{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unit Root Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This setup code is required to run in an IPython notebook_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "\n",
    "warnings.simplefilter(\"ignore\")\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "\n",
    "seaborn.set_style(\"darkgrid\")\n",
    "plt.rc(\"figure\", figsize=(16, 6))\n",
    "plt.rc(\"savefig\", dpi=90)\n",
    "plt.rc(\"font\", family=\"sans-serif\")\n",
    "plt.rc(\"font\", size=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most examples will make use of the Default premium, which is the difference between the yields of BAA and AAA rated corporate bonds. The data is downloaded from FRED using pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import arch.data.default\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "default_data = arch.data.default.load()\n",
    "default = default_data.BAA.copy()\n",
    "default.name = \"default\"\n",
    "default = default - default_data.AAA.values\n",
    "fig = default.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Default premium is clearly highly persistent.  A simple check of the autocorrelations confirms this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf = pd.DataFrame(sm.tsa.stattools.acf(default), columns=[\"ACF\"])\n",
    "fig = acf[1:].plot(kind=\"bar\", title=\"Autocorrelations\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Augmented Dickey-Fuller Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Augmented Dickey-Fuller test is the most common unit root test used.  It is a regression of the first difference of the variable  on its lagged level as well as additional lags of the first difference.  The null is that the series contains a unit root, and the (one-sided) alternative is that the series is stationary. \n",
    "\n",
    "By default, the number of lags is selected by minimizing the AIC across a range of lag lengths (which can be set using `max_lag` when initializing the model).  Additionally, the basic test includes a constant in the ADF regression.\n",
    "\n",
    "These results indicate that the Default premium is stationary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Augmented Dickey-Fuller Results   \n",
      "=====================================\n",
      "Test Statistic                 -3.356\n",
      "P-value                         0.013\n",
      "Lags                               21\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -3.44 (1%), -2.86 (5%), -2.57 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import ADF\n",
    "\n",
    "adf = ADF(default)\n",
    "print(adf.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of lags can be directly set using `lags`.  Changing the number of lags makes no difference to the conclusion.\n",
    "\n",
    "**Note**: The ADF assumes residuals are white noise, and that the number of lags is sufficient to pick up any dependence in the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setting the number of lags"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Augmented Dickey-Fuller Results   \n",
      "=====================================\n",
      "Test Statistic                 -3.582\n",
      "P-value                         0.006\n",
      "Lags                                5\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -3.44 (1%), -2.86 (5%), -2.57 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "adf = ADF(default, lags=5)\n",
    "print(adf.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deterministic terms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The deterministic terms can be altered using `trend`.  The options are:\n",
    "\n",
    "* `'nc'` : No deterministic terms\n",
    "* `'c'` : Constant only\n",
    "* `'ct'` : Constant and time trend\n",
    "* `'ctt'` : Constant, time trend and time-trend squared\n",
    "\n",
    "Changing the type of constant also makes no difference for this data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Augmented Dickey-Fuller Results   \n",
      "=====================================\n",
      "Test Statistic                 -3.786\n",
      "P-value                         0.017\n",
      "Lags                                5\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant and Linear Time Trend\n",
      "Critical Values: -3.97 (1%), -3.41 (5%), -3.13 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "adf = ADF(default, trend=\"ct\", lags=5)\n",
    "print(adf.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ADF uses a standard regression when computing results.  These can be accesses using `regression`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.095\n",
      "Model:                            OLS   Adj. R-squared:                  0.090\n",
      "Method:                 Least Squares   F-statistic:                     17.83\n",
      "Date:                Tue, 18 May 2021   Prob (F-statistic):           1.30e-22\n",
      "Time:                        13:22:02   Log-Likelihood:                 630.15\n",
      "No. Observations:                1194   AIC:                            -1244.\n",
      "Df Residuals:                    1186   BIC:                            -1204.\n",
      "Df Model:                           7                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Level.L1      -0.0248      0.007     -3.786      0.000      -0.038      -0.012\n",
      "Diff.L1        0.2229      0.029      7.669      0.000       0.166       0.280\n",
      "Diff.L2       -0.0525      0.030     -1.769      0.077      -0.111       0.006\n",
      "Diff.L3       -0.1363      0.029     -4.642      0.000      -0.194      -0.079\n",
      "Diff.L4       -0.0510      0.030     -1.727      0.084      -0.109       0.007\n",
      "Diff.L5        0.0440      0.029      1.516      0.130      -0.013       0.101\n",
      "const          0.0383      0.013      2.858      0.004       0.012       0.065\n",
      "trend      -1.586e-05   1.29e-05     -1.230      0.219   -4.11e-05    9.43e-06\n",
      "==============================================================================\n",
      "Omnibus:                      665.553   Durbin-Watson:                   2.000\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           146083.295\n",
      "Skew:                          -1.425   Prob(JB):                         0.00\n",
      "Kurtosis:                      57.113   Cond. No.                     5.70e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 5.7e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "reg_res = adf.regression\n",
    "print(reg_res.summary().as_text())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "resids = pd.DataFrame(reg_res.resid)\n",
    "resids.index = default.index[6:]\n",
    "resids.columns = [\"resids\"]\n",
    "fig = resids.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the number lags was directly set, it is good to check whether the residuals appear to be white noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf = pd.DataFrame(sm.tsa.stattools.acf(reg_res.resid), columns=[\"ACF\"])\n",
    "fig = acf[1:].plot(kind=\"bar\", title=\"Residual Autocorrelations\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dickey-Fuller GLS Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Dickey-Fuller GLS test is an improved version of the ADF which uses a GLS-detrending regression before running an ADF regression with no additional deterministic terms.  This test is only available with a constant or constant and time trend (`trend='c'` or  `trend='ct'`).\n",
    "\n",
    "The results of this test agree with the ADF results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      Dickey-Fuller GLS Results      \n",
      "=====================================\n",
      "Test Statistic                 -2.322\n",
      "P-value                         0.020\n",
      "Lags                               21\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -2.59 (1%), -1.96 (5%), -1.64 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import DFGLS\n",
    "\n",
    "dfgls = DFGLS(default)\n",
    "print(dfgls.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trend can be altered using `trend`.  The conclusion is the same. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      Dickey-Fuller GLS Results      \n",
      "=====================================\n",
      "Test Statistic                 -3.464\n",
      "P-value                         0.009\n",
      "Lags                               21\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant and Linear Time Trend\n",
      "Critical Values: -3.43 (1%), -2.86 (5%), -2.58 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "dfgls = DFGLS(default, trend=\"ct\")\n",
    "print(dfgls.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Phillips-Perron Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Phillips-Perron test is similar to the ADF except that the regression run does not include lagged values of the first differences.  Instead, the PP test fixed the t-statistic using a long run variance estimation, implemented using a Newey-West covariance estimator.  \n",
    "\n",
    "By default, the number of lags is automatically set, although this can be overridden using `lags`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Phillips-Perron Test (Z-tau)    \n",
      "=====================================\n",
      "Test Statistic                 -3.898\n",
      "P-value                         0.002\n",
      "Lags                               23\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -3.44 (1%), -2.86 (5%), -2.57 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import PhillipsPerron\n",
    "\n",
    "pp = PhillipsPerron(default)\n",
    "print(pp.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is important that the number of lags is sufficient to pick up any dependence in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Phillips-Perron Test (Z-tau)    \n",
      "=====================================\n",
      "Test Statistic                 -4.024\n",
      "P-value                         0.001\n",
      "Lags                               12\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -3.44 (1%), -2.86 (5%), -2.57 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "pp = PhillipsPerron(default, lags=12)\n",
    "print(pp.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trend can be changed as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Phillips-Perron Test (Z-tau)    \n",
      "=====================================\n",
      "Test Statistic                 -4.262\n",
      "P-value                         0.004\n",
      "Lags                               12\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant and Linear Time Trend\n",
      "Critical Values: -3.97 (1%), -3.41 (5%), -3.13 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "pp = PhillipsPerron(default, trend=\"ct\", lags=12)\n",
    "print(pp.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the PP testing framework includes two types of tests. One which uses an ADF-type regression of the first difference on the level, the other which regresses the level on the level.  The default is the `tau` test, which is similar to an ADF regression, although this can be changed using `test_type='rho'`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Phillips-Perron Test (Z-rho)    \n",
      "=====================================\n",
      "Test Statistic                -36.114\n",
      "P-value                         0.002\n",
      "Lags                               12\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant and Linear Time Trend\n",
      "Critical Values: -29.16 (1%), -21.60 (5%), -18.17 (10%)\n",
      "Null Hypothesis: The process contains a unit root.\n",
      "Alternative Hypothesis: The process is weakly stationary.\n"
     ]
    }
   ],
   "source": [
    "pp = PhillipsPerron(default, test_type=\"rho\", trend=\"ct\", lags=12)\n",
    "print(pp.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KPSS Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The KPSS test differs from the three previous in that the null is a stationary process and the alternative is a unit root.  \n",
    "\n",
    "Note that here the null is rejected which indicates that the series might be a unit root."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    KPSS Stationarity Test Results   \n",
      "=====================================\n",
      "Test Statistic                  1.088\n",
      "P-value                         0.002\n",
      "Lags                               20\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: 0.74 (1%), 0.46 (5%), 0.35 (10%)\n",
      "Null Hypothesis: The process is weakly stationary.\n",
      "Alternative Hypothesis: The process contains a unit root.\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import KPSS\n",
    "\n",
    "kpss = KPSS(default)\n",
    "print(kpss.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Changing the trend does not alter the conclusion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    KPSS Stationarity Test Results   \n",
      "=====================================\n",
      "Test Statistic                  0.393\n",
      "P-value                         0.000\n",
      "Lags                               20\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant and Linear Time Trend\n",
      "Critical Values: 0.22 (1%), 0.15 (5%), 0.12 (10%)\n",
      "Null Hypothesis: The process is weakly stationary.\n",
      "Alternative Hypothesis: The process contains a unit root.\n"
     ]
    }
   ],
   "source": [
    "kpss = KPSS(default, trend=\"ct\")\n",
    "print(kpss.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Zivot-Andrews Test\n",
    "\n",
    "The Zivot-Andrews test allows the possibility of a single structural break in the series. Here we test the default using the test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Zivot-Andrews Results        \n",
      "=====================================\n",
      "Test Statistic                 -4.900\n",
      "P-value                         0.040\n",
      "Lags                               21\n",
      "-------------------------------------\n",
      "\n",
      "Trend: Constant\n",
      "Critical Values: -5.28 (1%), -4.81 (5%), -4.57 (10%)\n",
      "Null Hypothesis: The process contains a unit root with a single structural break.\n",
      "Alternative Hypothesis: The process is trend and break stationary.\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import ZivotAndrews\n",
    "\n",
    "za = ZivotAndrews(default)\n",
    "print(za.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variance Ratio Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variance ratio tests are not usually used as unit root tests, and are instead used for testing whether a financial return series is a pure random walk versus having some predictability.  This example uses the excess return on the market from Ken French's data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            Mkt-RF          SMB          HML           RF\n",
      "count  1109.000000  1109.000000  1109.000000  1109.000000\n",
      "mean      0.659946     0.206555     0.368864     0.274220\n",
      "std       5.327524     3.191132     3.482352     0.253377\n",
      "min     -29.130000   -16.870000   -13.280000    -0.060000\n",
      "25%      -1.970000    -1.560000    -1.320000     0.030000\n",
      "50%       1.020000     0.070000     0.140000     0.230000\n",
      "75%       3.610000     1.730000     1.740000     0.430000\n",
      "max      38.850000    36.700000    35.460000     1.350000\n"
     ]
    }
   ],
   "source": [
    "import arch.data.frenchdata\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "ff = arch.data.frenchdata.load()\n",
    "excess_market = ff.iloc[:, 0]  # Excess Market\n",
    "print(ff.describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variance ratio compares the variance of a 1-period return to that of a multi-period return. The comparison length has to be set when initializing the test.  \n",
    "\n",
    "This example compares 1-month to 12-month returns, and the null that the series is a pure random walk is rejected. Negative values indicate some positive autocorrelation in the returns (momentum)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Variance-Ratio Test Results     \n",
      "=====================================\n",
      "Test Statistic                 -5.029\n",
      "P-value                         0.000\n",
      "Lags                               12\n",
      "-------------------------------------\n",
      "\n",
      "Computed with overlapping blocks (de-biased)\n"
     ]
    }
   ],
   "source": [
    "from arch.unitroot import VarianceRatio\n",
    "\n",
    "vr = VarianceRatio(excess_market, 12)\n",
    "print(vr.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default the VR test uses all overlapping blocks to estimate the variance of the long period's return.  This can be changed by setting  `overlap=False`.  This lowers the power but does not change the conclusion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Variance-Ratio Test Results     \n",
      "=====================================\n",
      "Test Statistic                 -6.206\n",
      "P-value                         0.000\n",
      "Lags                               12\n",
      "-------------------------------------\n",
      "\n",
      "Computed with non-overlapping blocks\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\git\\arch\\arch\\unitroot\\unitroot.py:1679: InvalidLengthWarning: \n",
      "The length of y is not an exact multiple of 12, and so the final\n",
      "4 observations have been dropped.\n",
      "\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "warnings.simplefilter(\"always\")  # Restore warnings\n",
    "\n",
    "vr = VarianceRatio(excess_market, 12, overlap=False)\n",
    "print(vr.summary().as_text())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: The warning is intentional. It appears here since when it is not possible to use all data since the data length is not an integer multiple of the long period when using non-overlapping blocks.  There is little reason to use `overlap=False`."
   ]
  }
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