435 lines
83 KiB
Plaintext
435 lines
83 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# EWMA : Moyennes Mobiles Pondérées Exponentiellement"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import pandas as pd\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"airline = pd.read_csv('airline_passengers.csv',index_col=\"Month\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"airline.dropna(inplace=True)\n",
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"airline.index = pd.to_datetime(airline.index)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div>\n",
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"<style scoped>\n",
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" .dataframe tbody tr th:only-of-type {\n",
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" vertical-align: middle;\n",
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" }\n",
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"\n",
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" .dataframe tbody tr th {\n",
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" vertical-align: top;\n",
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" }\n",
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"\n",
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" .dataframe thead th {\n",
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" text-align: right;\n",
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" }\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>Thousands of Passengers</th>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>Month</th>\n",
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" <th></th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>1949-01-01</th>\n",
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" <td>112.0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1949-02-01</th>\n",
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" <td>118.0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1949-03-01</th>\n",
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" <td>132.0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1949-04-01</th>\n",
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" <td>129.0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1949-05-01</th>\n",
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" <td>121.0</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>"
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],
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"text/plain": [
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" Thousands of Passengers\n",
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"Month \n",
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"1949-01-01 112.0\n",
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"1949-02-01 118.0\n",
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"1949-03-01 132.0\n",
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"1949-04-01 129.0\n",
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"1949-05-01 121.0"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"airline.head()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# SMA\n",
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"## Moyenne Mobile Simple\n",
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"\n",
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"Nous avons déjà montré comment créer une moyenne mobile simple, pour une révision rapide:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"airline['6-month-SMA']=airline['Thousands of Passengers'].rolling(window=6).mean()\n",
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"airline['12-month-SMA']=airline['Thousands of Passengers'].rolling(window=12).mean()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div>\n",
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"<style scoped>\n",
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" .dataframe tbody tr th:only-of-type {\n",
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" vertical-align: middle;\n",
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" }\n",
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"\n",
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" .dataframe tbody tr th {\n",
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" vertical-align: top;\n",
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" }\n",
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"\n",
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" .dataframe thead th {\n",
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" text-align: right;\n",
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" }\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>Thousands of Passengers</th>\n",
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" <th>6-month-SMA</th>\n",
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" <th>12-month-SMA</th>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>Month</th>\n",
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" <th></th>\n",
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" <th></th>\n",
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" <th></th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>1949-01-01</th>\n",
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" <td>112.0</td>\n",
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" <td>NaN</td>\n",
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" <td>NaN</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1949-02-01</th>\n",
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" <td>118.0</td>\n",
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" <td>NaN</td>\n",
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" <td>NaN</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1949-03-01</th>\n",
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" <td>132.0</td>\n",
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" <td>NaN</td>\n",
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" <td>NaN</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1949-04-01</th>\n",
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" <td>129.0</td>\n",
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" <td>NaN</td>\n",
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" <td>NaN</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1949-05-01</th>\n",
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" <td>121.0</td>\n",
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" <td>NaN</td>\n",
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" <td>NaN</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>"
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],
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"text/plain": [
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" Thousands of Passengers 6-month-SMA 12-month-SMA\n",
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"Month \n",
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"1949-01-01 112.0 NaN NaN\n",
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"1949-02-01 118.0 NaN NaN\n",
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"1949-03-01 132.0 NaN NaN\n",
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"1949-04-01 129.0 NaN NaN\n",
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"1949-05-01 121.0 NaN NaN"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"airline.head()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<matplotlib.axes._subplots.AxesSubplot at 0x116b6eed0>"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 432x288 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {
|
|||
|
|
"needs_background": "light"
|
|||
|
|
},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"airline.plot()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"# EWMA\n",
|
|||
|
|
"## Moyennes Mobiles Pondérées Exponentiellement \n",
|
|||
|
|
"\n",
|
|||
|
|
"Nous venons de montrer comment calculer la moyenne mobile simple SMA à partir d'une période, mais la SMA de base a quelques \"faiblesses\".\n",
|
|||
|
|
"* Des périodes plus petites entraîneront plus de bruit, plutôt que de signal.\n",
|
|||
|
|
"* Elle sera toujours décalée par la taille de la période\n",
|
|||
|
|
"* Elle n'atteindra jamais le sommet ou la vallée complète des données en raison du calcul de la moyenne.\n",
|
|||
|
|
"* Ne vous informe pas vraiment sur les comportements futurs possibles, tout ce qu'elle fait vraiment c'est de décrire les tendances dans vos données.\n",
|
|||
|
|
"* Des valeurs historiques extrêmes peuvent fausser votre SMA de manière significative.\n",
|
|||
|
|
"\n",
|
|||
|
|
"Pour aider à résoudre certains de ces problèmes, nous pouvons utiliser une moyenne mobile pondérée exponentielle (EWMA)."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"EWMA nous permettra de réduire l'effet de décalage de la SMA et d'accorder plus de poids aux valeurs qui se sont produites plus récemment (en appliquant plus de poids aux valeurs plus récentes, d'où le nom). La quantité de poids appliquée aux valeurs les plus récentes dépendra des paramètres réels utilisés dans l'EWMA et du nombre de périodes correspondant à une taille de fenêtre.\n",
|
|||
|
|
"[Tous les détails sur les mathématiques qui se cachent derrière cela peuvent être trouvés ici](http://pandas.pydata.org/pandas-docs/stable/computation.html#exponentially-weighted-windows)\n",
|
|||
|
|
"Voici la version abrégée de l'explication de EWMA.\n",
|
|||
|
|
"\n",
|
|||
|
|
"La formule de EWMA est la suivante :"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"$ y_t = \\frac{\\sum\\limits_{i=0}^t w_i x_{t-i}}{\\sum\\limits_{i=0}^t w_i} $"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Où x_t est la valeur d'entrée, w_i est le poids appliqué (notez comment il peut passer de i=0 à t), et y_t est la sortie.\n",
|
|||
|
|
"\n",
|
|||
|
|
"Maintenant la question est, comment définir le terme de poids w_i ?\n",
|
|||
|
|
"\n",
|
|||
|
|
"Cela dépend du paramètre d'ajustement que vous fournissez à la méthode .ewm().\n",
|
|||
|
|
"\n",
|
|||
|
|
"Lorsque l'ajustement est True (par défaut), les moyennes pondérées sont calculées à l'aide de poids :\n",
|
|||
|
|
"\n",
|
|||
|
|
"### $y_t = \\frac{x_t + (1 - \\alpha)x_{t-1} + (1 - \\alpha)^2 x_{t-2} + ...\n",
|
|||
|
|
"+ (1 - \\alpha)^t x_{0}}{1 + (1 - \\alpha) + (1 - \\alpha)^2 + ...\n",
|
|||
|
|
"+ (1 - \\alpha)^t}$"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Lorsque adjust=False est spécifié, les moyennes mobiles sont calculées comme suit :\n",
|
|||
|
|
"\n",
|
|||
|
|
"### $\\begin{split}y_0 &= x_0 \\\\\n",
|
|||
|
|
"y_t &= (1 - \\alpha) y_{t-1} + \\alpha x_t,\\end{split}$\n",
|
|||
|
|
"\n",
|
|||
|
|
"ce qui équivaut à utiliser ces valeurs de poids :\n",
|
|||
|
|
"\n",
|
|||
|
|
" \\begin{split}w_i = \\begin{cases}\n",
|
|||
|
|
" \\alpha (1 - \\alpha)^i & \\text{si } i < t \\\\\n",
|
|||
|
|
" (1 - \\alpha)^i & \\text{si } i = t.\n",
|
|||
|
|
"\\end{cases}\\end{split}"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Quand adjust=True nous avons y0=x0 et à partir de la formule ci-dessus nous avons yt=αxt+(1-α)yt-1, donc il y a une hypothèse que x0 n'est pas une valeur ordinaire mais plutôt un moment pondéré exponentiellement de la série infinie jusque-là.\n",
|
|||
|
|
"\n",
|
|||
|
|
"Il faut avoir 0<α≤1, et bien que depuis la version 0.18.0 il soit possible de passer α directement, il est souvent plus facile de penser à la portée (span), au centre de masse (com) ou à la demi-vie (half-life) d'un moment pondéré exponetiellement :"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"\\begin{split}\\alpha =\n",
|
|||
|
|
" \\begin{cases}\n",
|
|||
|
|
" \\frac{2}{s + 1}, & \\text{pour span}\\ s \\geq 1\\\\\n",
|
|||
|
|
" \\frac{1}{1 + c}, & \\text{pour com}\\ c \\geq 0\\\\\n",
|
|||
|
|
" 1 - \\exp^{\\frac{\\log 0.5}{h}}, & \\text{pour halflife}\\ h > 0\n",
|
|||
|
|
" \\end{cases}\\end{split}"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"* span correspond à ce que l'on appelle communément une \"moyenne mobile pondérée exponentiellement au jour N\".\n",
|
|||
|
|
"* com correspond a une interprétation plus physique et peut être considéré en termes de portée: c=(s-1)/2\n",
|
|||
|
|
"* halflife est la période de temps pendant laquelle le poids exponentiel est réduit de moitié.\n",
|
|||
|
|
"* alpha spécifie directement le facteur de lissage."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 8,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"airline['EWMA12'] = airline['Thousands of Passengers'].ewm(span=12).mean()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 9,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"<matplotlib.axes._subplots.AxesSubplot at 0x116e9ed10>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 9,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 432x288 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {
|
|||
|
|
"needs_background": "light"
|
|||
|
|
},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"airline[['Thousands of Passengers','EWMA12']].plot()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {
|
|||
|
|
"collapsed": true
|
|||
|
|
},
|
|||
|
|
"source": [
|
|||
|
|
"Super ! C'est tout pour l'instant, passons à la modélisation ARIMA !"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"metadata": {
|
|||
|
|
"anaconda-cloud": {},
|
|||
|
|
"kernelspec": {
|
|||
|
|
"display_name": "Python 3",
|
|||
|
|
"language": "python",
|
|||
|
|
"name": "python3"
|
|||
|
|
},
|
|||
|
|
"language_info": {
|
|||
|
|
"codemirror_mode": {
|
|||
|
|
"name": "ipython",
|
|||
|
|
"version": 3
|
|||
|
|
},
|
|||
|
|
"file_extension": ".py",
|
|||
|
|
"mimetype": "text/x-python",
|
|||
|
|
"name": "python",
|
|||
|
|
"nbconvert_exporter": "python",
|
|||
|
|
"pygments_lexer": "ipython3",
|
|||
|
|
"version": "3.7.5"
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
"nbformat": 4,
|
|||
|
|
"nbformat_minor": 2
|
|||
|
|
}
|