{
 "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",
    "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 pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "import arch.data.default\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.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.trend = 'ct'\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:                Wed, 29 Jan 2020   Prob (F-statistic):           1.30e-22\n",
      "Time:                        18:15:39   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",
      "Warnings:\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": {
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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.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.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.trend = 'ct'\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                         0.000\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.test_type = 'rho'\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.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 numpy as np\n",
    "import pandas as pd\n",
    "import arch.data.frenchdata\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",
    "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:1533: 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",
      "  InvalidLengthWarning,\n"
     ]
    }
   ],
   "source": [
    "warnings.simplefilter('always')  # Restore warnings\n",
    "\n",
    "vr.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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