micro_price_replicatioon.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "069b22a3",
   "metadata": {},
   "source": [
    "## micro price replication \n",
    "1. symmetrize data\n",
    "    - (It,St,It+1,St+1,dM) ==> (1-It,St,1-It+1,St+1,-dM)\n",
    "2. Estimate Q, T, R\n",
    "3. Calculate G1\n",
    "4. Calculate G* ==> micro price adjustment \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "60a59594",
   "metadata": {},
   "outputs": [],
   "source": [
    "# load libraries \n",
    "import math\n",
    "import decimal \n",
    "import numpy as np \n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\"\n",
    "\n",
    "from scipy.linalg import block_diag\n",
    "from scipy.linalg import eig\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "909c6052",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time_seconds</th>\n",
       "      <th>bid_price</th>\n",
       "      <th>bid_size</th>\n",
       "      <th>ask_price</th>\n",
       "      <th>ask_size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1645142400</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>1.863301</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>0.950000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1645142401</td>\n",
       "      <td>0.07138</td>\n",
       "      <td>0.499840</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>18.225881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1645142403</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>0.499840</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>18.225881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1645142404</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>0.914646</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>0.950000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1645142405</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>0.499840</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>18.571515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64214</th>\n",
       "      <td>1645228793</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>1.549840</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>3.821804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64215</th>\n",
       "      <td>1645228794</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>1.549840</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>3.820255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64216</th>\n",
       "      <td>1645228796</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>2.221340</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>2.644555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64217</th>\n",
       "      <td>1645228797</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>4.066678</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>2.644555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64218</th>\n",
       "      <td>1645228798</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>3.707040</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>2.644555</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>64219 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       time_seconds  bid_price  bid_size  ask_price   ask_size\n",
       "0        1645142400    0.07137  1.863301    0.07139   0.950000\n",
       "1        1645142401    0.07138  0.499840    0.07139  18.225881\n",
       "2        1645142403    0.07137  0.499840    0.07139  18.225881\n",
       "3        1645142404    0.07137  0.914646    0.07139   0.950000\n",
       "4        1645142405    0.07137  0.499840    0.07139  18.571515\n",
       "...             ...        ...       ...        ...        ...\n",
       "64214    1645228793    0.06950  1.549840    0.06951   3.821804\n",
       "64215    1645228794    0.06950  1.549840    0.06951   3.820255\n",
       "64216    1645228796    0.06950  2.221340    0.06951   2.644555\n",
       "64217    1645228797    0.06950  4.066678    0.06951   2.644555\n",
       "64218    1645228798    0.06950  3.707040    0.06951   2.644555\n",
       "\n",
       "[64219 rows x 5 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load data \n",
    "df_data = pd.read_csv('eth_btc_coinbase.csv.gz', compression='gzip')\n",
    "\n",
    "# split the price and volume \n",
    "df_data[[\"bid_price\", \"bid_size\"]] = df_data[\"bid_price_bid_size\"].str.split(pat=\"_\", expand=True).astype(float)\n",
    "df_data[[\"ask_price\", \"ask_size\"]] = df_data[\"ask_price_ask_size\"].str.split(pat=\"_\", expand=True).astype(float)\n",
    "\n",
    "# drop original \n",
    "df_data = df_data.drop([\"bid_price_bid_size\", \"ask_price_ask_size\"], axis=1)\n",
    "\n",
    "df_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3db57b2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def processing_data(df_data, n_imb, n_spread, dt, is_filter_symm=True):\n",
    "    \"\"\"\n",
    "    processing data for micro price construction \n",
    "    \"\"\"\n",
    "    \n",
    "    ## 1. calculate relevant indicators \n",
    "    # find tick size \n",
    "    # minimum of absolute spread is the tick size \n",
    "    spread = df_data[\"ask_price\"] - df_data[\"bid_price\"]\n",
    "    ticksize = np.round(min(spread.loc[spread > 0]) * 1e6) / 1e6\n",
    "\n",
    "    # spread in terms of tick \n",
    "    df_data['spread'] = np.round((df_data['ask_price'] - df_data['bid_price']) / ticksize) * ticksize\n",
    "\n",
    "    # mid price\n",
    "    df_data['mid'] = (df_data['ask_price'] + df_data['bid_price'])/2\n",
    "\n",
    "    # weighed mid price \n",
    "    df_data['wmid'] = (\n",
    "        (df_data['ask_price'] * df_data['bid_size'] + df_data['bid_price']*df_data['ask_size'])\n",
    "        / (df_data['ask_size'] + df_data['bid_size'])\n",
    "    )\n",
    "\n",
    "    # orderbook imbalance \n",
    "    df_data[\"imb\"] = df_data[\"bid_size\"] / (df_data[\"bid_size\"] + df_data[\"ask_size\"])\n",
    "\n",
    "    # discretize imbalance into percentiles\n",
    "    df_data['imb_bucket'] = pd.qcut(df_data['imb'], n_imb, labels=False)\n",
    "\n",
    "    # next\n",
    "    df_data['next_mid'] = df_data['mid'].shift(-dt)\n",
    "    df_data['next_wmid'] = df_data['wmid'].shift(-dt)\n",
    "    df_data['next_spread'] = df_data['spread'].shift(-dt)\n",
    "    df_data['next_imb_bucket'] = df_data['imb_bucket'].shift(-dt)\n",
    "\n",
    "    # mid price difference -- half tick \n",
    "    df_data[\"dM\"] = np.round((df_data['next_mid'] - df_data['mid']) / ticksize * 2) * ticksize / 2\n",
    "    # weighted mid price difference -- half tick \n",
    "    df_data[\"dwM\"] = np.round((df_data['next_wmid'] - df_data['wmid']) / ticksize * 2) * ticksize / 2\n",
    "    \n",
    "    if is_filter_symm:\n",
    "        # filter out spreads >= n_spread\n",
    "        df_data = df_data.loc[(df_data[\"spread\"] <= n_spread * ticksize)]\n",
    "        # filter out dM > 1.1 * ticksize\n",
    "        df_data = df_data.loc[(df_data[\"dM\"] <= ticksize*1.1) & (df_data[\"dM\"] >= -ticksize*1.1)]\n",
    "\n",
    "        ## 2. symmetrize data\n",
    "        #    - (It,St,It+1,St+1,dM) ==> (1-It,St,1-It+1,St+1,-dM)\n",
    "\n",
    "        df_data_symm = df_data.copy(deep=True)\n",
    "        df_data_symm['imb_bucket'] = n_imb - 1 - df_data_symm['imb_bucket']\n",
    "        df_data_symm['next_imb_bucket'] = n_imb - 1 - df_data_symm['next_imb_bucket']\n",
    "        df_data_symm['dM'] = -df_data_symm['dM']\n",
    "\n",
    "        df_data = pd.concat([df_data, df_data_symm])\n",
    "    \n",
    "    return df_data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cde47422",
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_transi_prob(df_data, K, n_imb, n_spread):\n",
    "    \"\"\"\n",
    "    Function to estimate transition probabiliies [Q, T, R]\n",
    "    \"\"\"\n",
    "  \n",
    "    # Q ==> transient states, 瞬时状态  [nm * nm] \n",
    "    # Xt := (It,St)\n",
    "    # probability that mid_price dont change, known Xt, Xt+1\n",
    "\n",
    "    # locate all that don't move \n",
    "    no_move = df_data[df_data['dM'] == 0]\n",
    "\n",
    "    # count \n",
    "    # no need to use next_spread, coz mid_price not move, next_spread should stay the same \n",
    "    no_move_counts = no_move.pivot_table(index=['next_imb_bucket'], \n",
    "                                         columns=['spread', 'imb_bucket'], \n",
    "                                         values='time_seconds',\n",
    "                                         fill_value=0, \n",
    "                                         aggfunc='count').unstack()\n",
    "\n",
    "    # resize to [n * n] ==> first matrix when m=1 \n",
    "    Q_counts = np.resize(np.array(no_move_counts[0:(n_imb*n_imb)]), (n_imb,n_imb))\n",
    "\n",
    "    # loop over all spreads and add block matrices\n",
    "    for i in range(1,n_spread):\n",
    "        Qi = np.resize(np.array(no_move_counts[(i*n_imb*n_imb):(i+1)*(n_imb*n_imb)]),(n_imb,n_imb))\n",
    "        Q_counts = block_diag(Q_counts, Qi)\n",
    "\n",
    "    # R2 ==> transient matrix, 瞬时状态 [nm * nm] ==> represents T in the paper \n",
    "    # Xt := (It,St)\n",
    "    # probability that mid_price do change, known Xt, Xt+1\n",
    "\n",
    "    # locate all that move \n",
    "    do_move = df_data[df_data['dM'] != 0]\n",
    "\n",
    "    # count all moves \n",
    "    # 必须要对齐，index, columns 位置要正确\n",
    "    move_counts = do_move.pivot_table(index=['spread', 'imb_bucket'], \n",
    "                                      columns=['next_spread', 'next_imb_bucket'], \n",
    "                                      values='time_seconds',\n",
    "                                      fill_value=0, \n",
    "                                      aggfunc='count')\n",
    "    # R2 = T \n",
    "    # resize to [nm * nm] \n",
    "    R2_counts = np.resize(np.array(move_counts), (n_imb*n_spread, n_imb*n_spread))\n",
    "\n",
    "    # R ==> absorbing states, [nm * 4]\n",
    "    move_counts2 = do_move.pivot_table(index=['dM'], \n",
    "                                       columns=['spread', 'imb_bucket'], \n",
    "                                       values='time_seconds',\n",
    "                                       fill_value=0, \n",
    "                                       aggfunc='count').unstack()\n",
    "\n",
    "    R_counts = np.resize(np.array(move_counts2), (n_imb*n_spread,4))\n",
    "    \n",
    "    # T1 = [Q_counts, R_counts]\n",
    "    # combine them and calculate probability from count \n",
    "    T1 = np.concatenate((Q_counts, R_counts), axis=1).astype(float)\n",
    "\n",
    "    # probability known Xt, Xt+1 = (count_i) / (count_dont_move + count_move)\n",
    "    for i in range(0, n_imb*n_spread):\n",
    "        T1[i, :] = T1[i, :] / T1[i, :].sum()\n",
    "\n",
    "    # return Q, R1 in probability \n",
    "    Q = T1[:,0:(n_imb*n_spread)]\n",
    "    R1 = T1[:,(n_imb*n_spread):]\n",
    "\n",
    "    # T2 = [Q_counts, R2_counts]\n",
    "    # combine them and calculate probability from count \n",
    "    T2 = np.concatenate((Q_counts, R2_counts), axis=1).astype(float)\n",
    "\n",
    "    # probability known Xt, Xt+1 = (count_i) / (count_dont_move + count_move)\n",
    "    for i in range(0, n_imb*n_spread):\n",
    "        T2[i, :] = T2[i, :] / T2[i, :].sum()\n",
    "\n",
    "    # return Q2, R2 in probability \n",
    "    Q2 = T2[:, 0:(n_imb*n_spread)]\n",
    "    R2 = T2[:, (n_imb*n_spread):]\n",
    "    \n",
    "    # Calculate G1 [nm * 1]\n",
    "    # G1 = (1-Q)**-1 * R * K \n",
    "    G1 = np.dot(np.dot(np.linalg.inv(np.eye(n_imb*n_spread) - Q), R1), K)\n",
    "    \n",
    "    # Calculate G* ==> micro price adjustment \n",
    "    # B = (1-Q)**-1 * R2 [nm*nm]\n",
    "    B = np.dot(np.linalg.inv( np.eye(n_imb*n_spread) - Q), R2)\n",
    "    \n",
    "    return G1,B,Q,Q2,R1,R2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "38371823",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_cal_G6(G1, B):\n",
    "    \"\"\"\n",
    "    calculate micro price \n",
    "    \"\"\"\n",
    "    G2=np.dot(B,G1)+G1\n",
    "    G3=G2+np.dot(np.dot(B,B),G1)\n",
    "    G4=G3+np.dot(np.dot(np.dot(B,B),B),G1)\n",
    "    G5=G4+np.dot(np.dot(np.dot(np.dot(B,B),B),B),G1)\n",
    "    G6=G5+np.dot(np.dot(np.dot(np.dot(np.dot(B,B),B),B),B),G1)\n",
    "    return G6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "53f369cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Inputs \n",
    "\n",
    "# number of imbalance \n",
    "n_imb = 7\n",
    "# number of spread \n",
    "n_spread = 2\n",
    "# delta t \n",
    "dt = 1\n",
    "\n",
    "# grid of mid price change [half tick, one tick]\n",
    "K = np.array([-0.00001, -0.000005, 0.000005, 0.00001])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "969fbd37",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time_seconds</th>\n",
       "      <th>bid_price</th>\n",
       "      <th>bid_size</th>\n",
       "      <th>ask_price</th>\n",
       "      <th>ask_size</th>\n",
       "      <th>spread</th>\n",
       "      <th>mid</th>\n",
       "      <th>wmid</th>\n",
       "      <th>imb</th>\n",
       "      <th>imb_bucket</th>\n",
       "      <th>next_mid</th>\n",
       "      <th>next_wmid</th>\n",
       "      <th>next_spread</th>\n",
       "      <th>next_imb_bucket</th>\n",
       "      <th>dM</th>\n",
       "      <th>dwM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1645142400</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>1.863301</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>0.950000</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071383</td>\n",
       "      <td>0.662318</td>\n",
       "      <td>4</td>\n",
       "      <td>0.071385</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>-0.000005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1645142401</td>\n",
       "      <td>0.07138</td>\n",
       "      <td>0.499840</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>18.225881</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.071385</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.026693</td>\n",
       "      <td>0</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071371</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.000005</td>\n",
       "      <td>-0.000010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1645142403</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>0.499840</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>18.225881</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071371</td>\n",
       "      <td>0.026693</td>\n",
       "      <td>0</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1645142404</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>0.914646</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>0.950000</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.490520</td>\n",
       "      <td>3</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071371</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1645142405</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>0.499840</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>18.571515</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071371</td>\n",
       "      <td>0.026209</td>\n",
       "      <td>0</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071371</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64213</th>\n",
       "      <td>1645228792</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>0.499840</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>3.821804</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069501</td>\n",
       "      <td>0.115660</td>\n",
       "      <td>5</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069503</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64214</th>\n",
       "      <td>1645228793</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>1.549840</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>3.821804</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069503</td>\n",
       "      <td>0.288522</td>\n",
       "      <td>4</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069503</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64215</th>\n",
       "      <td>1645228794</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>1.549840</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>3.820255</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069503</td>\n",
       "      <td>0.288606</td>\n",
       "      <td>4</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64216</th>\n",
       "      <td>1645228796</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>2.221340</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>2.644555</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.456512</td>\n",
       "      <td>3</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069506</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>2.0</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64217</th>\n",
       "      <td>1645228797</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>4.066678</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>2.644555</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069506</td>\n",
       "      <td>0.605951</td>\n",
       "      <td>2</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069506</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>89320 rows × 16 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       time_seconds  bid_price  bid_size  ask_price   ask_size   spread  \\\n",
       "0        1645142400    0.07137  1.863301    0.07139   0.950000  0.00002   \n",
       "1        1645142401    0.07138  0.499840    0.07139  18.225881  0.00001   \n",
       "2        1645142403    0.07137  0.499840    0.07139  18.225881  0.00002   \n",
       "3        1645142404    0.07137  0.914646    0.07139   0.950000  0.00002   \n",
       "4        1645142405    0.07137  0.499840    0.07139  18.571515  0.00002   \n",
       "...             ...        ...       ...        ...        ...      ...   \n",
       "64213    1645228792    0.06950  0.499840    0.06951   3.821804  0.00001   \n",
       "64214    1645228793    0.06950  1.549840    0.06951   3.821804  0.00001   \n",
       "64215    1645228794    0.06950  1.549840    0.06951   3.820255  0.00001   \n",
       "64216    1645228796    0.06950  2.221340    0.06951   2.644555  0.00001   \n",
       "64217    1645228797    0.06950  4.066678    0.06951   2.644555  0.00001   \n",
       "\n",
       "            mid      wmid       imb  imb_bucket  next_mid  next_wmid  \\\n",
       "0      0.071380  0.071383  0.662318           4  0.071385   0.071380   \n",
       "1      0.071385  0.071380  0.026693           0  0.071380   0.071371   \n",
       "2      0.071380  0.071371  0.026693           0  0.071380   0.071380   \n",
       "3      0.071380  0.071380  0.490520           3  0.071380   0.071371   \n",
       "4      0.071380  0.071371  0.026209           0  0.071380   0.071371   \n",
       "...         ...       ...       ...         ...       ...        ...   \n",
       "64213  0.069505  0.069501  0.115660           5  0.069505   0.069503   \n",
       "64214  0.069505  0.069503  0.288522           4  0.069505   0.069503   \n",
       "64215  0.069505  0.069503  0.288606           4  0.069505   0.069505   \n",
       "64216  0.069505  0.069505  0.456512           3  0.069505   0.069506   \n",
       "64217  0.069505  0.069506  0.605951           2  0.069505   0.069506   \n",
       "\n",
       "       next_spread  next_imb_bucket        dM       dwM  \n",
       "0          0.00001              0.0  0.000005 -0.000005  \n",
       "1          0.00002              0.0 -0.000005 -0.000010  \n",
       "2          0.00002              3.0  0.000000  0.000010  \n",
       "3          0.00002              0.0  0.000000 -0.000010  \n",
       "4          0.00002              0.0  0.000000  0.000000  \n",
       "...            ...              ...       ...       ...  \n",
       "64213      0.00001              4.0 -0.000000  0.000000  \n",
       "64214      0.00001              4.0 -0.000000  0.000000  \n",
       "64215      0.00001              3.0 -0.000000  0.000000  \n",
       "64216      0.00001              2.0 -0.000000  0.000000  \n",
       "64217      0.00001              3.0 -0.000000 -0.000000  \n",
       "\n",
       "[89320 rows x 16 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# processing data \n",
    "df_data_to_use = processing_data(df_data, n_imb, n_spread, dt)\n",
    "\n",
    "# estimation of transition probabiliies\n",
    "G1,B,Q,Q2,R1,R2 = estimate_transi_prob(df_data_to_use, K, n_imb, n_spread)\n",
    "\n",
    "# calculate micro price \n",
    "G6 = f_cal_G6(G1, B)\n",
    "df_data_to_use\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "2aaea492",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1040x480 with 0 Axes>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x26112cedac0>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x26112cedf10>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2611263a490>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'ETHBTC microprice adjustment')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Imbalance')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1040x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot \n",
    "imb=np.linspace(0,1,n_imb)\n",
    "plt.figure(figsize=(13, 6), dpi=80)\n",
    "for i in range(0,n_spread):\n",
    "    plt.plot(imb,G6[(0+i*n_imb):(n_imb+i*n_imb)],label=\"spread = \"+str(i+1))\n",
    "# plt.ylim(-0.005,0.005)\n",
    "plt.legend(loc='upper left')\n",
    "plt.title('ETHBTC microprice adjustment')\n",
    "plt.xlabel('Imbalance')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfbff0ab",
   "metadata": {},
   "source": [
    "### out of sample test   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "ff0529f1",
   "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>time_seconds</th>\n",
       "      <th>bid_price</th>\n",
       "      <th>bid_size</th>\n",
       "      <th>ask_price</th>\n",
       "      <th>ask_size</th>\n",
       "      <th>spread</th>\n",
       "      <th>mid</th>\n",
       "      <th>wmid</th>\n",
       "      <th>imb</th>\n",
       "      <th>imb_bucket</th>\n",
       "      <th>next_mid</th>\n",
       "      <th>next_wmid</th>\n",
       "      <th>next_spread</th>\n",
       "      <th>next_imb_bucket</th>\n",
       "      <th>dM</th>\n",
       "      <th>dwM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1645142400</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>1.863301</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>0.950000</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071383</td>\n",
       "      <td>0.662318</td>\n",
       "      <td>4</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071371</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1645142401</td>\n",
       "      <td>0.07138</td>\n",
       "      <td>0.499840</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>18.225881</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.071385</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.026693</td>\n",
       "      <td>0</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>3.0</td>\n",
       "      <td>-0.000005</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1645142403</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>0.499840</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>18.225881</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071371</td>\n",
       "      <td>0.026693</td>\n",
       "      <td>0</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071371</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1645142404</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>0.914646</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>0.950000</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.490520</td>\n",
       "      <td>3</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071371</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1645142405</td>\n",
       "      <td>0.07137</td>\n",
       "      <td>0.499840</td>\n",
       "      <td>0.07139</td>\n",
       "      <td>18.571515</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.071371</td>\n",
       "      <td>0.026209</td>\n",
       "      <td>0</td>\n",
       "      <td>0.071385</td>\n",
       "      <td>0.071383</td>\n",
       "      <td>0.00003</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>0.000015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64214</th>\n",
       "      <td>1645228793</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>1.549840</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>3.821804</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069503</td>\n",
       "      <td>0.288522</td>\n",
       "      <td>2</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64215</th>\n",
       "      <td>1645228794</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>1.549840</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>3.820255</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069503</td>\n",
       "      <td>0.288606</td>\n",
       "      <td>2</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069506</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64216</th>\n",
       "      <td>1645228796</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>2.221340</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>2.644555</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.456512</td>\n",
       "      <td>3</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069506</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64217</th>\n",
       "      <td>1645228797</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>4.066678</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>2.644555</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069506</td>\n",
       "      <td>0.605951</td>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64218</th>\n",
       "      <td>1645228798</td>\n",
       "      <td>0.06950</td>\n",
       "      <td>3.707040</td>\n",
       "      <td>0.06951</td>\n",
       "      <td>2.644555</td>\n",
       "      <td>0.00001</td>\n",
       "      <td>0.069505</td>\n",
       "      <td>0.069506</td>\n",
       "      <td>0.583639</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>64219 rows × 16 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       time_seconds  bid_price  bid_size  ask_price   ask_size   spread  \\\n",
       "0        1645142400    0.07137  1.863301    0.07139   0.950000  0.00002   \n",
       "1        1645142401    0.07138  0.499840    0.07139  18.225881  0.00001   \n",
       "2        1645142403    0.07137  0.499840    0.07139  18.225881  0.00002   \n",
       "3        1645142404    0.07137  0.914646    0.07139   0.950000  0.00002   \n",
       "4        1645142405    0.07137  0.499840    0.07139  18.571515  0.00002   \n",
       "...             ...        ...       ...        ...        ...      ...   \n",
       "64214    1645228793    0.06950  1.549840    0.06951   3.821804  0.00001   \n",
       "64215    1645228794    0.06950  1.549840    0.06951   3.820255  0.00001   \n",
       "64216    1645228796    0.06950  2.221340    0.06951   2.644555  0.00001   \n",
       "64217    1645228797    0.06950  4.066678    0.06951   2.644555  0.00001   \n",
       "64218    1645228798    0.06950  3.707040    0.06951   2.644555  0.00001   \n",
       "\n",
       "            mid      wmid       imb  imb_bucket  next_mid  next_wmid  \\\n",
       "0      0.071380  0.071383  0.662318           4  0.071380   0.071371   \n",
       "1      0.071385  0.071380  0.026693           0  0.071380   0.071380   \n",
       "2      0.071380  0.071371  0.026693           0  0.071380   0.071371   \n",
       "3      0.071380  0.071380  0.490520           3  0.071380   0.071371   \n",
       "4      0.071380  0.071371  0.026209           0  0.071385   0.071383   \n",
       "...         ...       ...       ...         ...       ...        ...   \n",
       "64214  0.069505  0.069503  0.288522           2  0.069505   0.069505   \n",
       "64215  0.069505  0.069503  0.288606           2  0.069505   0.069506   \n",
       "64216  0.069505  0.069505  0.456512           3  0.069505   0.069506   \n",
       "64217  0.069505  0.069506  0.605951           4       NaN        NaN   \n",
       "64218  0.069505  0.069506  0.583639           3       NaN        NaN   \n",
       "\n",
       "       next_spread  next_imb_bucket        dM       dwM  \n",
       "0          0.00002              0.0  0.000000 -0.000015  \n",
       "1          0.00002              3.0 -0.000005 -0.000000  \n",
       "2          0.00002              0.0  0.000000 -0.000000  \n",
       "3          0.00002              0.0  0.000000 -0.000010  \n",
       "4          0.00003              3.0  0.000005  0.000015  \n",
       "...            ...              ...       ...       ...  \n",
       "64214      0.00001              3.0  0.000000  0.000000  \n",
       "64215      0.00001              4.0  0.000000  0.000005  \n",
       "64216      0.00001              3.0  0.000000  0.000000  \n",
       "64217          NaN              NaN       NaN       NaN  \n",
       "64218          NaN              NaN       NaN       NaN  \n",
       "\n",
       "[64219 rows x 16 columns]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2022-02-18 00:00:00\n",
      "2022-02-21 00:00:00\n"
     ]
    }
   ],
   "source": [
    "# load test data \n",
    "df_data_test = pd.read_csv('eth_btc_coinbase_test.csv.gz', compression='gzip')\n",
    "\n",
    "# split the price and volume \n",
    "df_data_test[[\"bid_price\", \"bid_size\"]] = df_data_test[\"bid_price_bid_size\"].str.split(pat=\"_\", expand=True).astype(float)\n",
    "df_data_test[[\"ask_price\", \"ask_size\"]] = df_data_test[\"ask_price_ask_size\"].str.split(pat=\"_\", expand=True).astype(float)\n",
    "\n",
    "# drop original \n",
    "df_data_test = df_data_test.drop([\"bid_price_bid_size\", \"ask_price_ask_size\"], axis=1)\n",
    "\n",
    "# 30 seconds performance \n",
    "dt = 2\n",
    "\n",
    "# processing data \n",
    "df_data_test_to_use = processing_data(df_data, n_imb, n_spread, dt, is_filter_symm=False)\n",
    "df_data_test_to_use\n",
    "print(pd.to_datetime(df_data.iloc[0,0], unit=\"s\"))\n",
    "print(pd.to_datetime(df_data_test.iloc[0,0], unit=\"s\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "c3cdeb97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1040x480 with 0 Axes>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<ErrorbarContainer object of 3 artists>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x26116bbb9d0>]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1040x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# out of sample test \n",
    "\n",
    "# find tick size \n",
    "# minimum of absolute spread is the tick size \n",
    "spread = df_data[\"ask_price\"] - df_data[\"bid_price\"]\n",
    "ticksize = np.round(min(spread.loc[spread > 0]) * 1e6) / 1e6\n",
    "    \n",
    "# mid price\n",
    "df_data_test['mid'] = (df_data_test['ask_price'] + df_data_test['bid_price'])/2\n",
    "\n",
    "# change of mid price \n",
    "df_data_test['dM'] = df_data_test['mid'].shift(dt)-df_data_test['mid']\n",
    "\n",
    "# spread in terms of tick \n",
    "df_data_test['spread'] = np.round((df_data_test['ask_price'] - df_data_test['bid_price']) / ticksize) * ticksize\n",
    "\n",
    "# orderbook imbalance \n",
    "df_data_test[\"imb\"] = df_data[\"bid_size\"] / (df_data_test[\"bid_size\"] + df_data_test[\"ask_size\"])\n",
    "\n",
    "# discretize imbalance into percentiles\n",
    "df_data_test['imb_bucket'] = pd.qcut(df_data_test['imb'], n_imb, labels=False)\n",
    "\n",
    "# weighted mid price \n",
    "df_data_test['wmid'] = df_data_test['imb'] * df_data_test['ask_price']+(1-df_data_test['imb'])*df_data_test['bid_price']\n",
    "\n",
    "# change of weighed mid price \n",
    "df_data_test['dW'] = df_data_test['wmid'].shift(dt)-df_data_test['wmid']\n",
    "\n",
    "# group by spread and imb_bucket\n",
    "grouped = df_data_test.groupby(['spread','imb_bucket'])\n",
    "res1min = grouped['dM'].aggregate(np.mean)\n",
    "std1 = grouped['dM'].aggregate(np.std)\n",
    "cnt1 = grouped.count()['dM']\n",
    "\n",
    "grouped2 = df_data_test.groupby(['spread','imb_bucket'])\n",
    "res1min2 = grouped2['dW'].aggregate(np.mean)\n",
    "std12 = grouped2['dW'].aggregate(np.std)\n",
    "cnt12 = grouped2.count()['dW']\n",
    "\n",
    "i=0\n",
    "imb = np.linspace(0,1,n_imb)\n",
    "plt.figure(figsize=(13, 6), dpi=80)\n",
    "plt.errorbar(imb,\n",
    "             res1min[(0+i*n_imb):(n_imb+i*n_imb)],\n",
    "             yerr = np.sqrt(dt)*std1[(0+i*n_imb):(n_imb+i*n_imb)]/np.sqrt(cnt1[(0+i*n_imb):(n_imb+i*n_imb)]), \n",
    "             capthick = 5,\n",
    "             label = 'empirical E[M_{t+'+str(dt)+'s}-M_t]')\n",
    "# plt.errorbar(imb,\n",
    "#              res1min2[(0+i*n_imb):(n_imb+i*n_imb)],\n",
    "#              yerr = np.sqrt(dt)*std12[(0+i*n_imb):(n_imb+i*n_imb)]/np.sqrt(cnt12[(0+i*n_imb):(n_imb+i*n_imb)]), \n",
    "#              capthick = 5,\n",
    "#              label = 'empirical E[wM_{t+'+str(dt)+'s}-wM_t]')\n",
    "\n",
    "\n",
    "plt.plot(imb,G6[(0+i*n_imb):(n_imb+i*n_imb)],label=\"spread = \"+str(i+1))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "5df51abb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(spread   imb_bucket\n",
       " 0.00001  0            -9.659091e-07\n",
       "          1            -1.019737e-06\n",
       "          2            -5.698529e-07\n",
       "          3            -2.707581e-07\n",
       "          4            -9.305556e-07\n",
       "          5            -5.452865e-07\n",
       "          6            -1.688889e-06\n",
       " Name: dM, dtype: float64,\n",
       " spread   imb_bucket\n",
       " 0.00001  0             0.000007\n",
       "          1             0.000008\n",
       "          2             0.000023\n",
       "          3             0.000090\n",
       "          4             0.000006\n",
       "          5             0.000004\n",
       "          6            -0.000215\n",
       " Name: dW, dtype: float64)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res1min[(0+i*n_imb):(n_imb+i*n_imb)], res1min2[(0+i*n_imb):(n_imb+i*n_imb)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "10b32dd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAD4CAYAAADGmmByAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAai0lEQVR4nO3df4xV533n8ffHkAB16t/xLGbYHVYgVCAKXo8oK/9zG9J66rQ7ZGtL42YDVqhILSylu1S70KxkRl4kO6uULtoY7aSOjL11MOvUMortbb04V91KNgQnTjB2WE/iWXsCMnLsUiYVrAd/94/7THIZLnMv88w9997p5yUd3XO/53nOeZ6HI315zjl3jiICMzOz6bqi1Q0wM7PO5kRiZmZZnEjMzCyLE4mZmWVxIjEzsyxzW92A6brhhhuip6en1c2YcT//+c+58sorW92MtuIxqc3jcjGPSW3V4/Lyyy+/GxEfn8n9d2wi6enp4ciRI61uxowrl8uUSqVWN6OteExq87hczGNSW/W4SPq/M71/X9oyM7MsTiRmZpbFicTMzLI4kZiZWZaGE4mkOZK+L+nb6ft1kp6X9Eb6vLaq7HZJw5KOS7qtKn6LpKNp225JSvF5kp5I8UOSemawj2Zm1kSXMyP5EvB61fdtwMGIWAYcTN+RtAIYAFYCfcBDkuakOnuAzcCytPSl+Cbg/YhYCuwCHpxWb8zMrHANJRJJ3cBngD+vCvcDe9P6XmB9VXxfRJyLiDeBYWCNpIXAVRHxYlT+5PCjk+pM7OtJYN3EbMXMzNpbo78j+TPg3wO/WhXrioiTABFxUtKNKb4IeKmq3GiKfZDWJ8cn6ryd9jUu6TRwPfBudSMkbaYyo6Grq4tyudxg8zvH2NjYrOxXDo9JbR6Xi3lMamv2uNRNJJJ+BzgVES9LKjWwz1oziZgiPlWdCwMRQ8AQQG9vb8zGHx75B1UX85jU5nG5mMektmaPSyMzkluBfyXpdmA+cJWk/w68I2lhmo0sBE6l8qPA4qr63cCJFO+uEa+uMyppLnA18N40+2Q2q/Rse6ZmfOsnxrn7EtsaMfLAZ6Zd16xa3XskEbE9IrojoofKTfQXIuLfAAeAjanYRuDptH4AGEhPYi2hclP9cLoMdkbS2nT/Y8OkOhP7uiMdw69uNDPrADl/a+sBYL+kTcBbwJ0AEXFM0n7gNWAc2BIR51Ode4BHgAXAc2kBeBh4TNIwlZnIQEa7zMysQJeVSCKiDJTT+s+AdZcotxPYWSN+BFhVI36WlIjMzKyz+JftZmaWxYnEzMyyOJGYmVkWJxIzM8viRGJmZlmcSMzMLIsTiZmZZXEiMTOzLE4kZmaWxYnEzMyy5PytLTOrZcfVM7q7kfm14+UrBhmZf98FsZ6zj8/osc0a4RmJmZllcSIxM7MsTiRmZpbFicTMzLI4kZiZWRYnEjMzy1I3kUiaL+mwpB9IOiZpMMV3SPqppFfScntVne2ShiUdl3RbVfwWSUfTtt3p3e2k97s/keKHJPU0oa9mZtYEjcxIzgGfiohPAquBPklr07ZdEbE6Lc8CSFpB5Z3rK4E+4CFJc1L5PcBmYFla+lJ8E/B+RCwFdgEPZvfMzMwKUTeRRMVY+vqRtMQUVfqBfRFxLiLeBIaBNZIWAldFxIsREcCjwPqqOnvT+pPAuonZipmZtbeGftmeZhQvA0uBr0XEIUm/DdwraQNwBNgaEe8Di4CXqqqPptgHaX1ynPT5NkBEjEs6DVwPvDupHZupzGjo6uqiXC433tMOMTY2Niv7laPjxmT5YCGHGZt3E+VJx9r64XjD9TtqTBvUcedKQZo9Lg0lkog4D6yWdA3wlKRVVC5T3U9ldnI/8FXgC0CtmURMEafOtup2DAFDAL29vVEqlRppfkcpl8vMxn7l6Lgx2dFfyGHKywcpHb/wT6TcfRl/ImXkc6UZblHrddy5UpBmj8tlPbUVEX8HlIG+iHgnIs5HxIfA14E1qdgosLiqWjdwIsW7a8QvqCNpLnA18N7ltM3MzFqjkae2Pp5mIkhaAHwa+FG65zHhs8Craf0AMJCexFpC5ab64Yg4CZyRtDbd/9gAPF1VZ2NavwN4Id1HMTOzNtfIpa2FwN50n+QKYH9EfFvSY5JWU7kENQJ8ESAijknaD7wGjANb0qUxgHuAR4AFwHNpAXgYeEzSMJWZyEB+18zMrAh1E0lE/BC4uUb881PU2QnsrBE/AqyqET8L3FmvLWZm1n78y3YzM8viRGJmZlmcSMzMLIsTiZmZZXEiMTOzLE4kZmaWxYnEzMyyOJGYmVkWJxIzM8viRGJmZlmcSMzMLIsTiZmZZXEiMTOzLE4kZmaWxYnEzMyyOJGYmVkWJxIzM8vSyDvb50s6LOkHko5JGkzx6yQ9L+mN9HltVZ3tkoYlHZd0W1X8FklH07bd6d3tpPe7P5HihyT1NKGvZmbWBI3MSM4Bn4qITwKrgT5Ja4FtwMGIWAYcTN+RtILKO9dXAn3AQ+l97wB7gM3AsrT0pfgm4P2IWArsAh7M75qZmRWhbiKJirH09SNpCaAf2Jvie4H1ab0f2BcR5yLiTWAYWCNpIXBVRLwYEQE8OqnOxL6eBNZNzFbMzKy9zW2kUJpRvAwsBb4WEYckdUXESYCIOCnpxlR8EfBSVfXRFPsgrU+OT9R5O+1rXNJp4Hrg3Unt2ExlRkNXVxflcrnBbnaOsbGxWdmvHB03JssHCznM2LybKE861tYPxxuu31Fj2qCOO1cK0uxxaSiRRMR5YLWka4CnJK2aonitmURMEZ+qzuR2DAFDAL29vVEqlaZoRmcql8vMxn7l6Lgx2dFfyGHKywcpHb/vgtjdZx9vuP7I50oz3KLW67hzpSDNHpfLemorIv4OKFO5t/FOulxF+jyVio0Ci6uqdQMnUry7RvyCOpLmAlcD711O28zMrDUaeWrr42kmgqQFwKeBHwEHgI2p2Ebg6bR+ABhIT2ItoXJT/XC6DHZG0tp0/2PDpDoT+7oDeCHdRzEzszbXyKWthcDedJ/kCmB/RHxb0ovAfkmbgLeAOwEi4pik/cBrwDiwJV0aA7gHeARYADyXFoCHgcckDVOZiQzMROfMzKz56iaSiPghcHON+M+AdZeosxPYWSN+BLjo/kpEnCUlIjMz6yz+ZbuZmWVxIjEzsyxOJGZmlsWJxMzMsjiRmJlZFicSMzPL4kRiZmZZnEjMzCyLE4mZmWVxIjEzsyxOJGZmlsWJxMzMsjiRmJlZFicSMzPL4kRiZmZZnEjMzCyLE4mZmWVp5J3tiyV9R9Lrko5J+lKK75D0U0mvpOX2qjrbJQ1LOi7ptqr4LZKOpm2707vbSe93fyLFD0nqaUJfzcysCRqZkYwDWyPi14C1wBZJK9K2XRGxOi3PAqRtA8BKoA94KL3vHWAPsBlYlpa+FN8EvB8RS4FdwIP5XTMzsyLUTSQRcTIivpfWzwCvA4umqNIP7IuIcxHxJjAMrJG0ELgqIl6MiAAeBdZX1dmb1p8E1k3MVszMrL3NvZzC6ZLTzcAh4FbgXkkbgCNUZi3vU0kyL1VVG02xD9L65Djp822AiBiXdBq4Hnh30vE3U5nR0NXVRblcvpzmd4SxsbFZ2a8cHTcmywcLOczYvJsoTzrW1g/HG67fUWPaoI47VwrS7HFpOJFI+hjwLeCPIuLvJe0B7gcifX4V+AJQayYRU8Sps+2XgYghYAigt7c3SqVSo83vGOVymdnYrxwdNyY7+gs5THn5IKXj910Qu/vs4w3XH/lcaYZb1Hodd64UpNnj0tBTW5I+QiWJ/EVE/CVARLwTEecj4kPg68CaVHwUWFxVvRs4keLdNeIX1JE0F7gaeG86HTIzs2I18tSWgIeB1yPiT6viC6uKfRZ4Na0fAAbSk1hLqNxUPxwRJ4EzktamfW4Anq6qszGt3wG8kO6jmJlZm2vk0tatwOeBo5JeSbE/Ae6StJrKJagR4IsAEXFM0n7gNSpPfG2JiPOp3j3AI8AC4Lm0QCVRPSZpmMpMZCCnU2ZmVpy6iSQi/pba9zCenaLOTmBnjfgRYFWN+FngznptMTOz9uNftpuZWRYnEjMzy+JEYmZmWZxIzMwsixOJmZllcSIxM7MsTiRmZpbFicTMzLI4kZiZWRYnEjMzy+JEYmZmWZxIzMwsixOJmZllcSIxM7MsTiRmZpbFicTMzLI4kZiZWZZG3tm+WNJ3JL0u6ZikL6X4dZKel/RG+ry2qs52ScOSjku6rSp+i6Sjadvu9O520vvdn0jxQ5J6mtBXMzNrgkZmJOPA1oj4NWAtsEXSCmAbcDAilgEH03fStgFgJdAHPCRpTtrXHmAzsCwtfSm+CXg/IpYCu4AHZ6BvZmZWgLqJJCJORsT30voZ4HVgEdAP7E3F9gLr03o/sC8izkXEm8AwsEbSQuCqiHgxIgJ4dFKdiX09CaybmK2YmVl7m3s5hdMlp5uBQ0BXRJyESrKRdGMqtgh4qaraaIp9kNYnxyfqvJ32NS7pNHA98O6k42+mMqOhq6uLcrl8Oc3vCGNjY7OyXzk6bkyWDxZymLF5N1GedKytH443XL+jxrRBHXeuFKTZ49JwIpH0MeBbwB9FxN9PMWGotSGmiE9V58JAxBAwBNDb2xulUqlOqztPuVxmNvYrR8eNyY7+Qg5TXj5I6fh9F8TuPvt4w/VHPlea4Ra1XsedKwVp9rg0lEgkfYRKEvmLiPjLFH5H0sI0G1kInErxUWBxVfVu4ESKd9eIV9cZlTQXuBp4bxr9MftHbWT+7zdeeMcMHnjH6RncmXWaRp7aEvAw8HpE/GnVpgPAxrS+EXi6Kj6QnsRaQuWm+uF0GeyMpLVpnxsm1ZnY1x3AC+k+ipmZtblGZiS3Ap8Hjkp6JcX+BHgA2C9pE/AWcCdARByTtB94jcoTX1si4nyqdw/wCLAAeC4tUElUj0kapjITGcjrlpmZFaVuIomIv6X2PQyAdZeosxPYWSN+BFhVI36WlIjMzKyz+JftZmaWxYnEzMyyOJGYmVkWJxIzM8viRGJmZlmcSMzMLIsTiZmZZXEiMTOzLE4kZmaWxYnEzMyyOJGYmVkWJxIzM8tyWW9INLNL69n2DAAj81vcELOCeUZiZmZZnEjMzCyLE4mZmWVxIjEzsyyNvLP9G5JOSXq1KrZD0k8lvZKW26u2bZc0LOm4pNuq4rdIOpq27U7vbSe92/2JFD8kqWeG+2hmZk3UyIzkEaCvRnxXRKxOy7MAklZQed/6ylTnIUlzUvk9wGZgWVom9rkJeD8ilgK7gAen2RczM2uBuokkIv4GeK/B/fUD+yLiXES8CQwDayQtBK6KiBcjIoBHgfVVdfam9SeBdROzFTMza38590julfTDdOnr2hRbBLxdVWY0xRal9cnxC+pExDhwGrg+o11mZlag6f4gcQ9wPxDp86vAF4BaM4mYIk6dbReQtJnK5TG6urool8uX1ehOMDY2Niv7laNTxmTrJ8YBKF8xWMjxxubdRHl5Mceqq03+fTrlXClas8dlWokkIt6ZWJf0deDb6esosLiqaDdwIsW7a8Sr64xKmgtczSUupUXEEDAE0NvbG6VSaTrNb2vlcpnZ2K8cnTImd//il+33FXK88vJBSseLOVZdd51udQuAzjlXitbscZnWpa10z2PCZ4GJJ7oOAAPpSawlVG6qH46Ik8AZSWvT/Y8NwNNVdTam9TuAF9J9FDMz6wB1ZySSvgmUgBskjQL3ASVJq6lcghoBvggQEcck7QdeA8aBLRFxPu3qHipPgC0AnksLwMPAY5KGqcxEBmagX2ZmVpC6iSQi7qoRfniK8juBnTXiR4BVNeJngTvrtcPMzNqTf9luZmZZnEjMzCyLE4mZmWVxIjEzsyxOJGZmlsWJxMzMsjiRmJlZFicSMzPL4kRiZmZZnEjMzCyLE4mZmWVxIjEzsyxOJGZmlsWJxMzMsjiRmJlZFicSMzPL4kRiZmZZ6iYSSd+QdErSq1Wx6yQ9L+mN9Hlt1bbtkoYlHZd0W1X8FklH07bd6d3tpPe7P5HihyT1zHAfzcysiRqZkTwC9E2KbQMORsQy4GD6jqQVVN65vjLVeUjSnFRnD7AZWJaWiX1uAt6PiKXALuDB6XbGzMyKVzeRRMTfAO9NCvcDe9P6XmB9VXxfRJyLiDeBYWCNpIXAVRHxYkQE8OikOhP7ehJYNzFbMTOz9jfdeyRdEXESIH3emOKLgLeryo2m2KK0Pjl+QZ2IGAdOA9dPs11mZlawuTO8v1oziZgiPlWdi3cubaZyeYyuri7K5fI0mtjexsbGZmW/cnTKmGz9xDgA5SsGCzne2LybKC8v5lh1tcm/T6ecK0Vr9rhMN5G8I2lhRJxMl61OpfgosLiqXDdwIsW7a8Sr64xKmgtczcWX0gCIiCFgCKC3tzdKpdI0m9++yuUys7FfOTplTO7e9gwAI/PvK+R45eWDlI4Xc6y67jrd6hYAnXOuFK3Z4zLdS1sHgI1pfSPwdFV8ID2JtYTKTfXD6fLXGUlr0/2PDZPqTOzrDuCFdB/FzMw6QN0ZiaRvAiXgBkmjwH3AA8B+SZuAt4A7ASLimKT9wGvAOLAlIs6nXd1D5QmwBcBzaQF4GHhM0jCVmcjAjPTMzMwKUTeRRMRdl9i07hLldwI7a8SPAKtqxM+SEpGZmXUe/7LdzMyyOJGYmVkWJxIzM8viRGJmZlmcSMzMLIsTiZmZZXEiMTOzLE4kZmaWxYnEzMyyOJGYmVkWJxIzM8viRGJmZlmcSMzMLIsTiZmZZXEiMTOzLE4kZmaWxYnEzMyyOJGYmVmWrEQiaUTSUUmvSDqSYtdJel7SG+nz2qry2yUNSzou6baq+C1pP8OSdktSTrvMzKw4MzEj+Y2IWB0Rven7NuBgRCwDDqbvSFoBDAArgT7gIUlzUp09wGZgWVr6ZqBdZmZWgGZc2uoH9qb1vcD6qvi+iDgXEW8Cw8AaSQuBqyLixYgI4NGqOmZm1ubmZtYP4K8lBfDfImII6IqIkwARcVLSjansIuClqrqjKfZBWp8cv4ikzVRmLnR1dVEulzOb337GxsZmZb9ydMqYbP3EOADlKwYLOd7YvJsoLy/mWHW1yb9Pp5wrRWv2uOQmklsj4kRKFs9L+tEUZWvd94gp4hcHK4lqCKC3tzdKpdJlNrf9lctlZmO/cnTKmNy97RkARubfV8jxyssHKR0v5lj19Pzg8V+sjzzwmZa1o1POlaI1e1yyLm1FxIn0eQp4ClgDvJMuV5E+T6Xio8DiqurdwIkU764RNzOzDjDtRCLpSkm/OrEO/BbwKnAA2JiKbQSeTusHgAFJ8yQtoXJT/XC6DHZG0tr0tNaGqjpmZtbmci5tdQFPpSd15wKPR8T/lPRdYL+kTcBbwJ0AEXFM0n7gNWAc2BIR59O+7gEeARYAz6XFzMw6wLQTSUT8BPhkjfjPgHWXqLMT2FkjfgRYNd22mJlZ6+TebDdrXzuuLvRwI/MLPZxZ2/CfSDEzsyxOJGZmlsWJxMzMsjiRmJlZFicSMzPL4kRiZmZZnEjMzCyLE4mZmWVxIjEzsyxOJGZmlsV/IsXMso3M//1fftlR8MF3nC74gDaZZyRmZpbFicTMzLI4kZiZWRYnEjMzy+JEYmZmWdrmqS1JfcB/AeYAfx4RD7S4STZTcl8wtXwQdvTPTFvMbMa1RSKRNAf4GvCbwCjwXUkHIuK11rbMzNpe9X9UivxPhx87/oW2SCTAGmA4vQceSfuAfsCJZKYU/NpZM/vHQxHR6jYg6Q6gLyL+IH3/PPDrEXHvpHKbgc3p63LgeKENLcYNwLutbkSb8ZjU5nG5mMektupx+WcR8fGZ3Hm7zEhUI3ZRhouIIWCo+c1pHUlHIqK31e1oJx6T2jwuF/OY1NbscWmXp7ZGgcVV37uBEy1qi5mZXYZ2SSTfBZZJWiLpo8AAcKDFbTIzswa0xaWtiBiXdC/wV1Qe//1GRBxrcbNaZVZfupsmj0ltHpeLeUxqa+q4tMXNdjMz61ztcmnLzMw6lBOJmZllcSJpEknXSXpe0hvp89pLlOuTdFzSsKRtjdSXtD2VPy7pthr7PCDp1eb0bPqKHhNJvyLpGUk/knRMUlv92Z1L9bNquyTtTtt/KOlf1Kubc960gyLHRNJvSnpZ0tH0+alienn5ij5X0vZ/KmlM0h/XbWBEeGnCAnwF2JbWtwEP1igzB/gx8M+BjwI/AFZMVR9YkcrNA5ak+nOq9vmvgceBV1s9Bq0eE+BXgN9IZT4K/G/gt1s9DvX6WVXmduA5Kr+zWgscatZ50w5LC8bkZuCmtL4K+Gmrx6AdxqVqn98C/gfwx/Xa6BlJ8/QDe9P6XmB9jTK/+NMwEfH/gIk/DTNV/X5gX0Sci4g3geG0HyR9DPh3wH+a0Z7MnELHJCL+ISK+A5D29T0qv1FqB1P1c0I/8GhUvARcI2lhnbqXfd60kULHJCK+HxETv1c7BsyXNK9JfctR9LmCpPXAT6iMS11OJM3TFREnAdLnjTXKLALervo+mmJT1Z+qzv3AV4F/mIkONEErxgQASdcAvwsczOvCjKnb5inKNGWM2kDRY1Lt94DvR8S5abe+eQodF0lXAv8BGGy0gW3xO5JOJel/Af+kxqYvN7qLGrF6z2PXrCNpNbA0Iv6tpJ4Gjz/j2mlMqto0F/gmsDvSHwZtA43081JlZnyM2kTRY1LZobQSeBD4rUbKt0DR4zII7IqIMalW9Ys5kWSIiE9fapukdyQtjIiTaYp5qkaxqf40zKXqX6rOvwRukTRC5d/1RknliChNo2vT1mZjMmEIeCMi/uzyetNUjfxZoEuV+egUdac7Ru2g6DFBUjfwFLAhIn48I72YeUWPy68Dd0j6CnAN8KGksxHxXy/ZwlbfSJqtC/CfufBG1ldqlJlL5TrkEn55I2zlVPWBlVx40/QnTLppCvTQnjfbCx8TKveLvgVc0er+N9rPqjKf4cIbqIebed60emnBmFyTyv1eq/veTuMyab87aOBme8sHabYuwPVUrse/kT6vS/GbgGeryt0O/B8qT1Z8uV79tO3LqfxxajyFRPsmkkLHhMr/vgJ4HXglLX/Q6nGYqp/AHwJ/mNZF5YVvPwaOAr3NPG/aYSlyTID/CPy86tx4Bbix1WPQ6nGZdNwdNJBI/CdSzMwsi5/aMjOzLE4kZmaWxYnEzMyyOJGYmVkWJxIzM8viRGJmZlmcSMzMLMv/B7lpxC7oBuT7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_data[\"dM\"].hist()\n",
    "df_data_test[\"dM\"].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "95e6de2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_data[\"spread\"].hist()\n",
    "df_data_test[\"spread\"].hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6835a9e",
   "metadata": {},
   "source": [
    "### Check the functions \n",
    "from https://github.com/shaileshkakkar/MicroPriceIndicator/blob/master/Micro-Price%20Reproduction.ipynb, \n",
    "we got the script. we check our estimations are similar compared to theirs \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce81b6d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to estimate transition probabiliies \n",
    "# from https://github.com/shaileshkakkar/MicroPriceIndicator/blob/master/Micro-Price%20Reproduction.ipynb\n",
    "\n",
    "def estimate_old(T):\n",
    "    no_move=T[T['dM']==0]\n",
    "    no_move_counts=no_move.pivot_table(index=[ 'next_imb_bucket'], \n",
    "                     columns=['spread', 'imb_bucket'], \n",
    "                     values='time',\n",
    "                     fill_value=0, \n",
    "                     aggfunc='count').unstack()\n",
    "\n",
    "    #print no_move_counts\n",
    "    Q_counts=np.resize(np.array(no_move_counts[0:(n_imb*n_imb)]),(n_imb,n_imb))\n",
    "    # loop over all spreads and add block matrices\n",
    "    for i in range(1,n_spread):\n",
    "        Qi=np.resize(np.array(no_move_counts[(i*n_imb*n_imb):(i+1)*(n_imb*n_imb)]),(n_imb,n_imb))\n",
    "        Q_counts=block_diag(Q_counts,Qi)\n",
    "    #print Q_counts\n",
    "    move_counts=T[(T['dM']!=0)].pivot_table(index=['dM'], \n",
    "                         columns=['spread', 'imb_bucket'], \n",
    "                         values='time',\n",
    "                         fill_value=0, \n",
    "                         aggfunc='count').unstack()\n",
    "\n",
    "    R_counts=np.resize(np.array(move_counts),(n_imb*n_spread,4))\n",
    "    T1=np.concatenate((Q_counts,R_counts),axis=1).astype(float)\n",
    "    for i in range(0,n_imb*n_spread):\n",
    "        T1[i]=T1[i]/T1[i].sum()\n",
    "    Q=T1[:,0:(n_imb*n_spread)]\n",
    "    R1=T1[:,(n_imb*n_spread):]\n",
    "\n",
    "    move_counts=T[(T['dM']!=0)].pivot_table(index=['spread','imb_bucket'], \n",
    "                     columns=['next_spread', 'next_imb_bucket'], \n",
    "                     values='time',\n",
    "                     fill_value=0, \n",
    "                     aggfunc='count') #.unstack()\n",
    "\n",
    "    R2_counts=np.resize(np.array(move_counts),(n_imb*n_spread,n_imb*n_spread))\n",
    "    T2=np.concatenate((Q_counts,R2_counts),axis=1).astype(float)\n",
    "\n",
    "    for i in range(0,n_imb*n_spread):\n",
    "        T2[i]=T2[i]/T2[i].sum()\n",
    "    R2=T2[:,(n_imb*n_spread):]\n",
    "    Q2=T2[:,0:(n_imb*n_spread)]\n",
    "    G1=np.dot(np.dot(np.linalg.inv(np.eye(n_imb*n_spread)-Q),R1),K)\n",
    "    B=np.dot(np.linalg.inv(np.eye(n_imb*n_spread)-Q),R2)\n",
    "    \n",
    "    return G1,B,Q,Q2,R1,R2,K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "26ca8487",
   "metadata": {},
   "outputs": [],
   "source": [
    "# modify names \n",
    "df_T = df_data.copy(deep=True)\n",
    "df_T.rename(columns={'bid_price': 'bid'}, inplace=True)\n",
    "df_T.rename(columns={'ask_price': 'ask'}, inplace=True)\n",
    "df_T.rename(columns={'ask_size': 'as'}, inplace=True)\n",
    "df_T.rename(columns={'bid_size': 'bs'}, inplace=True)\n",
    "df_T.rename(columns={'time_seconds': 'time'}, inplace=True)\n",
    "df_T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "63b52053",
   "metadata": {},
   "outputs": [],
   "source": [
    "K = np.array([-0.01, -0.005, 0.005, 0.01])\n",
    "K = np.array([-0.1, -0.05, 0.05, 0.1])\n",
    "\n",
    "# our estimation\n",
    "G1,B,Q,Q2,R1,R2, = estimate_transi_prob(df_data, K, n_imb, n_spread)\n",
    "\n",
    "# estimation from github \n",
    "G1_,B_,Q_,Q2_,R1_,R2_,K = estimate_old(df_T)\n",
    "(G1_==G1).all(),(B_ == B).all(), (Q_ == Q).all(), (R1_ == R1).all(), (R2_ == R2).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2384f744",
   "metadata": {},
   "source": [
    "### Fine tuning parameters \n",
    "1. n_imbalance \n",
    "2. n_spread \n",
    "3. data time length\n",
    "4. forecasting power "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "92b3c11d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1. n_imbalance\n",
    "# 2. n_spread\n",
    "# 3. forecasting power"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "250b0432",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_imb_1 = 5 \n",
    "n_spread_1 = 2\n",
    "G1,B,Q,Q2,R1,R2, = estimate_transi_prob(processing_data(df_data, n_imb_1, n_spread_1), K, n_imb_1, n_spread_1)\n",
    "G_1 = f_cal_G6(G1, B)\n",
    "\n",
    "n_imb = 5\n",
    "n_spread = 4\n",
    "G1,B,Q,Q2,R1,R2, = estimate_transi_prob(processing_data(df_data, n_imb, n_spread), K, n_imb, n_spread)\n",
    "G_2 = f_cal_G6(G1, B)\n",
    "G_1, G_2\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6477b522",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1. n_imbalance\n",
    "\n",
    "lst_n_imb = [5, 10, 20]\n",
    "n_spread = 2\n",
    "\n",
    "plt.figure(figsize=(13, 6), dpi=80)\n",
    "\n",
    "for n_imb in lst_n_imb:\n",
    "    # estimate \n",
    "    G1,B,Q,Q2,R1,R2, = estimate_transi_prob(processing_data(df_data, n_imb, n_spread), K, n_imb, n_spread)\n",
    "    # micro price \n",
    "    G_1 = f_cal_G6(G1, B)\n",
    "    \n",
    "    # plot \n",
    "    imb = np.linspace(0,1,n_imb)\n",
    "    \n",
    "    for i in range(0,n_spread):\n",
    "        plt.plot(imb,G_1[(0+i*n_imb):(n_imb+i*n_imb)], \n",
    "                 label=\"spread = \" + str(i+1) + \", n_imb = \" + str(n_imb))\n",
    "\n",
    "\n",
    "plt.legend(loc='upper left')\n",
    "plt.title('ETHBTC microprice adjustment')\n",
    "plt.xlabel('Imbalance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07e0d234",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2. n_spread\n",
    "\n",
    "n_imb = 5\n",
    "lst_n_spread = [2,4,6]\n",
    "\n",
    "\n",
    "for n_spread in lst_n_spread:\n",
    "    # estimate \n",
    "    G1,B,Q,Q2,R1,R2, = estimate_transi_prob(processing_data(df_data, n_imb, n_spread), K, n_imb, n_spread)\n",
    "    # micro price \n",
    "    G_1 = f_cal_G6(G1, B)\n",
    "    \n",
    "    # plot \n",
    "    imb = np.linspace(0,1,n_imb)\n",
    "    \n",
    "    plt.figure(figsize=(13, 6), dpi=80)\n",
    "    \n",
    "    for i in range(0,n_spread):\n",
    "        plt.plot(imb,G_1[(0+i*n_imb):(n_imb+i*n_imb)], \n",
    "                 label=\"spread = \" + str(i+1) + \", n_spread = \" + str(n_spread))\n",
    "    \n",
    "    plt.legend(loc='upper left')\n",
    "    plt.title('ETHBTC microprice adjustment')\n",
    "    plt.xlabel('Imbalance')\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2b47cf53",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 3. data time length\n"
   ]
  }
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