AFML 5.2.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "# Fractional differentiate\n",
    "\n",
    "This notebook will cover exercise answer.\n",
    "\n",
    "* Exercise 5.4\n",
    "* Exercise 5.5\n",
    "\n",
    "As we go along, there will be some explanations.\n",
    "\n",
    "Stationarity is a key concept in time-series, by now the idea itself has been demostrated in previous notebooks (Feat Importance).\n",
    "\n",
    "Most of the functions below can be found under research/Features\n",
    "\n",
    "Contact: boyboi86@gmail.com"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Num of CPU core:  4\n",
      "Machine info:  Windows-10-10.0.18362-SP0\n",
      "Python 3.7.4 (default, Aug  9 2019, 18:34:13) [MSC v.1915 64 bit (AMD64)]\n",
      "Numpy 1.17.3\n",
      "Pandas 1.0.3\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Wei_X\\Anaconda3\\lib\\site-packages\\statsmodels\\tools\\_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
      "  import pandas.util.testing as tm\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1500x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numba import njit\n",
    "import pandas as pd\n",
    "import research as rs\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "from scipy.stats import jarque_bera\n",
    "\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "from statsmodels.tsa.stattools import coint\n",
    "\n",
    "p = print\n",
    "\n",
    "#pls take note of version\n",
    "#numba 0.49.1 #https://github.com/numba/numba/issues/4255\n",
    "#numpy 1.17.3\n",
    "#pandas 1.0.3\n",
    "\n",
    "dollar = pd.read_csv('./research/Sample_data/dollar_bars.txt', \n",
    "                 sep=',', \n",
    "                 header=0, \n",
    "                 parse_dates = True, \n",
    "                 index_col=['date_time'])\n",
    "\n",
    "# For most part of the func we only use 'close'\n",
    "\n",
    "close = dollar['close'].to_frame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#The same func can be found under research/Feature\n",
    "@njit\n",
    "def getWeights(d, size):\n",
    "    w=[1.]\n",
    "    for k in np.arange(1,size):\n",
    "        w_ = -w[-1]/k*(d-k+1)\n",
    "        w.append(w_)\n",
    "    w=np.array(w[::-1]).reshape(-1,1)\n",
    "    return w\n",
    "\n",
    "def fracDiff(series, d, thres=.01):\n",
    "    w=getWeights(d, series.shape[0])\n",
    "    w_=np.cumsum(abs(w))\n",
    "    w_/=w_[-1]\n",
    "    skip = w_[w_>thres].shape[0]\n",
    "    df={}\n",
    "    for name in series.columns:\n",
    "        seriesF,df_=series[[name]].fillna(method='ffill').dropna(),pd.Series(index=series.index, dtype=float)\n",
    "        for iloc in range(skip,seriesF.shape[0]):\n",
    "            loc=seriesF.index[iloc]\n",
    "            if not np.isfinite(series.loc[loc,name]): continue\n",
    "            df_[loc]=np.dot(w[-(iloc+1):,:].T,seriesF.loc[:loc])[0,0]\n",
    "        df[name]=df_.copy(deep=True)\n",
    "    df=pd.concat(df,axis=1)\n",
    "    return df\n",
    "\n",
    "@njit\n",
    "def getWeights_FFD(d, thres):\n",
    "    w,k=[1.],1\n",
    "    while True:\n",
    "        w_ = -w[-1]/k*(d-k+1)\n",
    "        if abs(w_) < thres:\n",
    "            break\n",
    "        w.append(w_); k+=1\n",
    "    return np.array(w[::-1]).reshape(-1,1)\n",
    "\n",
    "# need to refactor to optimze if not will take forever if threshold too low\n",
    "def fracDiff_FFD(series, d, thres=1e-2):\n",
    "    w, df = getWeights_FFD(d, thres), {}\n",
    "    width = len(w)-1\n",
    "    for name in series.columns:\n",
    "        seriesF,df_=series[[name]].fillna(method='ffill').dropna(),pd.Series(index=series.index, dtype=float)\n",
    "        for iloc in range(width, seriesF.shape[0]):\n",
    "            loc0, loc1 = seriesF.index[iloc - width], seriesF.index[iloc]\n",
    "            if not np.isfinite(series.loc[loc1,name]): continue\n",
    "            df_[loc1]=np.dot(w.T,seriesF.loc[loc0:loc1])[0,0]\n",
    "        df[name]=df_.copy(deep=True)\n",
    "    df=pd.concat(df,axis=1)\n",
    "    return df\n",
    "\n",
    "def min_value(data: pd.Series, func, thres = 0.01, pval_threshold: float = 0.05):\n",
    "    d_domain = np.linspace(start = 0, \n",
    "                           stop = 2, \n",
    "                           num=100, \n",
    "                           endpoint=True, \n",
    "                           retstep=False, \n",
    "                           dtype=float)\n",
    "    \n",
    "    for d in d_domain:\n",
    "        df1 = np.log(data).resample('1D').last() # pls note downcast to daily obs\n",
    "        df2 = func(df1, d, thres = thres).dropna()\n",
    "        p(df2)\n",
    "        df2 = adfuller(df2.squeeze(), maxlag=1, regression='c', autolag=None)\n",
    "        try:\n",
    "            if df2[1] <= pval_threshold:\n",
    "                return d\n",
    "        except:\n",
    "            p('Something is wrong! Most likely required d value more than 2!!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "Function used: Fixed Window FD\n",
      "[               close\n",
      "date_time           \n",
      "2015-01-01  7.628882\n",
      "2015-01-02  7.624741\n",
      "2015-01-03       NaN\n",
      "2015-01-04  7.621073\n",
      "2015-01-05  7.608871\n",
      "...              ...\n",
      "2016-12-26       NaN\n",
      "2016-12-27  7.723894\n",
      "2016-12-28  7.716572\n",
      "2016-12-29  7.716795\n",
      "2016-12-30  7.711997\n",
      "\n",
      "[730 rows x 1 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-05-25 16:33:50.062490 100.0% fracDiff_FFD done after 0.1 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[               close\n",
      "date_time           \n",
      "2015-01-01       NaN\n",
      "2015-01-02  7.470622\n",
      "2015-01-03       NaN\n",
      "2015-01-04  7.467037\n",
      "2015-01-05  7.454910\n",
      "...              ...\n",
      "2016-12-26       NaN\n",
      "2016-12-27  7.567874\n",
      "2016-12-28  7.560534\n",
      "2016-12-29  7.560904\n",
      "2016-12-30  7.556102\n",
      "\n",
      "[730 rows x 1 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-05-25 16:33:56.470437 100.0% fracDiff_FFD done after 0.1 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[               close\n",
      "date_time           \n",
      "2015-01-01       NaN\n",
      "2015-01-02       NaN\n",
      "2015-01-03       NaN\n",
      "2015-01-04  7.068588\n",
      "2015-01-05  7.056587\n",
      "...              ...\n",
      "2016-12-26       NaN\n",
      "2016-12-27  7.164342\n",
      "2016-12-28  7.156984\n",
      "2016-12-29  7.157486\n",
      "2016-12-30  7.152809\n",
      "\n",
      "[730 rows x 1 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-05-25 16:34:02.859933 100.0% fracDiff_FFD done after 0.1 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[               close\n",
      "date_time           \n",
      "2015-01-01       NaN\n",
      "2015-01-02       NaN\n",
      "2015-01-03       NaN\n",
      "2015-01-04       NaN\n",
      "2015-01-05       NaN\n",
      "...              ...\n",
      "2016-12-26       NaN\n",
      "2016-12-27  6.707145\n",
      "2016-12-28  6.699763\n",
      "2016-12-29  6.700404\n",
      "2016-12-30  6.695784\n",
      "\n",
      "[730 rows x 1 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-05-25 16:34:09.089784 100.0% fracDiff_FFD done after 0.09 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[               close\n",
      "date_time           \n",
      "2015-01-01       NaN\n",
      "2015-01-02       NaN\n",
      "2015-01-03       NaN\n",
      "2015-01-04       NaN\n",
      "2015-01-05       NaN\n",
      "...              ...\n",
      "2016-12-26       NaN\n",
      "2016-12-27  6.304567\n",
      "2016-12-28  6.297177\n",
      "2016-12-29  6.297951\n",
      "2016-12-30  6.293386\n",
      "\n",
      "[730 rows x 1 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-05-25 16:34:15.352723 100.0% fracDiff_FFD done after 0.09 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[               close\n",
      "date_time           \n",
      "2015-01-01       NaN\n",
      "2015-01-02       NaN\n",
      "2015-01-03       NaN\n",
      "2015-01-04       NaN\n",
      "2015-01-05       NaN\n",
      "...              ...\n",
      "2016-12-26       NaN\n",
      "2016-12-27  5.896106\n",
      "2016-12-28  5.888724\n",
      "2016-12-29  5.889650\n",
      "2016-12-30  5.885129\n",
      "\n",
      "[730 rows x 1 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-05-25 16:34:21.623674 100.0% fracDiff_FFD done after 0.09 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[               close\n",
      "date_time           \n",
      "2015-01-01       NaN\n",
      "2015-01-02       NaN\n",
      "2015-01-03       NaN\n",
      "2015-01-04       NaN\n",
      "2015-01-05       NaN\n",
      "...              ...\n",
      "2016-12-26       NaN\n",
      "2016-12-27  5.490007\n",
      "2016-12-28  5.482573\n",
      "2016-12-29  5.483666\n",
      "2016-12-30  5.479205\n",
      "\n",
      "[730 rows x 1 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-05-25 16:34:27.884056 100.0% fracDiff_FFD done after 0.09 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[               close\n",
      "date_time           \n",
      "2015-01-01       NaN\n",
      "2015-01-02       NaN\n",
      "2015-01-03       NaN\n",
      "2015-01-04       NaN\n",
      "2015-01-05       NaN\n",
      "...              ...\n",
      "2016-12-26       NaN\n",
      "2016-12-27  5.092027\n",
      "2016-12-28  5.084561\n",
      "2016-12-29  5.085761\n",
      "2016-12-30  5.081371\n",
      "\n",
      "[730 rows x 1 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-05-25 16:34:34.446722 100.0% fracDiff_FFD done after 0.1 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d value to attain stationarity: 0.141414\n",
      "Min d Value: 0.141414\n",
      "ADF pVal: 0.03250 with critical value: 5.0%\n"
     ]
    }
   ],
   "source": [
    "# Take optimal value to pass stationary test\n",
    "# if you are keen.. adfuller can provide full test result.. go to statsmodel API documentation for more details\n",
    "# When you run this min_value func from rs, you may encounter memory issue.\n",
    "test_val = 0.05\n",
    "\n",
    "log_price = close.apply(np.log)\n",
    "\n",
    "# this func is the same as others as seen above except input has to be log by users, func will no long do it.\n",
    "# you have more flexiblility to input log price series or non-log, as well as cumsum()\n",
    "mv = rs.min_value(data = log_price,\n",
    "                  FFD = True,\n",
    "                  thres = 0.01,\n",
    "                  pval_threshold = test_val,\n",
    "                  num = 100,\n",
    "                  num_threads = 21)\n",
    "\n",
    "# Do not set autolag to 'AIC'\n",
    "adf_pval = adfuller(fracDiff_FFD(log_price, d=0.141414).dropna().squeeze(), \n",
    "                    maxlag=1, \n",
    "                    regression='c', \n",
    "                    autolag=None)[1]\n",
    "\n",
    "p(\"Min d Value: {0:.6f}\\nADF pVal: {1:.5f} with critical value: {2}%\".format(mv, adf_pval, test_val * 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ffd0 = fracDiff_FFD(log_price, d = 0.141)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>close</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>24070.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.036285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.028770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>4.947561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.021549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>5.040763</td>\n",
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       "      <th>75%</th>\n",
       "      <td>5.053797</td>\n",
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       "      <th>max</th>\n",
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       "              close\n",
       "count  24070.000000\n",
       "mean       5.036285\n",
       "std        0.028770\n",
       "min        4.947561\n",
       "25%        5.021549\n",
       "50%        5.040763\n",
       "75%        5.053797\n",
       "max        5.102104"
      ]
     },
     "execution_count": 5,
     "metadata": {},
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   "source": [
    "ffd0.describe() # initial num count 24079 before FFD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "ffd1 = fracDiff_FFD(ffd0.dropna(), d = -0.141)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "      <th>close</th>\n",
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       "      <th>count</th>\n",
       "      <td>24047.000000</td>\n",
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       "      <th>mean</th>\n",
       "      <td>8.400578</td>\n",
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       "      <th>std</th>\n",
       "      <td>0.047928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>8.256572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>8.375772</td>\n",
       "    </tr>\n",
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       "      <th>50%</th>\n",
       "      <td>8.408035</td>\n",
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       "      <th>75%</th>\n",
       "      <td>8.429675</td>\n",
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       "              close\n",
       "count  24047.000000\n",
       "mean       8.400578\n",
       "std        0.047928\n",
       "min        8.256572\n",
       "25%        8.375772\n",
       "50%        8.408035\n",
       "75%        8.429675\n",
       "max        8.508450"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ffd1.describe() # after second FFD based on first FFD but with -d value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Further investgation on negative d value\n",
    "\n",
    "Even without using FFD twice, just by using a single FFD with -d value. It will still produce NaNs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ffd2 = fracDiff_FFD(ffd1, d = -0.141)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>24024.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>14.012257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.079891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>13.774925</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>13.970740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>14.024726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>14.060666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>14.190578</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              close\n",
       "count  24024.000000\n",
       "mean      14.012257\n",
       "std        0.079891\n",
       "min       13.774925\n",
       "25%       13.970740\n",
       "50%       14.024726\n",
       "75%       14.060666\n",
       "max       14.190578"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ffd2.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Infinite observations\n",
    "\n",
    "When we try to get weight for FFD, using positive d value will produce appropriate \"discount\" to observation values.\n",
    "\n",
    "However, using negative d value we will instead get unlimited \"additive\" observation values, since we can never get to hit threshold.\n",
    "\n",
    "In short, convergence will not occur but instead divergence will take place.\n",
    "\n",
    "#### getWeights_FFD function warning\n",
    "\n",
    "The function getWeight_FFD would have cause infinite loop when we use negative d value if we did not put a threshold limit condition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.01016333],\n",
       "       [0.01055764],\n",
       "       [0.01098661],\n",
       "       [0.01145519],\n",
       "       [0.01196927],\n",
       "       [0.01253603],\n",
       "       [0.01316425],\n",
       "       [0.01386484],\n",
       "       [0.01465143],\n",
       "       [0.01554144],\n",
       "       [0.01655735],\n",
       "       [0.01772882],\n",
       "       [0.01909576],\n",
       "       [0.02071327],\n",
       "       [0.02265975],\n",
       "       [0.0250507 ],\n",
       "       [0.02806408],\n",
       "       [0.03198967],\n",
       "       [0.03733476],\n",
       "       [0.0450794 ],\n",
       "       [0.0574077 ],\n",
       "       [0.0804405 ],\n",
       "       [0.141     ],\n",
       "       [1.        ]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getWeights_FFD(-0.141, 0.01) # negative value which led to divergence (right to left)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.01050548],\n",
       "       [-0.01203071],\n",
       "       [-0.01403203],\n",
       "       [-0.01676467],\n",
       "       [-0.02070138],\n",
       "       [-0.02682221],\n",
       "       [-0.0375267 ],\n",
       "       [-0.0605595 ],\n",
       "       [-0.141     ],\n",
       "       [ 1.        ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getWeights_FFD(0.141, 0.01) # positive value for convergence (left to right)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 5.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date_time</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-01-01 23:00:23.723</th>\n",
       "      <td>7.628882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-02 07:07:35.156</th>\n",
       "      <td>7.632401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-02 09:35:57.204</th>\n",
       "      <td>7.630704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-02 12:59:42.176</th>\n",
       "      <td>7.630947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-02 14:19:33.847</th>\n",
       "      <td>7.632280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-02 14:33:39.311</th>\n",
       "      <td>7.632643</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            close\n",
       "date_time                        \n",
       "2015-01-01 23:00:23.723  7.628882\n",
       "2015-01-02 07:07:35.156  7.632401\n",
       "2015-01-02 09:35:57.204  7.630704\n",
       "2015-01-02 12:59:42.176  7.630947\n",
       "2015-01-02 14:19:33.847  7.632280\n",
       "2015-01-02 14:33:39.311  7.632643"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_price.head(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>close</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>24079.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>91747.193481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>52961.243656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>7.628882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>45974.457645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>91742.869713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>137500.145350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>183724.410799</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               close\n",
       "count   24079.000000\n",
       "mean    91747.193481\n",
       "std     52961.243656\n",
       "min         7.628882\n",
       "25%     45974.457645\n",
       "50%     91742.869713\n",
       "75%    137500.145350\n",
       "max    183724.410799"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cumsum_logp = log_price.cumsum()\n",
    "cumsum_logp.dropna(inplace = True)\n",
    "cumsum_logp.describe() #initial count 24079 if no NaNs count should be same"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date_time</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-01-01 23:00:23.723</th>\n",
       "      <td>7.628882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-02 07:07:35.156</th>\n",
       "      <td>15.261283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-02 09:35:57.204</th>\n",
       "      <td>22.891987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-02 12:59:42.176</th>\n",
       "      <td>30.522934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-02 14:19:33.847</th>\n",
       "      <td>38.155214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-02 14:33:39.311</th>\n",
       "      <td>45.787857</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             close\n",
       "date_time                         \n",
       "2015-01-01 23:00:23.723   7.628882\n",
       "2015-01-02 07:07:35.156  15.261283\n",
       "2015-01-02 09:35:57.204  22.891987\n",
       "2015-01-02 12:59:42.176  30.522934\n",
       "2015-01-02 14:19:33.847  38.155214\n",
       "2015-01-02 14:33:39.311  45.787857"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cumsum_logp.head(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1aefb6d7888>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cumsum_logp.plot(figsize=(10,8)) # literally a straight line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "Cumumlative sum prices use threshold 1.e-5.\n",
    "\n",
    "Non-cumumlative prices use threshold 1.e-2.\n",
    "\n",
    "Otherwise threshold is too low.\n",
    "\n",
    "Log prices in theory may improve convergence, you may wish to check max likelihood estimation or AIC score."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this is a sample func on per tick, DO NOT use it otherwise it will take forever if per tick.\n",
    "\n",
    "def minVal_cs(data: pd.Series, thres: float = 1e-5, pval_threshold: float = 0.05, d_range: list = [1.9, 2.0] ):\n",
    "    d_domain = np.linspace(start = d_range[0], \n",
    "                           stop = d_range[1], \n",
    "                           num=1e9, \n",
    "                           endpoint=True, \n",
    "                           retstep=False, \n",
    "                           dtype=float)\n",
    "    \n",
    "    for d in d_domain:\n",
    "        try:\n",
    "            df1 = np.log(data).cumsum() #.resample('1h').last()# pls note downcast to daily obs\n",
    "            df1.dropna(inplace=True)\n",
    "            df2 = fracDiff_FFD(df1, d, thres = thres).dropna()\n",
    "            df2 = adfuller(df2.squeeze(), maxlag = 1,regression='c', autolag=None)\n",
    "            if df2[1] <= pval_threshold:\n",
    "                print(d)\n",
    "                return d\n",
    "        except:\n",
    "            p('Something is wrong! Most likely required d value beyond input parameter!!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.99999889\n"
     ]
    }
   ],
   "source": [
    "# Kindly refer to the ans d = 1.99999889 instead to save time, it may even crash\n",
    "\n",
    "#even with multiprocessing running this func will still take some time\n",
    "\"\"\"\n",
    "mv = rs.min_value(data = cumsum_logp,\n",
    "                  FFD = True,\n",
    "                  thres = 1e-5,\n",
    "                  pval_threshold = test_val,\n",
    "                  num = 1e9,\n",
    "                  num_threads = 21)\n",
    "\"\"\"\n",
    "\n",
    "minVal_cs(data = cumsum_logp, thres = 1e-5, pval_threshold = 0.05, d_range = [1.9999, 2.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "If you cumulative sum your financial time-series, before FFD. \n",
    "\n",
    "You will need to differentiate and in this case min d value is very close 2.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ADF pVal: 0.04165 with critical value: 5.0%\n"
     ]
    }
   ],
   "source": [
    "# if d value was 1.999999 ADF p value would be 0.01695 < 0.04165 < 0.05\n",
    "ffd3 = fracDiff_FFD(cumsum_logp, \n",
    "                    d = 1.99999889, \n",
    "                    thres=1e-5\n",
    "                   ).dropna()\n",
    "\n",
    "adf_pval = adfuller(ffd3.squeeze(), \n",
    "                    maxlag = 1,\n",
    "                    regression='c', \n",
    "                    autolag=None)[1]\n",
    "\n",
    "p(\"\\nADF pVal: {0:.5f} with critical value: {1}%\".format(adf_pval, test_val * 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1aefba36cc8>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fracdiff_series = pd.DataFrame(index=ffd3.index).assign(ffd3 = ffd3, #after fractional differentiate\n",
    "                                                        cumsum_logp = cumsum_logp, #cumulative sum of log price\n",
    "                                                        close = close) #original\n",
    "\n",
    "fracdiff_series[['ffd3', 'close']].plot(secondary_y='close', figsize=(10,8)) #not even remotely close"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>ffd3</th>\n",
       "      <th>cumsum_logp</th>\n",
       "      <th>close</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ffd3</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.998939</td>\n",
       "      <td>-0.405165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cumsum_logp</th>\n",
       "      <td>-0.998939</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.406330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>close</th>\n",
       "      <td>-0.405165</td>\n",
       "      <td>0.406330</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 ffd3  cumsum_logp     close\n",
       "ffd3         1.000000    -0.998939 -0.405165\n",
       "cumsum_logp -0.998939     1.000000  0.406330\n",
       "close       -0.405165     0.406330  1.000000"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fracdiff_series[['ffd3', 'cumsum_logp']].plot(secondary_y='cumsum_logp', figsize=(10,8)) #not even remotely close\n",
    "\n",
    "fracdiff_series.corr(method='pearson') # see correlation matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF pVal for original time-series: 0.29394421553033817\n",
      "\n",
      "ADF pVal for acummulative log price time-series: 0.9979035515620875\n",
      "\n",
      "Jarque Bera pVal: 0.00000\n",
      "\n",
      "Engel-Granger Coint pVal: 0.009683330960666188\n"
     ]
    }
   ],
   "source": [
    "p(\"ADF pVal for original time-series: {0}\\n\".format(adfuller(fracdiff_series['close'], \n",
    "                                  maxlag = 1, \n",
    "                                  regression = 'c', \n",
    "                                  autolag=None)[1]))\n",
    "\n",
    "p(\"ADF pVal for acummulative log price time-series: {0}\\n\".format(adfuller(fracdiff_series['cumsum_logp'], \n",
    "                                  maxlag = 1, \n",
    "                                  regression = 'c', \n",
    "                                  autolag=None)[1]))\n",
    "\n",
    "# time-series is not stationary since p-value is more than 0.05\n",
    "\n",
    "p(\"Jarque Bera pVal: {0:.5f}\\n\".format(jarque_bera(fracdiff_series['ffd3'])[1]))\n",
    "\n",
    "# time-series is not normal since p value is less than 0.05\n",
    "\n",
    "result = coint(fracdiff_series['ffd3'], fracdiff_series['close'], maxlag = 1, trend = 'c', autolag = None)\n",
    "\n",
    "p(\"Engel-Granger Coint pVal: {0}\".format(result[1]))\n",
    "\n",
    "# there is a long term relationship since p-value is less than 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Memory Persistance\n",
    "\n",
    "ADF p-val for original was 0.2939. Corr against FFD was -0.405165, inverse relation.\n",
    "\n",
    "ADF p-val for cumsum log price was 0.9979. Corr against FFD was -0.9989, inverse relation.\n",
    "\n",
    "ADF p-val for FFD using d value 1.99999889 was 0.04165.(Stationary).\n",
    "\n",
    "Coint p-val for FFD and original was 0.009683.\n",
    "\n",
    "Initially we preserve time series memory by log price, however as we cumsum the log price time series we cause these memory to accumulate which increases ADF p-value and more \"unstationary\" since we created a linear trend.\n",
    "\n",
    "In most cases, d value was less than 1 but due to this new cumsum log price we end up using above 1 which will cause \"decay\" to be very aggressive which is reflected in the graph ffd3 vs original time series.\n",
    "\n",
    "However, when perform Engel-Granger Coint test, test result states the two seemingly negatively correlated time-series do have a long term relationship. Most likely due to the memory persistance, which achieved p-value of 0.009683 lower than critical size 0.01.\n",
    "\n",
    ">\"Log prices have memory but are non-stationary. Cointegration is the trick that makes regression works on non-stationary series, so that memory is preserved.\"\n",
    ">\n",
    "> Advances in Financial Machine Learning, page 88, section 5.7\n",
    "\n",
    "### Conclusion\n",
    "\n",
    "This is an important finding since we require a stationary series with maximum memory preserved to ensure machine learning use it as key predictive feature effectively."
   ]
  }
 ],
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