{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Autoregressive (AR) Models\n",
    "> A Summary of lecture \"Time Series Analysis in Python\", via datacamp\n",
    "\n",
    "- toc: true \n",
    "- badges: true\n",
    "- comments: true\n",
    "- author: Chanseok Kang\n",
    "- categories: [Python, Datacamp, Time_Series_Analysis]\n",
    "- image: images/arma_forecast.png"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "plt.rcParams['figure.figsize'] = (10, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Describe AR Model\n",
    "- Mathematical Description of AR(1) Model\n",
    "$$ R_t = \\mu + \\phi R_{t-1} + \\epsilon_t $$\n",
    "    - Since only one lagged value or right hand side, this is called,\n",
    "        - AR model of order 1 or, AR(1) model\n",
    "    - AR paramter $\\phi$\n",
    "    - For stationary, $-1 < \\phi < 1$\n",
    "- Interpretation of AR(1) Parameter\n",
    "    - Negative $\\phi$: Mean Reversion\n",
    "    - Positive $\\phi$: Momentum\n",
    "- High order AR Models\n",
    "    - AR(1)\n",
    "    $$ R_t = \\mu + \\phi_1 R_{t-1} + \\epsilon_t $$\n",
    "    - AR(2)\n",
    "    $$ R_t = \\mu + \\phi_1 R_{t-1} + \\phi_2 R_{t-2} + \\epsilon_t $$\n",
    "    - AR(3)\n",
    "    $$ R_t = \\mu + \\phi_1 R_{t-1} + \\phi_2 R_{t-2} + \\phi_3 R_{t-3} + \\epsilon_t $$\n",
    "    - $\\cdots$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate AR(1) Time Series\n",
    "You will simulate and plot a few AR(1) time series, each with a different parameter, $\\phi$, using the ```arima_process``` module in statsmodels. In this exercise, you will look at an AR(1) model with a large positive $\\phi$ and a large negative $\\phi$, but feel free to play around with your own parameters.\n",
    "\n",
    "There are a few conventions when using the arima_process module that require some explanation. First, these routines were made very generally to handle both AR and MA models. We will cover MA models next, so for now, just ignore the MA part. Second, when inputting the coefficients, you must include the zero-lag coefficient of 1, and the sign of the other coefficients is opposite what we have been using (to be consistent with the time series literature in signal processing). For example, for an AR(1) process with $\\phi$=0.9, the array representing the AR parameters would be ```ar = np.array([1, -0.9])```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.tsa.arima_process import ArmaProcess\n",
    "\n",
    "# Plot 1: AR parameter = +0.9\n",
    "plt.subplot(2, 1, 1)\n",
    "ar1 = np.array([1, -0.9])\n",
    "ma1 = np.array([1])\n",
    "AR_object1 = ArmaProcess(ar1, ma1)\n",
    "simulated_data_1 = AR_object1.generate_sample(nsample=1000)\n",
    "plt.plot(simulated_data_1);\n",
    "\n",
    "# Plot 2: AR parameter = -0.9\n",
    "plt.subplot(2, 1, 2)\n",
    "ar2 = np.array([1, 0.9])\n",
    "ma2 = np.array([1])\n",
    "AR_object2 = ArmaProcess(ar2, ma2)\n",
    "simulated_data_2 = AR_object2.generate_sample(nsample=1000)\n",
    "plt.plot(simulated_data_2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare the ACF for Several AR Time Series\n",
    "The autocorrelation function decays exponentially for an AR time series at a rate of the AR parameter. For example, if the AR parameter, $\\phi=+0.9$, the first-lag autocorrelation will be $0.9$, the second-lag will be $(0.9)^2=0.81$, the third-lag will be $(0.9)^3=0.729$, etc. A smaller AR parameter will have a steeper decay, and for a negative AR parameter, say $-0.9$, the decay will flip signs, so the first-lag autocorrelation will be $-0.9$, the second-lag will be $(−0.9)^2=0.81$, the third-lag will be $(−0.9)^3=−0.729$, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf\n",
    "\n",
    "# AR parameter = +0.3\n",
    "ar3 = np.array([1, -0.3])\n",
    "ma3 = np.array([1])\n",
    "AR_object3 = ArmaProcess(ar3, ma3)\n",
    "simulated_data_3 = AR_object3.generate_sample(nsample=1000)\n",
    "\n",
    "# Plot 1: AR parameter = +0.9\n",
    "plot_acf(simulated_data_1, alpha=1, lags=20);\n",
    "\n",
    "# Plot 2: AR parameter = -0.9\n",
    "plot_acf(simulated_data_2, alpha=1, lags=20);\n",
    "\n",
    "# Plot 3: AR parameter = +0.3\n",
    "plot_acf(simulated_data_3, alpha=1, lags=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating and Forecasting AR Model\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating an AR Model\n",
    "You will estimate the AR(1) parameter, $\\phi$, of one of the simulated series that you generated in the earlier exercise. Since the parameters are known for a simulated series, it is a good way to understand the estimation routines before applying it to real data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                              ARMA Model Results                              \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   No. Observations:                 1000\n",
      "Model:                     ARMA(1, 0)   Log Likelihood               -1398.596\n",
      "Method:                       css-mle   S.D. of innovations              0.979\n",
      "Date:                Mon, 08 Jun 2020   AIC                           2803.192\n",
      "Time:                        11:48:11   BIC                           2817.915\n",
      "Sample:                             0   HQIC                          2808.788\n",
      "                                                                              \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.7849      0.300      2.618      0.009       0.197       1.372\n",
      "ar.L1.y        0.8976      0.014     64.878      0.000       0.871       0.925\n",
      "                                    Roots                                    \n",
      "=============================================================================\n",
      "                  Real          Imaginary           Modulus         Frequency\n",
      "-----------------------------------------------------------------------------\n",
      "AR.1            1.1141           +0.0000j            1.1141            0.0000\n",
      "-----------------------------------------------------------------------------\n",
      "When the true phi=0.9, the estimate of phi (and the constant) are:\n",
      "[0.78487563 0.89762208]\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.tsa.arima_model import ARMA\n",
    "\n",
    "# Fit an AR(1) model to the first simulated data\n",
    "mod = ARMA(simulated_data_1, order=(1, 0))\n",
    "res = mod.fit()\n",
    "\n",
    "# Print out summary information on the fit\n",
    "print(res.summary())\n",
    "\n",
    "# Print out the estimate for the constant and for phi\n",
    "print(\"When the true phi=0.9, the estimate of phi (and the constant) are:\")\n",
    "print(res.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forecasting with an AR Model\n",
    "In addition to estimating the parameters of a model that you did in the last exercise, you can also do forecasting, both in-sample and out-of-sample using statsmodels. The in-sample is a forecast of the next data point using the data up to that point, and the out-of-sample forecasts any number of data points in the future. These forecasts can be made using either the ```predict()``` method if you want the forecasts in the form of a series of data, or using the ```plot_predict()``` method if you want a plot of the forecasted data. You supply the starting point for forecasting and the ending point, which can be any number of data points after the data set ends."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Forecast the first AR(1) model\n",
    "mod = ARMA(simulated_data_1, order=(1, 0))\n",
    "res = mod.fit()\n",
    "res.plot_predict(start=990, end=1010);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's Forecast Interest Rates\n",
    "You will now use the forecasting techniques you learned in the last exercise and apply it to real data rather than simulated data. You will revisit a dataset from the first chapter: the annual data of 10-year interest rates going back 56 years, which is in a Series called ```interest_rate_data```. Being able to forecast interest rates is of enormous importance, not only for bond investors but also for individuals like new homeowners who must decide between fixed and floating rate mortgages.\n",
    "\n",
    "You saw in the first chapter that there is some mean reversion in interest rates over long horizons. In other words, when interest rates are high, they tend to drop and when they are low, they tend to rise over time. Currently they are below long-term rates, so they are expected to rise, but an AR model attempts to quantify how much they are expected to rise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Preprocess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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>US10Y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DATE</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1962-01-02</th>\n",
       "      <td>4.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1962-01-03</th>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1962-01-04</th>\n",
       "      <td>3.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1962-01-05</th>\n",
       "      <td>4.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1962-01-08</th>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            US10Y\n",
       "DATE             \n",
       "1962-01-02   4.06\n",
       "1962-01-03   4.03\n",
       "1962-01-04   3.99\n",
       "1962-01-05   4.02\n",
       "1962-01-08   4.03"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bonds = pd.read_csv('./dataset/daily_rates.csv', index_col=0)\n",
    "bonds.index = pd.to_datetime(bonds.index, format=\"%Y-%m-%d\")\n",
    "bonds.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>US10Y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DATE</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1962-12-31</th>\n",
       "      <td>3.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-12-31</th>\n",
       "      <td>4.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1964-12-31</th>\n",
       "      <td>4.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1965-12-31</th>\n",
       "      <td>4.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1966-12-31</th>\n",
       "      <td>4.64</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            US10Y\n",
       "DATE             \n",
       "1962-12-31   3.85\n",
       "1963-12-31   4.14\n",
       "1964-12-31   4.21\n",
       "1965-12-31   4.65\n",
       "1966-12-31   4.64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interest_rate_data = bonds.resample(rule='A').last()\n",
    "interest_rate_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Forecast interest rates using an AR(1) model\n",
    "mod = ARMA(interest_rate_data, order=(1, 0))\n",
    "res = mod.fit()\n",
    "\n",
    "# Plot the original series and the forecasted series\n",
    "res.plot_predict(start=0, end='2022');\n",
    "plt.legend(fontsize=8);\n",
    "plt.savefig('../images/arma_forecast.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare AR Model with Random Walk\n",
    "Sometimes it is difficult to distinguish between a time series that is slightly mean reverting and a time series that does not mean revert at all, like a random walk. You will compare the ACF for the slightly mean-reverting interest rate series of the last exercise with a simulated random walk with the same number of observations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Preprocess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "simulated_data = np.array([5.        , 4.77522278, 5.60354317, 5.96406402, 5.97965372,\n",
    "       6.02771876, 5.5470751 , 5.19867084, 5.01867859, 5.50452928,\n",
    "       5.89293842, 4.6220103 , 5.06137835, 5.33377592, 5.09333293,\n",
    "       5.37389022, 4.9657092 , 5.57339283, 5.48431854, 4.68588587,\n",
    "       5.25218625, 4.34800798, 4.34544412, 4.72362568, 4.12582912,\n",
    "       3.54622069, 3.43999885, 3.77116252, 3.81727011, 4.35256176,\n",
    "       4.13664247, 3.8745768 , 4.01630403, 3.71276593, 3.55672457,\n",
    "       3.07062647, 3.45264414, 3.28123729, 3.39193866, 3.02947806,\n",
    "       3.88707349, 4.28776889, 3.47360734, 3.33260631, 3.09729579,\n",
    "       2.94652178, 3.50079273, 3.61020341, 4.23021143, 3.94289347,\n",
    "       3.58422345, 3.18253962, 3.26132564, 3.19777388, 3.43527681,\n",
    "       3.37204482])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the interest rate series and the simulated random walk series side-by-side\n",
    "fig, axes = plt.subplots(2, 1)\n",
    "\n",
    "# Plot the autocorrelation of the interest rate series in the top plot\n",
    "fig = plot_acf(interest_rate_data, alpha=1, lags=12, ax=axes[0]);\n",
    "\n",
    "# Plot the autocorrelation of the simulated random walk series in the bottom plot\n",
    "fig = plot_acf(simulated_data, alpha=1, lags=12, ax=axes[1]);\n",
    "\n",
    "# Label axes\n",
    "axes[0].set_title(\"Interest Rate Data\");\n",
    "axes[1].set_title(\"Simulated Random Walk Data\");\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choosing the Right Model\n",
    "- Identifying the Order of an AR Model\n",
    "    - The order of an AR(p) model will usually be unknown\n",
    "    - Two techniques to determine order\n",
    "        - Partial Autocorrelation Funciton\n",
    "        - Information criteria\n",
    "- Partial Autocorrelation Function (PACF)\n",
    "$$ \\begin{aligned} R_t &= \\phi_{0,1} + \\color{red}{\\phi_{1,1}} R_{t-1} + \\epsilon_{1t} \\\\ \n",
    "R_t &= \\phi_{0,2} + \\phi_{1,2} R_{t-1} + \\color{red}{\\phi_{2,2}} R_{t-2} + \\epsilon_{2t} \\\\\n",
    "R_t &= \\phi_{0,3} + \\phi_{1,3} R_{t-1} + \\phi_{2,3} R_{t-2} + \\color{red}{\\phi_{3,3}} R_{t-3} + \\epsilon_{3t} \\\\\n",
    "R_t &= \\phi_{0,4} + \\phi_{1,4} R_{t-1} + \\phi_{2,4} R_{t-2} + \\phi_{3,4} R_{t-3} + \\color{red}{\\phi_{4,4}} R_{t-4} + \\epsilon_{4t} \\\\\n",
    "\\end{aligned} $$\n",
    "- Information Criteria\n",
    "    - Information criteria: adjusts goodness-of-fit for number of parameters\n",
    "    - Two popular adjusted goodness-of-fit measures\n",
    "        - AIC ([Akaike Information Criterion](https://en.wikipedia.org/wiki/Akaike_information_criterion))\n",
    "        - BIC ([Bayesian Information Criterion](https://en.wikipedia.org/wiki/Bayesian_information_criterion))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimate Order of Model: PACF\n",
    "One useful tool to identify the order of an AR model is to look at the Partial Autocorrelation Function (PACF). In this exercise, you will simulate two time series, an AR(1) and an AR(2), and calculate the sample PACF for each. You will notice that for an AR(1), the PACF should have a significant lag-1 value, and roughly zeros after that. And for an AR(2), the sample PACF should have significant lag-1 and lag-2 values, and zeros after that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpgGFKkiSpQENhKiLOjYiNEbEpIj76PP3eFhEZEcuaV6IkSdLUNWmYioh+4BpgBbAEWBkRS8bpdxTwe8APm12kJEnSVNXImamzgE2ZuTkzh4FbgPPH6fdHwJ8CTzexPkmSpCmtkTB1HDBYNz1UtT0rIs4AFmbm3zexNkmSpCmvkTAV47TlszMj+oDPApdNekcRl0TE2ohYu23btsarlCRJmqIaCVNDwMK66eOBLXXTRwEvA9ZExIPAK4FV4w1Cz8xrM3NZZi6bN2/eoVctSZI0RTQSpu4EFkfESRExAFwArNo/MzOfzMy5mbkoMxcBdwDnZeballQsSZI0hUwapjJzH3ApcBuwAbg1M9dHxCcj4rxWFyhJkjSVzWikU2auBlaPabtigr7Ly8uSJEnqDn4DuiRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUgHDlCRJUoGGwlREnBsRGyNiU0R8dJz5H4qI+yLixxFxe0Sc2PxSJUmSpp5Jw1RE9APXACuAJcDKiFgyptuPgGWZ+XLgK8CfNrtQSZKkqaiRM1NnAZsyc3NmDgO3AOfXd8jM72bm7mryDuD45pYpSZI0NTUSpo4DBuumh6q2iVwMfLOkKEmSpG4xo4E+MU5bjtsx4reBZcCvTTD/EuASgBNOOKHBEiVJkqauRs5MDQEL66aPB7aM7RQRrwf+ADgvM/eOd0eZeW1mLsvMZfPmzTuUeiVJkqaURsLUncDiiDgpIgaAC4BV9R0i4gzgL6gFqa3NL1OSJGlqmjRMZeY+4FLgNmADcGtmro+IT0bEeVW3/wbMAr4cEesiYtUEdydJktRTGhkzRWauBlaPabui7vbrm1yXJElSV/Ab0CVJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgoYpiRJkgrM6HQBkjTdjIwmazZuZf2WnZy+YDbLT51Pf190uixJh8gwJUltNDKaXHj9D1k3uIM9wyPMHOhn6cI53HTx2QYqqUt5mU9db2Q0uX3DY1x9+/3cvuExRkazK9eh6WHNxq2sG9zB7uEREtg9PMK6wR2s2bi106VJOkSemRrjBw9sb7jvzj3PHPQyaq7R0eSqb25g09ZdDO8bZWBGH6fMn8XlK06jr0nv8tuxjnYYHU3WDe7gwe2/YNExL2DpwjldVX+v+Na9j7JneOQ5bXuGR/jWvY9y5EDzDslub00nrzr5mI6u3zClrrZucAebtu5i775RAPbuG2XT1l2sG9zBmSe+qGvW0Wq9Egh7waJjXsDAjL5n/54ABmb0seiYFzRtHW7v6cfw3FmGKXW1B7f/guG6FyWA4X2jPLj9F00LOu1YB7T2YNgLgbBXLF04h1Pmz2L9zx6H/hkcftgMTpk/i6UL5zRtHW7vxvVCCDE8d15DYSoizgU+B/QD12Xmp8bMPxz4IvCvge3A2zPzweaWKh2oHe/ye+FMQrsCYa9o5QtsX19w+YrTeN/vX8bIrGO59P2XNP0FvBfeALRDr4QQw3PnTRqmIqIfuAb4dWAIuDMiVmXmfXXdLgZ+npmnRMQFwH8F3t6KgqeTdhyouv1g2I53+b1wJqEdgbBXtOMFtq8vGNi+CbZv4swTP9KU+6zXC28A2qFXQohvljqvkTNTZwGbMnMzQETcApwP1Iep84Erq9tfAT4fEZGZfuTpEDmwujHteJffC2cS2hEI26XVbwB64QW2F94AtEOvhJBeebPUzW/uY7K8ExFvA87NzPdU0xcCZ2fmpXV97q36DFXTD1R9Hp/ofo8+8bT89ctvaMJDGN+6e9YBsPQVSw9quZ1PP9Nw3/vvuxeAxUtedlDraMRTT+/j4R17qN88EXDcnJkcdURzhrq1Yx3t0spt0Y51tGNbZCY/3bQZ+gdYsODFzDq8n4jmHqgyk117R3j6mRGOOKy/6evITH72xB72PDNCZu05mnlYPyccPbNp69n21F4e3zV8QPu8WQPMPerwpqwDWv832+rt3a7nqZV65Ri4f7/YvfcZIIi+aPp+sX89rdq/S/ft2Ucc1pQ6ns+t73/1XZm5bLx5jfy1jPcoxiawRvoQEZcAlwDMevHJDaz60B1siDoUrXzhfrr6g6qXCXufGWnaTt6OdUB7gk4r77sd65h1eD8zD+s/4EAy6/D+pq0jIjh1cev2u3Yc0HftHXn2OaqtE/Y8M8Kuvc37mz3isH4iOOAF9vDDmrctoPV/s63e3u16nqB1x5B27Hf7tfI4GBGccPRMdu0dYO8zIxzewjcyrdq/27Fvt1IjFQ4BC+umjwe2TNBnKCJmAC8Enhh7R5l5LXAtwLJly/Kv3/eqQ6m5pabKd0bd/dDPufo79z/ntO3hM/p416tPatrp53asY3Q0ed9t1zMy61je/K/e0FWnbdutm09xwy//nojadwFn1r7s9C0vP65pf09/e/cQX7lr6LmNCa96yTH8+zOPb8o6euHydzu083n6wJc+BsAVH17V1PuF9o1N7fbjYKv379J9ux3fM3Xr+yee10iYuhNYHBEnAQ8DFwDvGNNnFXAR8APgbcB3HC9VZv+Yh7EHqlYMrG7VOvYfbHcteSv0z+Dq79zvi9Lz6OsLzjzxRV01VqNeO8aftGNsyP4xct0cbNuhXc/T6GgyfMwpjMw6lrsf+nlLxkS2cr/rleNgq/fvbh/3NWmYysx9EXEpcBu1r0a4ITPXR8QngbWZuQq4HrgpIjZROyN1QSuLng7acaBq9Tr2D1BlxgDQnQNU1bh2HAzb8SYDuj/YtotBZHK9chxs9f7drn27VRq6EJmZq4HVY9quqLv9NPCbzS1N7Tigt3IdvfJJGTWmHQdDzxpNL70QRHrlONjq/bvb9+2pP6pLXavbT9vq4LTrYOhZo+mjF4JIrxwH23W1pFv3bcPUGJ3+Z4m95KyTjub7DzzOusEd7BkeYeZAP0sXzuH9y0+mv0vebejgvWbx3E6XoB6xe3gf3/jJI+yu+8fQMwf6Ofdlv9I1x+peOw66f4/PMKWW6e8Lbrr4bNZs3Mp9W3ayZMFslp86vysPIJLab/mp81m6cM4BQWT5qfM7XVrDPA5OD5N+aWerLFu2LNeuXduRdUuSusPIaBpENCVERNGXdkqS1BH9fcE5px3LOacd2+lSpAn1dboASZKkbmaYkiRJKmCYkiRJKmCYkiRJKmCYkiRJKmCYkiRJKmCYkiRJKmCYkiRJKmCYkiRJKtCxfycTEduAh1q8mrnA4y1eh6YOt/f04vaeXtze08dU3dYnZua88WZ0LEy1Q0Ssnej/6Kj3uL2nF7f39OL2nj66cVt7mU+SJKmAYUqSJKlAr4epaztdgNrK7T29uL2nF7f39NF127qnx0xJkiS1Wq+fmZIkSWqpng1TEXFuRGyMiE0R8dFO16PWiogHI+InEbEuItZ2uh41V0TcEBFbI+LeurajI+IfIuL+6veLOlmjmmOCbX1lRDxc7d/rIuKNnaxRzRMRCyPiuxGxISLWR8TvV+1dtX/3ZJiKiH7gGmAFsARYGRFLOluV2uB1mbm02z5Sq4bcCJw7pu2jwO2ZuRi4vZpW97uRA7c1wGer/XtpZq5uc01qnX3AZZl5GvBK4APV63VX7d89GaaAs4BNmbk5M4eBW4DzO1yTpEOUmd8DnhjTfD7wher2F4C3trUotcQE21o9KjMfycy7q9tPARuA4+iy/btXw9RxwGDd9FDVpt6VwLcj4q6IuKTTxagtjs3MR6B2QAbmd7getdalEfHj6jLglL7ko0MTEYuAM4Af0mX7d6+GqRinzY8t9rbXZOaZ1C7tfiAi/m2nC5LUNH8OnAwsBR4BPt3ZctRsETEL+Bvgg5m5s9P1HKxeDVNDwMK66eOBLR2qRW2QmVuq31uBv6N2qVe97bGIeDFA9Xtrh+tRi2TmY5k5kpmjwP/G/bunRMRh1ILUX2Xm31bNXbV/92qYuhNYHBEnRcQAcAGwqsM1qUUi4gURcdT+28AbgHuffyn1gFXARdXti4CvdbAWtdD+F9XKv8P9u2dERADXAxsy8zN1s7pq/+7ZL+2sPjr7P4B+4IbM/JMOl6QWiYiXUDsbBTAD+JLbu7dExM3Acmr/Tf4x4BPAV4FbgROAnwG/mZkOXO5yE2zr5dQu8SXwIPC+/eNp1N0i4rXA/wV+AoxWzZdTGzfVNft3z4YpSZKkdujVy3ySJEltYZiSJEkqYJiSJEkqYJiSJEkqYJiSJEkqYJiSJEkqYJiSJEkqYJiSJEkq8P8BFcTjDiB10kcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_pacf\n",
    "\n",
    "# Simulate AR(1) with phi=+0.6\n",
    "ma = np.array([1])\n",
    "ar = np.array([1, -0.6])\n",
    "AR_object = ArmaProcess(ar, ma)\n",
    "simulated_data_1 = AR_object.generate_sample(nsample=5000)\n",
    "\n",
    "# Plot PACF for AR(1)\n",
    "plot_pacf(simulated_data_1, lags=20);\n",
    "\n",
    "# simulated AR(2) with phi1=+0.6, phi2=+0.3\n",
    "ma = np.array([1])\n",
    "ar = np.array([1, -0.6, -0.3])\n",
    "AR_object = ArmaProcess(ar, ma)\n",
    "simulated_data_2 = AR_object.generate_sample(nsample=5000)\n",
    "\n",
    "# Plot PACF for AR(2)\n",
    "plot_pacf(simulated_data_2, lags=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimate Order of Model: Information Criteria\n",
    "Another tool to identify the order of a model is to look at the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). These measures compute the goodness of fit with the estimated parameters, but apply a penalty function on the number of parameters in the model. You will take the AR(2) simulated data from the last exercise, saved as simulated_data_2, and compute the BIC as you vary the order, p, in an AR(p) from 0 to 6.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fit the data to an AR(p) for p=0,...,6, and save the BIC\n",
    "BIC = np.zeros(7)\n",
    "\n",
    "for p in range(7):\n",
    "    mod = ARMA(simulated_data_2, order=(p, 0))\n",
    "    res = mod.fit()\n",
    "    # Save BIC for AR(p)\n",
    "    BIC[p] = res.bic\n",
    "    \n",
    "# Plot the BIC as a function of p\n",
    "plt.plot(range(1, 7), BIC[1:7], marker='o');\n",
    "plt.xlabel('Order of AR Model');\n",
    "plt.ylabel('Bayesian Information Criterion');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}