446 lines
85 KiB
Plaintext
446 lines
85 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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"___\n",
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"\n",
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"<a href='http://www.pieriandata.com'> <img src='../Pierian_Data_Logo.png' /></a>\n",
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"___\n",
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"<center>*Copyright Pierian Data 2017*</center>\n",
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"<center>*For more information, visit us at www.pieriandata.com*</center>"
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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": 19,
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"metadata": {
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"collapsed": true
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},
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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": 20,
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"metadata": {
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"collapsed": true
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},
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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": 21,
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"metadata": {
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"collapsed": true
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},
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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": 22,
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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>\n",
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" .dataframe thead tr:only-child th {\n",
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" text-align: right;\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: left;\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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"</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": 22,
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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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"## Simple Moving Average\n",
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"\n",
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"We've already shown how to create a simple moving average, for a quick review:"
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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": 23,
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"metadata": {
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"collapsed": true
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},
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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": 24,
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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>\n",
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|
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" .dataframe thead tr:only-child th {\n",
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" text-align: right;\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: left;\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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"</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": 24,
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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": 25,
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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 0x11760a978>"
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]
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},
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"execution_count": 25,
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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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|
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"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEKCAYAAAAcgp5RAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niouLuemmm+jSpQtdu3Z
|
|||
|
|
"text/plain": [
|
|||
|
|
"<matplotlib.figure.Figure at 0x11773cef0>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"airline.plot()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"# EWMA\n",
|
|||
|
|
"## Exponentially-weighted moving average \n",
|
|||
|
|
"\n",
|
|||
|
|
"We just showed how to calculate the SMA based on some window.However, basic SMA has some \"weaknesses\".\n",
|
|||
|
|
"* Smaller windows will lead to more noise, rather than signal\n",
|
|||
|
|
"* It will always lag by the size of the window\n",
|
|||
|
|
"* It will never reach to full peak or valley of the data due to the averaging.\n",
|
|||
|
|
"* Does not really inform you about possible future behaviour, all it really does is describe trends in your data.\n",
|
|||
|
|
"* Extreme historical values can skew your SMA significantly\n",
|
|||
|
|
"\n",
|
|||
|
|
"To help fix some of these issues, we can use an EWMA (Exponentially-weighted moving average)."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"EWMA will allow us to reduce the lag effect from SMA and it will put more weight on values that occured more recently (by applying more weight to the more recent values, thus the name). The amount of weight applied to the most recent values will depend on the actual parameters used in the EWMA and the number of periods given a window size.\n",
|
|||
|
|
"[Full details on Mathematics behind this can be found here](http://pandas.pydata.org/pandas-docs/stable/computation.html#exponentially-weighted-windows)\n",
|
|||
|
|
"Here is the shorter version of the explanation behind EWMA.\n",
|
|||
|
|
"\n",
|
|||
|
|
"The formula for EWMA is:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"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": [
|
|||
|
|
"Where x_t is the input value, w_i is the applied weight (Note how it can change from i=0 to t), and y_t is the output.\n",
|
|||
|
|
"\n",
|
|||
|
|
"Now the question is, how to we define the weight term w_i ?\n",
|
|||
|
|
"\n",
|
|||
|
|
"This depends on the adjust parameter you provide to the .ewm() method.\n",
|
|||
|
|
"\n",
|
|||
|
|
"When adjust is True (default), weighted averages are calculated using weights:\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": [
|
|||
|
|
"When adjust=False is specified, moving averages are calculated as:\n",
|
|||
|
|
"\n",
|
|||
|
|
"### $\\begin{split}y_0 &= x_0 \\\\\n",
|
|||
|
|
"y_t &= (1 - \\alpha) y_{t-1} + \\alpha x_t,\\end{split}$\n",
|
|||
|
|
"\n",
|
|||
|
|
"which is equivalent to using weights:\n",
|
|||
|
|
"\n",
|
|||
|
|
" \\begin{split}w_i = \\begin{cases}\n",
|
|||
|
|
" \\alpha (1 - \\alpha)^i & \\text{if } i < t \\\\\n",
|
|||
|
|
" (1 - \\alpha)^i & \\text{if } i = t.\n",
|
|||
|
|
"\\end{cases}\\end{split}"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"When adjust=True we have y0=x0 and from the last representation above we have yt=αxt+(1−α)yt−1, therefore there is an assumption that x0 is not an ordinary value but rather an exponentially weighted moment of the infinite series up to that point.\n",
|
|||
|
|
"\n",
|
|||
|
|
"One must have 0<α≤1, and while since version 0.18.0 it has been possible to pass α directly, it’s often easier to think about either the span, center of mass (com) or half-life of an EW moment:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"\\begin{split}\\alpha =\n",
|
|||
|
|
" \\begin{cases}\n",
|
|||
|
|
" \\frac{2}{s + 1}, & \\text{for span}\\ s \\geq 1\\\\\n",
|
|||
|
|
" \\frac{1}{1 + c}, & \\text{for center of mass}\\ c \\geq 0\\\\\n",
|
|||
|
|
" 1 - \\exp^{\\frac{\\log 0.5}{h}}, & \\text{for half-life}\\ h > 0\n",
|
|||
|
|
" \\end{cases}\\end{split}"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"* Span corresponds to what is commonly called an “N-day EW moving average”.\n",
|
|||
|
|
"* Center of mass has a more physical interpretation and can be thought of in terms of span: c=(s−1)/2\n",
|
|||
|
|
"* Half-life is the period of time for the exponential weight to reduce to one half.\n",
|
|||
|
|
"* Alpha specifies the smoothing factor directly."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 30,
|
|||
|
|
"metadata": {
|
|||
|
|
"collapsed": true
|
|||
|
|
},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"airline['EWMA12'] = airline['Thousands of Passengers'].ewm(span=12).mean()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 32,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"<matplotlib.axes._subplots.AxesSubplot at 0x10b146b00>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 32,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
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|
|||
|
|
"text/plain": [
|
|||
|
|
"<matplotlib.figure.Figure at 0x10b11a6d8>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"airline[['Thousands of Passengers','EWMA12']].plot()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {
|
|||
|
|
"collapsed": true
|
|||
|
|
},
|
|||
|
|
"source": [
|
|||
|
|
"Great! That is all for now, let's move on to ARIMA modeling!"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"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": "3.6.1"
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
"nbformat": 4,
|
|||
|
|
"nbformat_minor": 2
|
|||
|
|
}
|