python-pour-finance/08-Analyse-Time-Series/2-EWMA-Moyennes-mobiles-pon...

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# EWMA : Moyennes Mobiles Pondérées Exponentiellement"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"airline = pd.read_csv('airline_passengers.csv',index_col=\"Month\")"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"airline.dropna(inplace=True)\n",
"airline.index = pd.to_datetime(airline.index)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
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" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
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" 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>Thousands of Passengers</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Month</th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1949-01-01</th>\n",
" <td>112.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1949-02-01</th>\n",
" <td>118.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1949-03-01</th>\n",
" <td>132.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1949-04-01</th>\n",
" <td>129.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1949-05-01</th>\n",
" <td>121.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Thousands of Passengers\n",
"Month \n",
"1949-01-01 112.0\n",
"1949-02-01 118.0\n",
"1949-03-01 132.0\n",
"1949-04-01 129.0\n",
"1949-05-01 121.0"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"airline.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# SMA\n",
"## Moyenne Mobile Simple\n",
"\n",
"Nous avons déjà montré comment créer une moyenne mobile simple, pour une révision rapide:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"airline['6-month-SMA']=airline['Thousands of Passengers'].rolling(window=6).mean()\n",
"airline['12-month-SMA']=airline['Thousands of Passengers'].rolling(window=12).mean()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
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"\n",
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" 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>Thousands of Passengers</th>\n",
" <th>6-month-SMA</th>\n",
" <th>12-month-SMA</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Month</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1949-01-01</th>\n",
" <td>112.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1949-02-01</th>\n",
" <td>118.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1949-03-01</th>\n",
" <td>132.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1949-04-01</th>\n",
" <td>129.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1949-05-01</th>\n",
" <td>121.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Thousands of Passengers 6-month-SMA 12-month-SMA\n",
"Month \n",
"1949-01-01 112.0 NaN NaN\n",
"1949-02-01 118.0 NaN NaN\n",
"1949-03-01 132.0 NaN NaN\n",
"1949-04-01 129.0 NaN NaN\n",
"1949-05-01 121.0 NaN NaN"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"airline.head()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x116b6eed0>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"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": {
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\n",
"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
}