{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction: Time Series Features\n", "\n", "In this notebook, we will look at different approaches for encoding time series variables. The objective is to determine the most effective method for representing date and time in a time series." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2019-02-15T13:40:44.343418Z", "start_time": "2019-02-15T13:40:44.287685Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The autoreload extension is already loaded. To reload it, use:\n", " %reload_ext autoreload\n" ] }, { "data": { "text/html": [ "" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "\n", "%load_ext autoreload\n", "%autoreload 2\n", "\n", "import sys\n", "sys.path.append('../..')\n", "\n", "# Options for pandas\n", "pd.options.display.max_columns = 20\n", "pd.options.display.max_rows = 10\n", "\n", "# Display all cell outputs\n", "from IPython.core.interactiveshell import InteractiveShell\n", "InteractiveShell.ast_node_interactivity = 'all'\n", "\n", "import plotly.plotly as py\n", "import plotly.graph_objs as go\n", "from plotly.offline import iplot, init_notebook_mode\n", "init_notebook_mode(connected=True)\n", "\n", "import cufflinks\n", "cf.go_offline(connected=True)\n", "cf.set_config_file(theme='pearl')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Data: Building Energy Use\n", "\n", "We'll work with building energy use at a 15 minute frequency. Building energy data is a useful time series because it exhibits patterns at the daily, weekly, and yearly levels. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2019-02-15T13:42:08.724804Z", "start_time": "2019-02-15T13:42:08.502793Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " energy\n", "timestamp \n", "2014-01-01 06:15:00 43.012862\n", "2014-01-01 06:30:00 43.780204\n", "2014-01-01 06:45:00 43.012709\n", "2014-01-01 07:00:00 42.631804\n", "2014-01-01 07:15:00 42.627307" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data = pd.read_csv('data/building_1.csv', parse_dates=['timestamp'], usecols=['timestamp', 'energy'], index_col='timestamp').sort_index()\n", "data.head()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2019-02-15T13:43:49.081550Z", "start_time": "2019-02-15T13:43:47.622684Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": true }, "data": [ { "line": { "color": "rgba(31, 119, 180, 1.0)", "dash": "solid", "shape": "linear", "width": 1.3 }, "mode": "lines", "name": "energy", "text": "", "type": "scatter", "uid": 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"color": "#4D5663" }, "text": "Energy Use" }, "xaxis": { "gridcolor": "#E1E5ED", "showgrid": true, "tickfont": { "color": "#4D5663" }, "title": { "font": { "color": "#4D5663" }, "text": "" }, "zerolinecolor": "#E1E5ED" }, "yaxis": { "gridcolor": "#E1E5ED", "showgrid": true, "tickfont": { "color": "#4D5663" }, "title": { "font": { "color": "#4D5663" }, "text": "Energy (Kwh)" }, "zerolinecolor": "#E1E5ED" } } }, "text/html": [ "
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data.query('timestamp.dt.year == 2015').iplot(yTitle='Energy (Kwh)', title='Energy Use')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Time and Date Features\n", "\n", "The first set of features we'll build are those we intuitively think of: minute, hour, dayofweek, month, dayofyear, year." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2019-02-15T14:28:50.326293Z", "start_time": "2019-02-15T14:28:50.113498Z" } }, "outputs": [ { "data": { "text/html": [ "
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energytimestamp_minutetimestamp_hourtimestamp_dayofweektimestamp_monthtimestamp_dayofyeartimestamp_yearfrac_dayfrac_weektimestamp_daytimestamp_week
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2014-01-01 06:15:0043.01286215621120140.2604170.32291711
2014-01-01 06:30:0043.78020430621120140.2708330.32440511
2014-01-01 06:45:0043.01270945621120140.2812500.32589311
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\n", "
" ], "text/plain": [ " energy timestamp_minute timestamp_hour \\\n", "timestamp \n", "2014-01-01 06:15:00 43.012862 15 6 \n", "2014-01-01 06:30:00 43.780204 30 6 \n", "2014-01-01 06:45:00 43.012709 45 6 \n", "2014-01-01 07:00:00 42.631804 0 7 \n", "2014-01-01 07:15:00 42.627307 15 7 \n", "\n", " timestamp_dayofweek timestamp_month \\\n", "timestamp \n", "2014-01-01 06:15:00 2 1 \n", "2014-01-01 06:30:00 2 1 \n", "2014-01-01 06:45:00 2 1 \n", "2014-01-01 07:00:00 2 1 \n", "2014-01-01 07:15:00 2 1 \n", "\n", " timestamp_dayofyear timestamp_year frac_day frac_week \\\n", "timestamp \n", "2014-01-01 06:15:00 1 2014 0.260417 0.322917 \n", "2014-01-01 06:30:00 1 2014 0.270833 0.324405 \n", "2014-01-01 06:45:00 1 2014 0.281250 0.325893 \n", "2014-01-01 07:00:00 1 2014 0.291667 0.327381 \n", "2014-01-01 07:15:00 1 2014 0.302083 0.328869 \n", "\n", " timestamp_day timestamp_week \n", "timestamp \n", "2014-01-01 06:15:00 1 1 \n", "2014-01-01 06:30:00 1 1 \n", "2014-01-01 06:45:00 1 1 \n", "2014-01-01 07:00:00 1 1 \n", "2014-01-01 07:15:00 1 1 " ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "baseline_features = ['minute', 'hour', 'dayofweek', 'day', 'week', 'month', 'dayofyear', 'year']\n", "\n", "for feature in baseline_features:\n", " data['timestamp_' + feature] = getattr(data.index, feature)\n", "\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These are pretty straightforward. We should be careful to note the day of week goes from 0 (Monday) to 6 (Sunday)." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2019-02-15T14:28:53.489098Z", "start_time": "2019-02-15T14:28:53.398589Z" } }, "outputs": [ { "data": { "text/plain": [ "energy 100786\n", "timestamp_minute 4\n", "timestamp_hour 24\n", "timestamp_dayofweek 7\n", "timestamp_month 12\n", " ... \n", "timestamp_year 3\n", "frac_day 96\n", "frac_week 672\n", "timestamp_day 31\n", "timestamp_week 53\n", "Length: 11, dtype: int64" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data.apply(lambda x: x.nunique(), axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Fractional Features\n", "\n", "If we want to compress these features, we can convert them into fractions of their respective interval. For example, fraction of the day, fraction of the month, fraction of the week, and fraction of the year," ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "ExecuteTime": { "end_time": "2019-02-15T14:29:02.576712Z", "start_time": "2019-02-15T14:29:02.173047Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": true }, "data": [ { "line": { "color": "rgba(31, 119, 180, 1.0)", "dash": "solid", "shape": "linear", "width": 1.3 }, "mode": "lines", "name": "frac_day", "text": "", "type": "scatter", "uid": "515ebd45-3211-4b19-aecf-142255d74593", "x": [ "2015-12-01 00:00:00", "2015-12-01 00:15:00", "2015-12-01 00:30:00", "2015-12-01 00:45:00", "2015-12-01 01:00:00", "2015-12-01 01:15:00", "2015-12-01 01:30:00", "2015-12-01 01:45:00", "2015-12-01 02:00:00", "2015-12-01 02:15:00", "2015-12-01 02:30:00", "2015-12-01 02:45:00", "2015-12-01 03:00:00", "2015-12-01 03:15:00", 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"title": { "font": { "color": "#4D5663" }, "text": "Fractional Month" }, "xaxis": { "gridcolor": "#E1E5ED", "showgrid": true, "tickfont": { "color": "#4D5663" }, "title": { "font": { "color": "#4D5663" }, "text": "" }, "zerolinecolor": "#E1E5ED" }, "yaxis": { "gridcolor": "#E1E5ED", "showgrid": true, "tickfont": { "color": "#4D5663" }, "title": { "font": { "color": "#4D5663" }, "text": "" }, "zerolinecolor": "#E1E5ED" } } }, "text/html": [ "
" ], "text/vnd.plotly.v1+html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data['frac_month' ] = (data['timestamp_day'] + data['frac_day']) / data.index.days_in_month\n", "\n", "data.query('timestamp.dt.year == 2015')['frac_month'].iplot(title='Fractional Month')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the fraction of the year, we have to find the number of days in the year which obeys the rules:\n", "\n", "1. 365 in a non-leap year\n", "2. 366 in a leap year which occurs:\n", " * When the year is divisible by 4 except:\n", " * Years divisible by 100 and not divisible by 400\n", " \n", "This logic is captured below" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "ExecuteTime": { "end_time": "2019-02-15T14:37:07.010661Z", "start_time": "2019-02-15T14:37:06.964023Z" } }, "outputs": [ { "data": { "text/plain": [ "array([365, 366, 366, 365, 365, 365, 365, 366])" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def find_days_in_year(years):\n", " return np.where((years % 4 == 0) & ((years % 100 != 0) | (years % 400 == 0)), 366, 365)\n", "\n", "\n", "find_days_in_year(np.array([1900, 2000, 2004, 2005, 2009, 2010, 3000, 3200]))" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "ExecuteTime": { "end_time": "2019-02-15T14:38:05.541801Z", "start_time": "2019-02-15T14:38:05.486015Z" } }, "outputs": [ { "data": { "text/plain": [ "array([365, 366])" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "days_in_year = find_days_in_year(data['timestamp_year'])\n", "np.unique(days_in_year)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "ExecuteTime": { "end_time": "2019-02-15T14:39:11.823853Z", "start_time": "2019-02-15T14:39:11.000758Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": true }, "data": [ { 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