>ETHUSD</td>\n",
       "      <td>157.10</td>\n",
       "      <td>158.10</td>\n",
       "      <td>156.87</td>\n",
       "      <td>158.04</td>\n",
       "      <td>144.262622</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unix Timestamp                 Date  Symbol    Open    High     Low  \\\n",
       "0   1586995200000  2020-04-16 00:00:00  ETHUSD  152.94  152.94  150.39   \n",
       "1   1586991600000  2020-04-15 23:00:00  ETHUSD  155.81  155.81  151.39   \n",
       "2   1586988000000  2020-04-15 22:00:00  ETHUSD  157.18  157.30  155.32   \n",
       "3   1586984400000  2020-04-15 21:00:00  ETHUSD  158.04  158.31  157.16   \n",
       "4   1586980800000  2020-04-15 20:00:00  ETHUSD  157.10  158.10  156.87   \n",
       "\n",
       "    Close       Volume  \n",
       "0  150.39   650.188125  \n",
       "1  152.94  4277.567299  \n",
       "2  155.81   106.337279  \n",
       "3  157.18    55.244131  \n",
       "4  158.04   144.262622  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import data\n",
    "historical_eth_hourly = pd.read_csv('data/ETH_1H.csv')\n",
    "historical_eth_hourly.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "historical_eth_hourly['Date'] = pd.to_datetime(historical_eth_hourly['Date'])\n",
    "historical_eth_hourly = historical_eth_hourly[historical_eth_hourly['Date']>'2017-01-01']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sort by date from earliest to latest\n",
    "sorted_historical_eth_hourly = historical_eth_hourly.sort_values(by='Date')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split into training and test data. \n",
    "train, test= np.split(sorted_historical_eth_hourly, [int(.9 *len(sorted_historical_eth_hourly))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unix Timestamp</th>\n",
       "      <th>Date</th>\n",
       "      <th>Symbol</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2887</th>\n",
       "      <td>1576602000000</td>\n",
       "      <td>2019-12-17 17:00:00</td>\n",
       "      <td>ETHUSD</td>\n",
       "      <td>128.31</td>\n",
       "      <td>128.31</td>\n",
       "      <td>126.38</td>\n",
       "      <td>127.46</td>\n",
       "      <td>402.271541</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2886</th>\n",
       "      <td>1576605600000</td>\n",
       "      <td>2019-12-17 18:00:00</td>\n",
       "      <td>ETHUSD</td>\n",
       "      <td>127.46</td>\n",
       "      <td>127.53</td>\n",
       "      <td>126.53</td>\n",
       "      <td>126.62</td>\n",
       "      <td>229.430010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2885</th>\n",
       "      <td>1576609200000</td>\n",
       "      <td>2019-12-17 19:00:00</td>\n",
       "      <td>ETHUSD</td>\n",
       "      <td>126.62</td>\n",
       "      <td>126.81</td>\n",
       "      <td>122.50</td>\n",
       "      <td>122.93</td>\n",
       "      <td>2012.801588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2884</th>\n",
       "      <td>1576612800000</td>\n",
       "      <td>2019-12-17 20:00:00</td>\n",
       "      <td>ETHUSD</td>\n",
       "      <td>122.93</td>\n",
       "      <td>123.20</td>\n",
       "      <td>120.44</td>\n",
       "      <td>120.94</td>\n",
       "      <td>2206.133446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2883</th>\n",
       "      <td>1576616400000</td>\n",
       "      <td>2019-12-17 21:00:00</td>\n",
       "      <td>ETHUSD</td>\n",
       "      <td>120.94</td>\n",
       "      <td>122.07</td>\n",
       "      <td>120.86</td>\n",
       "      <td>122.07</td>\n",
       "      <td>1044.554438</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Unix Timestamp                Date  Symbol    Open    High     Low  \\\n",
       "2887   1576602000000 2019-12-17 17:00:00  ETHUSD  128.31  128.31  126.38   \n",
       "2886   1576605600000 2019-12-17 18:00:00  ETHUSD  127.46  127.53  126.53   \n",
       "2885   1576609200000 2019-12-17 19:00:00  ETHUSD  126.62  126.81  122.50   \n",
       "2884   1576612800000 2019-12-17 20:00:00  ETHUSD  122.93  123.20  120.44   \n",
       "2883   1576616400000 2019-12-17 21:00:00  ETHUSD  120.94  122.07  120.86   \n",
       "\n",
       "       Close       Volume  \n",
       "2887  127.46   402.271541  \n",
       "2886  126.62   229.430010  \n",
       "2885  122.93  2012.801588  \n",
       "2884  120.94  2206.133446  \n",
       "2883  122.07  1044.554438  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'Eth Hourly data'}, xlabel='Date'>"
      ]
     },
     "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": [
    "train.plot(x='Date',y='Close',title='Eth Hourly data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kalman filter\n",
    "\n",
    "Kalman filters are a lightweight algorithm often in an economic context for reducing noise in signals. The Kalman Filter is trained on a subset of the data, and then the parameters are passed into a prediction function for use in subsequent samples. As Kalman filters are one step predictors, at each time step, the filters is retrained and the system state and parameters are updated. \n",
    "\n",
    "This implemention was refined by Andrew Clark in a [recent paper](https://ideas.repec.org/p/rdg/emxxdp/em-dp2020-22.html) that used Kalman filters embedded into a cadCAD model for forecasting exchange rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy.stats import gamma\n",
    "\n",
    "def kalman_filter(observations,initialValue,truthValues=None,plot=False,paramExport=False):\n",
    "    '''\n",
    "    Description:\n",
    "    Function to create a Kalman Filter for smoothing currency timestamps in order to search for the\n",
    "    intrinisic value.\n",
    "    \n",
    "    Parameters:\n",
    "    observations: Array of observations, i.e. predicted secondary market prices.\n",
    "    initialValue: Initial Starting value of filter\n",
    "    truthValues: Array of truth values, i.e. GPS location or secondary market prices. Or can be left\n",
    "    blank if none exist\n",
    "    plot: If True, plot the observations, truth values and kalman filter.\n",
    "    paramExport: If True, the parameters xhat,P,xhatminus,Pminus,K are returned to use in training.\n",
    "    \n",
    "    Example:\n",
    "    xhat,P,xhatminus,Pminus,K = kalman_filter(observations=train.Close.values[0:-1],\n",
    "                                              initialValue=train.Close.values[-1],paramExport=True)\n",
    "    '''\n",
    "    # intial parameters\n",
    "    n_iter = len(observations)\n",
    "    sz = (n_iter,) # size of array\n",
    "    if isinstance(truthValues,np.ndarray):\n",
    "        x = truthValues # truth value\n",
    "    z = observations# observations (normal about x, sigma=0.1)\n",
    "\n",
    "    Q = 1e-5 # process variance\n",
    "\n",
    "    # allocate space for arrays\n",
    "    xhat=np.zeros(sz)      # a posteri estimate of x\n",
    "    P=np.zeros(sz)         # a posteri error estimate\n",
    "    xhatminus=np.zeros(sz) # a priori estimate of x\n",
    "    Pminus=np.zeros(sz)    # a priori error estimate\n",
    "    K=np.zeros(sz)         # gain or blending factor\n",
    "\n",
    "    R = 0.5**2 # estimate of measurement variance, change to see effect\n",
    "\n",
    "    # intial guesses\n",
    "    xhat[0] = initialValue\n",
    "    P[0] = 1.0\n",
    "\n",
    "    for k in range(1,n_iter):\n",
    "        # time update\n",
    "        xhatminus[k] = xhat[k-1]\n",
    "        Pminus[k] = P[k-1]+Q\n",
    "\n",
    "        # measurement update\n",
    "        K[k] = Pminus[k]/( Pminus[k]+R )\n",
    "        xhat[k] = xhatminus[k]+K[k]*(z[k]-xhatminus[k])\n",
    "        P[k] = (1-K[k])*Pminus[k]\n",
    "\n",
    "    if plot==True:\n",
    "        plt.figure()\n",
    "        plt.plot(z,'k+',label='Actual data')\n",
    "        plt.plot(xhat,'b-',label='a posteri estimate')\n",
    "        if isinstance(truthValues,np.ndarray):\n",
    "            plt.plot(x,color='g',label='truth value')\n",
    "        plt.legend()\n",
    "        plt.title('Kalman Filter Estimates', fontweight='bold')\n",
    "        plt.xlabel('Iteration')\n",
    "        plt.ylabel('USD')\n",
    "        plt.show()\n",
    "\n",
    "    if paramExport==True:\n",
    "        return  xhat,P,xhatminus,Pminus,K\n",
    "\n",
    "    else:\n",
    "\n",
    "        return xhat\n",
    "\n",
    "def kalman_filter_predict(xhat,P,xhatminus,Pminus,K,observations,truthValues=None,paramExport=False):\n",
    "    '''\n",
    "    Description:\n",
    "    Function to predict a pre-trained Kalman Filter 1 step forward.\n",
    "    \n",
    "    Parameters:\n",
    "    xhat: Trained Kalman filter values - array\n",
    "    P: Trained Kalman variance - array\n",
    "    xhatminus: Trained Kalman xhat delta - array\n",
    "    Pminus: Trained Kalman variance delta - array\n",
    "    K: Kalman gain - array\n",
    "    observations: Array of observations, i.e. predicted secondary market prices.\n",
    "    truthValues: Array of truth values, i.e. GPS location or secondary market prices. Or can be left\n",
    "    blank if none exist\n",
    "    paramExport: If True, the parameters xhat,P,xhatminus,Pminus,K are returned to use in next predicted step.\n",
    "    \n",
    "    Example:\n",
    "    xhat,P,xhatminus,Pminus,K = kalman_filter_predict(xhatInput,PInput,\n",
    "                                                      xhatminusInput,PminusInput,KInput,observation,\n",
    "                                                       paramExport=True)\n",
    "    '''\n",
    "    # intial parameters\n",
    "    if isinstance(truthValues,np.ndarray):\n",
    "        x = truthValues # truth value\n",
    "    z = observations# observations (normal about x, sigma=0.1)\n",
    "\n",
    "    Q = 1e-5 # process variance\n",
    "\n",
    "    R = 0.5**2 # estimate of measurement variance, change to see effect\n",
    "\n",
    "\n",
    "    # time update\n",
    "    xhatminus = np.append(xhatminus,xhat[-1])\n",
    "    Pminus = np.append(Pminus,P[-1]+Q)\n",
    "\n",
    "    # measurement update\n",
    "    K = np.append(K,Pminus[-1]/( Pminus[-1]+R ))\n",
    "    xhat = np.append(xhat,xhatminus[-1]+K[-1]*(z[-1]-xhatminus[-1]))\n",
    "    P = np.append(P,(1-K[-1])*Pminus[-1])\n",
    "\n",
    "    if paramExport==True:\n",
    "        return  xhat,P,xhatminus,Pminus,K\n",
    "\n",
    "    else:\n",
    "\n",
    "        return xhat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Process training\n",
    "\n",
    "Fit the gamma distribution off of the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "633.7418267210845"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timesteps = 24 * 365 # 24 hours a day * 365 days a year \n",
    "# fit eth distribution\n",
    "fit_shape, fit_loc, fit_scale = gamma.fit(train.Close.values)\n",
    "sample = np.random.gamma(fit_shape, fit_scale, 100)[0]\n",
    "sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Eth Price IID Samples')"
      ]
     },
     "execution_count": 10,
     "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": [
    "# generate 100 samples for initialization of Kalman\n",
    "samples = np.random.gamma(fit_shape, fit_scale, 100)\n",
    "plt.hist(samples)\n",
    "plt.title('Histogram of Eth Price IID Samples')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# train kalman\n",
    "xhat,P,xhatminus,Pminus,K = kalman_filter(observations=samples[0:-1],\n",
    "                                          initialValue=samples[-1],paramExport=True,plot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation\n",
    "\n",
    "To test how our generator is working, we will make 100 predictions and compare to the test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "eth_values = []\n",
    "filter_values = {'xhat':xhat,'P':P,\n",
    "                 'xhatminus':xhatminus,'Pminus':Pminus,\n",
    "                 'K':K}\n",
    "\n",
    "for i in range(0,100):\n",
    "    sample = np.random.gamma(fit_shape, fit_scale, 1)[0]\n",
    "    eth_values.append(sample)\n",
    "    xhat,P,xhatminus,Pminus,K = kalman_filter_predict(filter_values['xhat'],\n",
    "                                                  filter_values['P'],\n",
    "                                                  filter_values['xhatminus'],\n",
    "                                                  filter_values['Pminus'],\n",
    "                                                  filter_values['K'],\n",
    "                                                  eth_values,\n",
    "                                                  paramExport=True)\n",
    "    filter_values = {'xhat':xhat,'P':P,\n",
    "                 'xhatminus':xhatminus,'Pminus':Pminus,\n",
    "                 'K':K}\n",
    "                                                                    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "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(xhat[100:], label = 'Predicted')\n",
    "plt.plot(test.head(100)['Close'].values, label = 'Actual')\n",
    "plt.xlabel('Predictions')\n",
    "plt.ylabel('Eth value in USD')\n",
    "# Set a title of the current axes.\n",
    "plt.title('Predicted vs actual')\n",
    "plt.legend()\n",
    "# Display a figure.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate data for simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "samples = np.random.gamma(fit_shape, fit_scale, 100)\n",
    "# train kalman\n",
    "xhat,P,xhatminus,Pminus,K = kalman_filter(observations=samples[0:-1],\n",
    "                                          initialValue=samples[-1],paramExport=True,plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "eth_values = []\n",
    "filter_values = {'xhat':xhat,'P':P,\n",
    "                 'xhatminus':xhatminus,'Pminus':Pminus,\n",
    "                 'K':K}\n",
    "\n",
    "for i in range(0,timesteps+1):\n",
    "    sample = np.random.gamma(fit_shape, fit_scale, 1)[0]\n",
    "    eth_values.append(sample)\n",
    "    xhat,P,xhatminus,Pminus,K = kalman_filter_predict(filter_values['xhat'],\n",
    "                                                  filter_values['P'],\n",
    "                                                  filter_values['xhatminus'],\n",
    "                                                  filter_values['Pminus'],\n",
    "                                                  filter_values['K'],\n",
    "                                                  eth_values,\n",
    "                                                  paramExport=True)\n",
    "    filter_values = {'xhat':xhat,'P':P,\n",
    "                 'xhatminus':xhatminus,'Pminus':Pminus,\n",
    "                 'K':K}\n",
    "                                                                    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Eth Price IID Samples')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEICAYAAACzliQjAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy86wFpkAAAACXBIWXMAAAsTAAALEwEAmpwYAAAbyklEQVR4nO3de5hcVZ3u8e9LuIzKJWBaTkgiHTHoCcwYoA14GBVFSYBxAvPMYDIzkDBo5OYZdGacwHgEcZgH5SYMCk8Y8giKCZHLkAPhEhFFHQI0ECDhIh1ITjqEpCXcIhon8Dt/7NWyaar6VpWqptf7eZ56au+11t577VVVv1q19q69FRGYmVketml2BczMrHEc9M3MMuKgb2aWEQd9M7OMOOibmWXEQd/MLCMO+m9zklZIOqTZ9WgmSUdLWiNpk6T96rC+n0r6XD3qVmHdfyPpjq2x7uFoa74WuXLQH8IkrZL0qR5psyT9ons+IvaJiJ/2sZ5WSSFp261U1WY7Hzg1InaMiId6ZqZ9/036Uuh+fCXlnSXpB4PdsKRDJL2e1vmKpCclHV+tfERcExGHDXZ7vdShszT/h0DZo36bJHVKWijpw32s8wRJT6R9Wi9psaSd6llvaw4HfavZEPgy2RNY0UeZD6Uvhe7Ht+q4/WcjYkdgZ+CfgSskTexZqInt1F2/nYCDgCeAn0s6tFJhSR8H/g2YERE7Af8TuLZRlbWty0H/ba78a0DSZEntkl5OvbMLU7G70/OLqbf3EUnbSPqqpNWSNki6WtIupfUel/Kel/R/emznLEnXSfqBpJeBWWnb90h6UdI6SZdK2r60vpB0sqSnUu/xG5L2kvRfqb4Ly+V77GPFukraQdImYATwsKSVA2y7qcAZwGdTuzxcyt5T0i9TXe+QNKqv9UXhP4EXgInpV9kvJV0k6XngrJ6/1CTtI2mJpI3pNTujtM9zJK1Mr8FCSbsNZP+q1K8zIr4G/AfwzSpFPwzc0/2rKSI2RsRVEfFKqtuRkh5Kr9saSWeV9qf7V+XxKe8FSSdK+rCkR9L749JS+e42ulTSS+nXRcUvo1T+7yQ9ntZ7u6Q9U7pSO29I9XpU0r61tNdw5aA/vFwMXBwROwN7AQtT+sfS88jUy70HmJUenwDeB+wIXAqQeqnfBf4GGA3sAozpsa1pwHXASOAa4DXgS8Ao4CPAocDJPZaZAhxA0dv8CjAX+FtgHLAvMKPKflWsa0RsTj1YKHrye1VtmQoi4jaKHu21qV0+VMr+a+B44D3A9sA/9rW+FKiPpmiTR1PygcDTwO7AOT3K7wT8GLgN2AN4P3Bnyv4icBTw8ZT3AvCdgexfH24A9pf0rgp59wJTJH1d0sGSduiR/xvgOIr9PBI4SdJRPcocCEwAPgt8G/gX4FPAPsAx6ddEuexKivfOmcANlb7gJE2j+JL+C6AF+DkwP2UfRvE+35vi/XoM8HyvLZCriPBjiD6AVcAm4MXS41XgFz3KfCpN3w18HRjVYz2tQADbltLuBE4uzX8A+G9gW+BrwPxS3juB35e2cxZwdx91Pw24sTQfwMGl+QeAfy7NXwB8u8q6qta1tO7391KXAF7u0Y5TSvvygx7lfwp8tTR/MnBblXUfArye1rkRWAZMT3mzgP/Xo/ys7teP4kvuoSrrfRw4tDQ/urzPFerQ2aP+n6uUVyrzwdQuY6ps/3Dg/6b92gRcCIyoUvbbwEU93mtjSvnPA58tzV8PnFZqj2cBlfLvA46tsC+3AieUym1D8XnYE/gk8CuKDsU2zfi8vl0e7ukPfUdFxMjuB2/tPZedQNHTeULS/ZL+rJeyewCrS/OrKQL+7ilvTXdGRLzKW3tNa8ozkvaWdLOk59KQz79R9NzK1pemf1thfkcq662u/bV/uR0j4vY+yj9Xmn61l7pBMWY+MiJ2i4hJEbGglLem6lLFL5xqQ1J7Ajem4ZAXKb4EXmNg+9ybMRTB+cVKmRFxa0R8BtiN4lfdLKD74PCBku6S1CXpJeBEanut10aK4slqite8pz2Bi0ttshEQxRfMTyh+qX4H2CBprqSdq+x71hz0h5GIeCoiZlAMSXwTuC79fK90KdVnKT5E3d4LbKH4cK4DxnZnSHoH8O6em+sxfxnFAcIJUQwvnUHxgayH3upaq619mdne1r+GYriqWt7hPb6o/igi1tapXkcDD0bEb3orFBGvR8SdwE8ohuAAfggsAsZFxC7A5dT2Wo+RVF7+vRSveU9rgC/0aJN3RMR/pbpeEhEHABMpOj//VEOdhi0H/WFE0t9KaomI7uEGKIYeutJzOcDMB74kabykHXljbHsLxVj9ZyT9r3Rw9Sz6/lDvRDGEsknSB4GT6rRbfdW1VuuBVknN+CzcDIyWdFo6KL2TpANT3uXAOaUDlS1pTHvQ0sHOMZLOpOi1n1Gl3DRJ0yXtmpaZTHFsYWkqshOwMSJ+l/L+upZ6UXRS/rek7ST9FcXZQosrlLscOF3SPqmeu6TypAPFB0rajuKYw+8o3vPWg4P+8DIVWKHijJaLKcaWf5uGZ84Bfpl+Gh8EzAO+T3Ec4BmKD8kXASJiRZpeQNHr3wRsADb3su1/pPjwvwJcQX1P8ata1wF4WG8+T//bKf1H6fl5SQ/Wpbb9FMXZMJ8GPkMxnPQUxcFqKF6/RcAdkl6hCLgHVlpPP+yR3hObgPuBPwYOiYhqfxJ7Afh8qs/LwA+A8yLimpR/MnB2qtfXeOOEgcG6l+Kg768p3qd/GRFvOQgbETdS/IJdkIYQl1Mce4DidNkrUt1XUwxHnldjvYYlvXkozeytUu/6RYqhm2eaXB0bRiTNojhQ+6fNrksu3NO3iiR9RtI70zGB8ylOQVzV3FqZWa0c9K2aaRQH056l+Ok9Pfyz0Oxtz8M7ZmYZcU/fzCwjzb5QVp9GjRoVra2tza6GmdnbxgMPPPDriGiplDfkg35rayvt7e3NroaZ2duGpNXV8jy8Y2aWEQd9M7OMOOibmWXEQd/MLCMO+mZmGXHQNzPLiIO+mVlGHPTNzDLioG9mlpE+/5EraRxwNcW9OQOYGxEXp7vVX0txI+RVwDER8UK67dnFwBEU9xadFREPpnXNBL6aVv2vEXFVfXfHctQ655ambHfVuUc2ZbtmtehPT38L8A8RMZHiTvOnSJoIzAHujIgJwJ1pHoo72UxIj9kU904lfUmcSXH3n8nAmZJ2reO+mJlZH/oM+hGxrrunnm7v9jgwhuJ669099auAo9L0NODqKCwFRkoaDUwBlkTExoh4AVhCcXs/MzNrkAGN6UtqBfajuKfl7hGxLmU9RzH8A8UXwprSYp0prVp6pe3MltQuqb2rq2sgVTQzs170O+in+6ReD5wWES+X89Idlep2N5aImBsRbRHR1tJS8eqgZmY2CP0K+pK2owj410TEDSl5fRq2IT1vSOlrgXGlxcemtGrpZmbWIH0G/XQ2zpXA4xFxYSlrETAzTc8EbiqlH6fCQcBLaRjoduAwSbumA7iHpTQzM2uQ/txE5WDgWOBRSctS2hnAucBCSScAq4FjUt5iitM1OyhO2TweICI2SvoGcH8qd3ZEbKzHTpiZWf/0GfQj4heAqmQfWqF8AKdUWdc8YN5AKmhmZvXjf+SamWXEQd/MLCMO+mZmGXHQNzPLiIO+mVlGHPTNzDLioG9mlhEHfTOzjDjom5llpD+XYTDrU7PuXmVmA+OevplZRhz0zcwy4qBvZpYRB30zs4w46JuZZcRB38wsI/25XeI8SRskLS+lXStpWXqs6r6jlqRWSb8t5V1eWuYASY9K6pB0SboNo5mZNVB/ztP/HnApcHV3QkR8tnta0gXAS6XyKyNiUoX1XAZ8HriX4paKU4FbB1xjMzMbtD57+hFxN1DxXrapt34MML+3dUgaDewcEUvT7RSvBo4acG3NzKwmtY7pfxRYHxFPldLGS3pI0s8kfTSljQE6S2U6U1pFkmZLapfU3tXVVWMVzcysW61BfwZv7uWvA94bEfsBXwZ+KGnnga40IuZGRFtEtLW0tNRYRTMz6zboa+9I2hb4C+CA7rSI2AxsTtMPSFoJ7A2sBcaWFh+b0szMrIFq6el/CngiIv4wbCOpRdKINP0+YALwdESsA16WdFA6DnAccFMN2zYzs0Hozymb84F7gA9I6pR0QsqazlsP4H4MeCSdwnkdcGJEdB8EPhn4D6ADWInP3DEza7g+h3ciYkaV9FkV0q4Hrq9Svh3Yd4D1MzOzOvI/cs3MMuKgb2aWEQd9M7OMOOibmWXEQd/MLCMO+mZmGRn0P3LNctc655ambHfVuUc2Zbs2PLinb2aWEQd9M7OMOOibmWXEQd/MLCMO+mZmGXHQNzPLiIO+mVlGHPTNzDLioG9mlhEHfTOzjPTndonzJG2QtLyUdpaktZKWpccRpbzTJXVIelLSlFL61JTWIWlO/XfFzMz60p+e/veAqRXSL4qISemxGEDSRIp75+6TlvmupBHpZunfAQ4HJgIzUlkzM2ug/twj925Jrf1c3zRgQURsBp6R1AFMTnkdEfE0gKQFqexjA6+ymZkNVi1j+qdKeiQN/+ya0sYAa0plOlNatfSKJM2W1C6pvaurq4YqmplZ2WCD/mXAXsAkYB1wQb0qBBARcyOiLSLaWlpa6rlqM7OsDep6+hGxvnta0hXAzWl2LTCuVHRsSqOXdDMza5BB9fQljS7NHg10n9mzCJguaQdJ44EJwH3A/cAESeMlbU9xsHfR4KttZmaD0WdPX9J84BBglKRO4EzgEEmTgABWAV8AiIgVkhZSHKDdApwSEa+l9ZwK3A6MAOZFxIp674yZmfWuP2fvzKiQfGUv5c8BzqmQvhhYPKDamZlZXfkfuWZmGXHQNzPLyKDO3rGhq3XOLc2ugpkNYe7pm5llxEHfzCwjDvpmZhlx0Dczy4iDvplZRhz0zcwy4qBvZpYRB30zs4w46JuZZcRB38wsIw76ZmYZcdA3M8uIg76ZWUb6DPqS5knaIGl5Ke08SU9IekTSjZJGpvRWSb+VtCw9Li8tc4CkRyV1SLpEkrbKHpmZWVX96el/D5jaI20JsG9E/AnwK+D0Ut7KiJiUHieW0i8DPk9x39wJFdZpZmZbWZ9BPyLuBjb2SLsjIrak2aXA2N7WkW6kvnNELI2IAK4GjhpUjc3MbNDqMab/d8Ctpfnxkh6S9DNJH01pY4DOUpnOlFaRpNmS2iW1d3V11aGKZmYGNQZ9Sf8CbAGuSUnrgPdGxH7Al4EfStp5oOuNiLkR0RYRbS0tLbVU0czMSgZ9u0RJs4A/Aw5NQzZExGZgc5p+QNJKYG9gLW8eAhqb0szMrIEG1dOXNBX4CvDnEfFqKb1F0og0/T6KA7ZPR8Q64GVJB6Wzdo4Dbqq59mZmNiB99vQlzQcOAUZJ6gTOpDhbZwdgSTrzcmk6U+djwNmS/ht4HTgxIroPAp9McSbQOyiOAZSPA5iZWQP0GfQjYkaF5CurlL0euL5KXjuw74BqZ2ZmdeV/5JqZZcRB38wsIw76ZmYZcdA3M8uIg76ZWUYc9M3MMuKgb2aWEQd9M7OMOOibmWXEQd/MLCMO+mZmGXHQNzPLiIO+mVlGHPTNzDLioG9mlhEHfTOzjDjom5llpF9BX9I8SRskLS+l7SZpiaSn0vOuKV2SLpHUIekRSfuXlpmZyj8laWb9d8fMzHrT357+94CpPdLmAHdGxATgzjQPcDjFDdEnALOBy6D4kqC4v+6BwGTgzO4vCjMza4x+Bf2IuBvY2CN5GnBVmr4KOKqUfnUUlgIjJY0GpgBLImJjRLwALOGtXyRmZrYV1TKmv3tErEvTzwG7p+kxwJpSuc6UVi39LSTNltQuqb2rq6uGKpqZWVldDuRGRABRj3Wl9c2NiLaIaGtpaanXas3MsldL0F+fhm1IzxtS+lpgXKnc2JRWLd3MzBqklqC/COg+A2cmcFMp/bh0Fs9BwEtpGOh24DBJu6YDuIelNDMza5Bt+1NI0nzgEGCUpE6Ks3DOBRZKOgFYDRyTii8GjgA6gFeB4wEiYqOkbwD3p3JnR0TPg8NmZrYV9SvoR8SMKlmHVigbwClV1jMPmNfv2pmZWV35H7lmZhlx0Dczy4iDvplZRhz0zcwy4qBvZpYRB30zs4w46JuZZcRB38wsIw76ZmYZcdA3M8uIg76ZWUYc9M3MMuKgb2aWEQd9M7OMOOibmWWkX9fTN7Oho3XOLU3b9qpzj2zatq0+Bt3Tl/QBSctKj5clnSbpLElrS+lHlJY5XVKHpCclTanPLpiZWX8NuqcfEU8CkwAkjaC4yfmNFLdHvCgizi+XlzQRmA7sA+wB/FjS3hHx2mDrYGZmA1OvMf1DgZURsbqXMtOABRGxOSKeobiH7uQ6bd/MzPqhXkF/OjC/NH+qpEckzZO0a0obA6wplelMaW8habakdkntXV1ddaqimZnVHPQlbQ/8OfCjlHQZsBfF0M864IKBrjMi5kZEW0S0tbS01FpFMzNL6tHTPxx4MCLWA0TE+oh4LSJeB67gjSGctcC40nJjU5qZmTVIPYL+DEpDO5JGl/KOBpan6UXAdEk7SBoPTADuq8P2zcysn2o6T1/Su4BPA18oJX9L0iQggFXdeRGxQtJC4DFgC3CKz9wxM2usmoJ+RPwGeHePtGN7KX8OcE4t2zQzs8HzZRjMzDLioG9mlhEHfTOzjDjom5llxEHfzCwjDvpmZhlx0Dczy4iDvplZRhz0zcwy4tslbgXNvJ2dmVlv3NM3M8uIg76ZWUYc9M3MMuKgb2aWEQd9M7OMOOibmWXEQd/MLCM1B31JqyQ9KmmZpPaUtpukJZKeSs+7pnRJukRSh6RHJO1f6/bNzKz/6tXT/0RETIqItjQ/B7gzIiYAd6Z5gMMpbog+AZgNXFan7ZuZWT9sreGdacBVafoq4KhS+tVRWAqMlDR6K9XBzMx6qEfQD+AOSQ9Imp3Sdo+IdWn6OWD3ND0GWFNatjOlvYmk2ZLaJbV3dXXVoYpmZgb1ufbOn0bEWknvAZZIeqKcGREhKQaywoiYC8wFaGtrG9CyZmZWXc09/YhYm543ADcCk4H13cM26XlDKr4WGFdafGxKMzOzBqgp6Et6l6SduqeBw4DlwCJgZio2E7gpTS8Cjktn8RwEvFQaBjIzs62s1uGd3YEbJXWv64cRcZuk+4GFkk4AVgPHpPKLgSOADuBV4Pgat29mZgNQU9CPiKeBD1VIfx44tEJ6AKfUsk0zMxs8/yPXzCwjDvpmZhlx0Dczy4iDvplZRhz0zcwy4qBvZpYRB30zs4w46JuZZcRB38wsIw76ZmYZcdA3M8uIg76ZWUYc9M3MMuKgb2aWEQd9M7OMOOibmWVk0EFf0jhJd0l6TNIKSX+f0s+StFbSsvQ4orTM6ZI6JD0paUo9dsDMzPqvljtnbQH+ISIeTPfJfUDSkpR3UUScXy4saSIwHdgH2AP4saS9I+K1GupgZmYDMOiefkSsi4gH0/QrwOPAmF4WmQYsiIjNEfEMxX1yJw92+2ZmNnB1GdOX1ArsB9ybkk6V9IikeZJ2TWljgDWlxTqp8iUhabakdkntXV1d9aiimZlRh6AvaUfgeuC0iHgZuAzYC5gErAMuGOg6I2JuRLRFRFtLS0utVTQzs6SmoC9pO4qAf01E3AAQEesj4rWIeB24gjeGcNYC40qLj01pZmbWILWcvSPgSuDxiLiwlD66VOxoYHmaXgRMl7SDpPHABOC+wW7fzMwGrpazdw4GjgUelbQspZ0BzJA0CQhgFfAFgIhYIWkh8BjFmT+n+MwdM7PGGnTQj4hfAKqQtbiXZc4BzhnsNs3MrDb+R66ZWUYc9M3MMlLLmL6ZZaZ1zi1N2e6qc49synaHI/f0zcwy4qBvZpYRB30zs4w46JuZZcRB38wsIw76ZmYZcdA3M8vIsD5Pv1nnFJtZfTXzszzc/iPgnr6ZWUYc9M3MMuKgb2aWkWE9pm9mVqvhdr0h9/TNzDLioG9mlpGGB31JUyU9KalD0pxGb9/MLGcNDfqSRgDfAQ4HJlLcT3diI+tgZpazRvf0JwMdEfF0RPweWABMa3AdzMyy1eizd8YAa0rzncCBPQtJmg3MTrObJD1Zp+2PAn5dp3UNN26b6tw21bltqqupbfTNmra9Z7WMIXnKZkTMBebWe72S2iOird7rHQ7cNtW5bapz21Q3VNum0cM7a4FxpfmxKc3MzBqg0UH/fmCCpPGStgemA4saXAczs2w1dHgnIrZIOhW4HRgBzIuIFQ2sQt2HjIYRt011bpvq3DbVDcm2UUQ0uw5mZtYg/keumVlGHPTNzDIybIK+pHGS7pL0mKQVkv6+lPdFSU+k9G+V0k9Pl4N4UtKU5tR866vWNpImSVoqaZmkdkmTU7okXZLa5hFJ+zd3D7YeSX8k6T5JD6e2+XpKHy/p3tQG16YTD5C0Q5rvSPmtTd2BraiXtrkmfWaWS5onabuUnv37ppR/iaRNpfmh876JiGHxAEYD+6fpnYBfUVzq4RPAj4EdUt570vNE4GFgB2A8sBIY0ez9aHDb3AEcntKPAH5amr4VEHAQcG+z92Erto2AHdP0dsC9aZ8XAtNT+uXASWn6ZODyND0duLbZ+9CEtjki5QmYX2qb7N83ab4N+D6wqVR+yLxvhk1PPyLWRcSDafoV4HGKfwCfBJwbEZtT3oa0yDRgQURsjohngA6Ky0QMO720TQA7p2K7AM+m6WnA1VFYCoyUNLrB1W6ItI/dPbLt0iOATwLXpfSrgKPS9LQ0T8o/VJIaU9vGqtY2EbE45QVwH8X/bcDvm0jXFzsP+EqPRYbM+2bYBP2y9NNpP4pv372Bj6afVD+T9OFUrNIlIcY0tKJN0KNtTgPOk7QGOB84PRXLqm0kjZC0DNgALKH41fdiRGxJRcr7/4e2SfkvAe9uaIUbqGfbRMS9pbztgGOB21JS1u+b1DanAosiYl2P4kPmfTPsgr6kHYHrgdMi4mWK/yLsRvFz85+AhcO1Z9aXCm1zEvCliBgHfAm4spn1a5aIeC0iJlH0WCcDH2xujYaOnm0jad9S9neBuyPi502pXJNVaJuPAX8F/HtTK9aHYRX0U8/jeuCaiLghJXcCN6SfY/cBr1NcCCmrS0JUaZuZQPf0j3hjeCurtukWES8CdwEfoRia6P7zYnn//9A2KX8X4PnG1rTxSm0zFUDSmUAL8OVSsdzfN58A3g90SFoFvFNSRyo2ZN43wybop977lcDjEXFhKes/KV4MJO0NbE9x5btFwPR0VH08MIFifHLY6aVtngU+nqY/CTyVphcBx6WzMQ4CXqrwc3VYkNQiaWSafgfwaYpjHncBf5mKzQRuStOL0jwp/ydpbHvYqdI2T0j6HDAFmBERr5cWyf1980BE/I+IaI2IVuDViHh/WmTIvG+G5FU2B+lgivHFR9M4G8AZwDxgnqTlwO+BmamxV0haCDwGbAFOiYjXGl/thqjWNp8HLk49j9/xxuWsF1OcidEBvAoc39DaNtZo4Kp0AG4bYGFE3CzpMWCBpH8FHuKNoa8rge+nHtxGijMxhqtqbbMFWA3ck0ZKb4iIs/H75uZeyg+Z940vw2BmlpFhM7xjZmZ9c9A3M8uIg76ZWUYc9M3MMuKgb2aWEQd9M7OMOOibmWXk/wO6f4+ChIl0hQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(xhat[100:])\n",
    "plt.title('Histogram of Eth Price IID Samples')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Predicted Eth Prices')"
      ]
     },
     "execution_count": 17,
     "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(xhat[100:])\n",
    "plt.title('Predicted Eth Prices')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8760"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timesteps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>Eth_price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>54.784675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>406.856839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>235.753768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>145.386789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>331.405293</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Eth_price\n",
       "0   54.784675\n",
       "1  406.856839\n",
       "2  235.753768\n",
       "3  145.386789\n",
       "4  331.405293"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eth_prices = pd.DataFrame(eth_values,columns=['Eth_price'])\n",
    "eth_prices.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# export data\n",
    "eth_prices.to_csv('data/eth_prices.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate Monte Carlo runs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_eth_timeseries(xhat, P, xhatminus, Pminus, K):\n",
    "    eth_values = []\n",
    "    filter_values = {'xhat':xhat,'P':P,\n",
    "                     'xhatminus':xhatminus,'Pminus':Pminus,\n",
    "                     'K':K}\n",
    "\n",
    "    for i in range(0,timesteps+1):\n",
    "        sample = np.random.gamma(fit_shape, fit_scale, 1)[0]\n",
    "        eth_values.append(sample)\n",
    "        xhat,P,xhatminus,Pminus,K = kalman_filter_predict(filter_values['xhat'],\n",
    "                                                      filter_values['P'],\n",
    "                                                      filter_values['xhatminus'],\n",
    "                                                      filter_values['Pminus'],\n",
    "                                                      filter_values['K'],\n",
    "                                                      eth_values,\n",
    "                                                      paramExport=True)\n",
    "        filter_values = {'xhat':xhat,'P':P,\n",
    "                     'xhatminus':xhatminus,'Pminus':Pminus,\n",
    "                     'K':K}\n",
    "\n",
    "    return eth_values, xhat, P, xhatminus, Pminus, K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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>294.069151</td>\n",
       "      <td>289.017021</td>\n",
       "      <td>311.479566</td>\n",
       "      <td>285.456136</td>\n",
       "      <td>304.561903</td>\n",
       "      <td>305.249439</td>\n",
       "      <td>285.852508</td>\n",
       "      <td>266.795212</td>\n",
       "      <td>315.128679</td>\n",
       "      <td>297.447705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>291.208252</td>\n",
       "      <td>286.293512</td>\n",
       "      <td>308.368393</td>\n",
       "      <td>288.932571</td>\n",
       "      <td>301.276414</td>\n",
       "      <td>303.457638</td>\n",
       "      <td>285.341682</td>\n",
       "      <td>270.216858</td>\n",
       "      <td>311.726000</td>\n",
       "      <td>294.586887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>292.287792</td>\n",
       "      <td>286.429957</td>\n",
       "      <td>306.696987</td>\n",
       "      <td>287.508217</td>\n",
       "      <td>303.735994</td>\n",
       "      <td>303.220909</td>\n",
       "      <td>288.147963</td>\n",
       "      <td>270.415639</td>\n",
       "      <td>310.038556</td>\n",
       "      <td>296.809637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>289.343698</td>\n",
       "      <td>285.480534</td>\n",
       "      <td>308.867090</td>\n",
       "      <td>287.181073</td>\n",
       "      <td>302.385064</td>\n",
       "      <td>306.232074</td>\n",
       "      <td>288.323926</td>\n",
       "      <td>268.505981</td>\n",
       "      <td>309.143930</td>\n",
       "      <td>293.718280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>286.827771</td>\n",
       "      <td>283.609768</td>\n",
       "      <td>310.211675</td>\n",
       "      <td>286.439339</td>\n",
       "      <td>300.952013</td>\n",
       "      <td>303.643975</td>\n",
       "      <td>286.063392</td>\n",
       "      <td>276.922179</td>\n",
       "      <td>314.526611</td>\n",
       "      <td>294.119983</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>8754</th>\n",
       "      <td>291.054350</td>\n",
       "      <td>273.183841</td>\n",
       "      <td>278.623425</td>\n",
       "      <td>283.930814</td>\n",
       "      <td>268.277872</td>\n",
       "      <td>277.211292</td>\n",
       "      <td>296.892119</td>\n",
       "      <td>295.057406</td>\n",
       "      <td>289.523762</td>\n",
       "      <td>295.089401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8755</th>\n",
       "      <td>290.618717</td>\n",
       "      <td>272.267694</td>\n",
       "      <td>278.507186</td>\n",
       "      <td>283.542749</td>\n",
       "      <td>268.235307</td>\n",
       "      <td>277.708453</td>\n",
       "      <td>298.132563</td>\n",
       "      <td>293.827073</td>\n",
       "      <td>288.674255</td>\n",
       "      <td>296.754460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8756</th>\n",
       "      <td>294.051768</td>\n",
       "      <td>276.645918</td>\n",
       "      <td>278.793335</td>\n",
       "      <td>286.448911</td>\n",
       "      <td>268.398035</td>\n",
       "      <td>279.435235</td>\n",
       "      <td>299.549150</td>\n",
       "      <td>293.808783</td>\n",
       "      <td>287.564452</td>\n",
       "      <td>295.050631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8757</th>\n",
       "      <td>292.504724</td>\n",
       "      <td>274.933665</td>\n",
       "      <td>277.735662</td>\n",
       "      <td>284.766537</td>\n",
       "      <td>268.450773</td>\n",
       "      <td>285.236146</td>\n",
       "      <td>297.973778</td>\n",
       "      <td>293.393772</td>\n",
       "      <td>287.940444</td>\n",
       "      <td>294.210482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8758</th>\n",
       "      <td>296.219229</td>\n",
       "      <td>276.330760</td>\n",
       "      <td>277.383716</td>\n",
       "      <td>286.261491</td>\n",
       "      <td>269.628730</td>\n",
       "      <td>284.857973</td>\n",
       "      <td>298.946032</td>\n",
       "      <td>292.130157</td>\n",
       "      <td>289.162735</td>\n",
       "      <td>293.422330</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8759 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               0           1           2           3           4           5  \\\n",
       "0     294.069151  289.017021  311.479566  285.456136  304.561903  305.249439   \n",
       "1     291.208252  286.293512  308.368393  288.932571  301.276414  303.457638   \n",
       "2     292.287792  286.429957  306.696987  287.508217  303.735994  303.220909   \n",
       "3     289.343698  285.480534  308.867090  287.181073  302.385064  306.232074   \n",
       "4     286.827771  283.609768  310.211675  286.439339  300.952013  303.643975   \n",
       "...          ...         ...         ...         ...         ...         ...   \n",
       "8754  291.054350  273.183841  278.623425  283.930814  268.277872  277.211292   \n",
       "8755  290.618717  272.267694  278.507186  283.542749  268.235307  277.708453   \n",
       "8756  294.051768  276.645918  278.793335  286.448911  268.398035  279.435235   \n",
       "8757  292.504724  274.933665  277.735662  284.766537  268.450773  285.236146   \n",
       "8758  296.219229  276.330760  277.383716  286.261491  269.628730  284.857973   \n",
       "\n",
       "               6           7           8           9  \n",
       "0     285.852508  266.795212  315.128679  297.447705  \n",
       "1     285.341682  270.216858  311.726000  294.586887  \n",
       "2     288.147963  270.415639  310.038556  296.809637  \n",
       "3     288.323926  268.505981  309.143930  293.718280  \n",
       "4     286.063392  276.922179  314.526611  294.119983  \n",
       "...          ...         ...         ...         ...  \n",
       "8754  296.892119  295.057406  289.523762  295.089401  \n",
       "8755  298.132563  293.827073  288.674255  296.754460  \n",
       "8756  299.549150  293.808783  287.564452  295.050631  \n",
       "8757  297.973778  293.393772  287.940444  294.210482  \n",
       "8758  298.946032  292.130157  289.162735  293.422330  \n",
       "\n",
       "[8759 rows x 10 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monte_carlo_runs = 10\n",
    "\n",
    "eth_values_mc = {}\n",
    "for run in range(0, monte_carlo_runs):\n",
    "    np.random.seed(seed=run)\n",
    "    \n",
    "    buffer_for_transcients = 100\n",
    "    samples = np.random.gamma(fit_shape, fit_scale, timesteps + buffer_for_transcients)\n",
    "    # train kalman\n",
    "    xhat,P,xhatminus,Pminus,K = kalman_filter(observations=samples[0:-1],\n",
    "                                              initialValue=samples[-1],paramExport=True,plot=False)\n",
    "    \n",
    "    # eth_values, _, _, _, _, _ = generate_eth_timeseries(xhat, P, xhatminus, Pminus, K)\n",
    "    eth_values_mc[run] = xhat[buffer_for_transcients:]\n",
    "    \n",
    "eth_values, xhat, P, xhatminus, Pminus, K = generate_eth_timeseries(xhat, P, xhatminus, Pminus, K)\n",
    "\n",
    "eth_values_mc_df = pd.DataFrame(eth_values_mc)\n",
    "eth_values_mc_df.to_csv('data/eth_values_mc.csv')\n",
    "eth_values_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.\n",
    "\n",
    "\n",
    "```\n",
    "    \n",
    "# partial_state_update_block.py\n",
    "partial_state_update_block = {\n",
    "    # Exogenous\n",
    "    'Exogenous': {\n",
    "        'policies': {\n",
    "        },\n",
    "        'variables': {\n",
    "            'eth_price': eth_price_mech,\n",
    "        }\n",
    "    },\n",
    "    \n",
    "# exogenousProcesses.py\n",
    "\n",
    "\n",
    "# import libraries\n",
    "import pandas as pd\n",
    "\n",
    "# import data\n",
    "eth_prices = pd.read_csv('data/eth_prices.csv')\n",
    "\n",
    "# mechanisms\n",
    "def eth_price_mech(params, step, sL, s, _input):\n",
    "    y = 'eth_price'\n",
    "    timestep = s['timestep'] \n",
    "    x = eth_prices.Eth_price.values[timestep]\n",
    "    return (y, x)\n",
    "\n",
    "    \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "In this notebook, we've read in hourly historical eth data from kaggle, defined functions for fitting and making predictions off of a gamma distribution, which is comminly used in for random walk calculations, and defined functions for de-noising kalman filter. We then validated the structure of these functions and predicted 100 timesteps for evaluation and demonstration purposes. Finally, we provided an overview of how to fit this code into cadCAD. Next steps could include:\n",
    "* Refining the Kalman filter hyperparameters\n",
    "* Refining the gamma prediction tuning parameter\n",
    "* More thorough model validation\n",
    "* Add seasonality\n",
    "\n"
   ]
  }
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