kongscn/adf_hl.nb

## adf_hl.nb
{
 "metadata": {
  "name": "",
  "signature": "sha256:67ef237c0c9ece746bfe2500e488c467aabd97c00c8d8aae000151ee8323a44c"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Implementation of Stationary Test and Half-Life Calculation with Python in Chen's Algorithmic Trading Chapter 2\n",
      "\n",
      "In the following example, we apply adf test and calculate half-life time according to Chen's book *Algorithmic Trading* chapter 2,\n",
      "using Python and `statsmodels` package."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import Quandl\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import statsmodels.api as sm\n",
      "import statsmodels.tsa.stattools as ts\n",
      "import scipy.io as sio"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Get USD/CAD Data from Quandl.com"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "startdate = '2007-07-22'\n",
      "enddate = '2012-03-28'\n",
      "qcode = 'CURRFX/USDCAD'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "url = Quandl.get(qcode, trim_start=startdate, trim_end=enddate, returns='url')\n",
      "df = Quandl.get(qcode, trim_start=startdate, trim_end=enddate)\n",
      "usdcad = df.Rate"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "usdcad.plot()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<matplotlib.axes.AxesSubplot at 0x848f198>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CDzzQ9tzHHwduu80qOn3FFZII7MILgfvvd69N1dXAqadahbEVRUkNIgIzx8zWlLHFTkTD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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x69ee860>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# ADF Test"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ts.adfuller(usdcad, maxlag=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "(-2.3466233030145998,\n",
        " 0.15737142688333444,\n",
        " 1,\n",
        " 1221,\n",
        " {'5%': -2.8639100200710828,\n",
        "  '1%': -3.435716995109265,\n",
        "  '10%': -2.568031835031368},\n",
        " -9562.9337394440736)"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Calculate Half-Life and Lookback"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "md = sm.OLS(usdcad.diff(), sm.add_constant(usdcad.shift()), missing='drop')\n",
      "mdf = md.fit()\n",
      "half_life = -np.log(2)/mdf.params[1]\n",
      "lookback = np.round(half_life)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "half_life, lookback"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(280.64173746164386, 281.0)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The OLS Regression Result"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(mdf.summary())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:                   Rate   R-squared:                       0.001\n",
        "Model:                            OLS   Adj. R-squared:                  0.000\n",
        "Method:                 Least Squares   F-statistic:                     1.394\n",
        "Date:                Thu, 04 Dec 2014   Prob (F-statistic):              0.238\n",
        "Time:                        16:21:17   Log-Likelihood:                 4558.0\n",
        "No. Observations:                1222   AIC:                            -9112.\n",
        "Df Residuals:                    1220   BIC:                            -9102.\n",
        "Df Model:                           1                                         \n",
        "Covariance Type:            nonrobust                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "const          0.0025      0.002      1.157      0.247        -0.002     0.007\n",
        "Rate          -0.0025      0.002     -1.181      0.238        -0.007     0.002\n",
        "==============================================================================\n",
        "Omnibus:                      157.966   Durbin-Watson:                   0.881\n",
        "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1621.257\n",
        "Skew:                           0.117   Prob(JB):                         0.00\n",
        "Kurtosis:                       8.638   Cond. No.                         26.5\n",
        "==============================================================================\n",
        "\n",
        "Warnings:\n",
        "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Wrap Into One Function"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def adf_hl(price):\n",
      "    \"\"\"Calculate ADF test and Half-Life time.\n",
      "    :param price: A pandas.Series of data.  \n",
      "    :return: (adf test result, half-life, lookback)  \n",
      "    \"\"\"\n",
      "    # ADF test\n",
      "    adftest = ts.adfuller(price, maxlag=1)\n",
      "    # Half-Life\n",
      "    md = sm.OLS(price.diff(), sm.add_constant(price.shift()), missing='drop')\n",
      "    mdf = md.fit()\n",
      "    half_life = -np.log(2)/mdf.params[1]\n",
      "    lookback = np.round(half_life)\n",
      "    return adftest, half_life, lookback"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "adf_hl(usdcad)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "((-2.3466233030145998,\n",
        "  0.15737142688333444,\n",
        "  1,\n",
        "  1221,\n",
        "  {'5%': -2.8639100200710828,\n",
        "   '1%': -3.435716995109265,\n",
        "   '10%': -2.568031835031368},\n",
        "  -9562.9337394440736),\n",
        " 280.64173746164386,\n",
        " 281.0)"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Why the Result Is Different?\n",
      "\n",
      "Because the **data is different**. \n",
      "Let's try it with the same data used in the Chen's book"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mat = sio.loadmat('inputData_USDCAD_20120426.mat')\n",
      "usdcad = mat['cl'][mat['hhmm']==1659]\n",
      "usdcad = pd.Series(usdcad, name='USDCAD')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "adf_hl(usdcad)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "((-1.8693961749348129,\n",
        "  0.34659219335600439,\n",
        "  0,\n",
        "  1236,\n",
        "  {'5%': -2.8638812231195359,\n",
        "   '1%': -3.4356517256484151,\n",
        "   '10%': -2.5680164989107781},\n",
        "  -8190.3235420441761),\n",
        " 117.47697667883388,\n",
        " 117.0)"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The ADF Result Is Still Different?\n",
      "\n",
      "When applying adf test, we need to choose the *right* lags. The lag used in Chen's book is fixed as 1, but in out code the lags are choosed automatically under a limit(here I set it to 1), and finally selected 0 in our example."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_,_,lookback = adf_hl(usdcad)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mktValue = -(usdcad - pd.rolling_mean(usdcad, lookback)) / pd.rolling_std(usdcad, lookback)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# pnl=lag(mktVal, 1).*(y-lag(y, 1))./lag(y, 1);\n",
      "pnl = mktValue.shift() * usdcad.diff() / usdcad.shift()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pnl.cumsum().plot()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "<matplotlib.axes.AxesSubplot at 0x91f2a58>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x924ba90>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}