Tutorial: Time Series Analysis with Pandas
In this tutorial, we will learn about the powerful time series tools in the pandas library.
Originally developed for financial time series such as daily stock market prices, the robust and flexible data structures in pandas can be applied to time series data in any domain, including business, science, engineering, public health, and many others. With these tools you can easily organize, transform, analyze, and visualize your data at any level of granularity — examining details during specific time periods of interest, and zooming out to explore variations on different time scales, such as monthly or annual aggregations, recurring patterns, and longterm trends.
In the broadest definition, a time series is any data set where the values are measured at different points in time. Many time series are uniformly spaced at a specific frequency, for example, hourly weather measurements, daily counts of web site visits, or monthly sales totals. Time series can also be irregularly spaced and sporadic, for example, timestamped data in a computer system’s event log or a history of 911 emergency calls. Pandas time series tools apply equally well to either type of time series.
This tutorial will focus mainly on the data wrangling and visualization aspects of time series analysis. Working with a time series of energy data, we’ll see how techniques such as timebased indexing, resampling, and rolling windows can help us explore variations in electricity demand and renewable energy supply over time. We’ll be covering the following topics:
 The data set: Open Power Systems Data
 Time series data structures
 Timebased indexing
 Visualizing time series data
 Seasonality
 Frequencies
 Resampling
 Rolling windows
 Trends
We’ll be using Python 3.6, pandas, matplotlib, and seaborn. To get the most out of this tutorial, you’ll want to be familiar with the basics of pandas and matplotlib.
The data set: Open Power Systems Data
In this tutorial, we’ll be working with daily time series of Open Power System Data (OPSD) for Germany, which has been rapidly expanding its renewable energy production in recent years . The data set includes countrywide totals of electricity consumption, wind power production, and solar power production for 20062017. You can download the data here .
Electricity production and consumption are reported as daily totals in gigawatthours (GWh). The columns of the data file are:

Date
— The date ( yyyymmdd format) 
Consumption
— Electricity consumption in GWh 
Wind
— Wind power production in GWh 
Solar
— Solar power production in GWh 
Wind+Solar
— Sum of wind and solar power production in GWh
We will explore how electricity consumption and production in Germany have varied over time, using pandas time series tools to answer questions such as:
 When is electricity consumption typically highest and lowest?
 How do wind and solar power production vary with seasons of the year?
 What are the longterm trends in electricity consumption, solar power, and wind power?
 How do wind and solar power production compare with electricity consumption, and how has this ratio changed over time?
Time series data structures
Before we dive into the OPSD data, let’s briefly introduce the main pandas data structures for working with dates and times. In pandas, a single point in time is represented as a Timestamp . We can use the to_datetime()
function to create Timestamps from strings in a wide variety of date/time formats. Let’s import pandas and convert a few dates and times to Timestamps.
import pandas as pd pd.to_datetime('20180115 3:45pm')
Timestamp('20180115 15:45:00')
pd.to_datetime('7/8/1952')
Timestamp('19520708 00:00:00')
As we can see, to_datetime()
automatically infers a date/time format based on the input. In the example above, the ambiguous date '7/8/1952'
is assumed to be month/day/year and is interpreted as July 8, 1952. Alternatively, we can use the dayfirst
parameter to tell pandas to interpret the date as August 7, 1952.
pd.to_datetime('7/8/1952', dayfirst=True)
Timestamp('19520807 00:00:00')
If we supply a list or array of strings as input to to_datetime()
, it returns a sequence of date/time values in a DatetimeIndex object, which is the core data structure that powers much of pandas time series functionality.
pd.to_datetime(['20180105', '7/8/1952', 'Oct 10, 1995'])
DatetimeIndex(['20180105', '19520708', '19951010'], dtype='datetime64[ns]', freq=None)
In the DatetimeIndex above, the data type datetime64[ns]
indicates that the underlying data is stored as 64
bit integers, in units of nanoseconds (ns). This data structure allows pandas to compactly store large sequences of date/time values and efficiently perform vectorized operations using NumPy datetime64 arrays .
If we’re dealing with a sequence of strings all in the same date/time format, we can explicitly specify it with the format
parameter. For very large data sets, this can greatly speed up the performance of to_datetime()
compared to the default behavior, where the format is inferred separately for each individual string. Any of the format codes from the strftime()
and strptime()
functions in Python’s builtin datetime module can be used. The example below uses the format codes %m
(numeric month), %d
(day of month), and %y
(2digit year) to specify the format.
pd.to_datetime(['2/25/10', '8/6/17', '12/15/12'], format='%m/%d/%y')
DatetimeIndex(['20100225', '20170806', '20121215'], dtype='datetime64[ns]', freq=None)
In addition to Timestamp and DatetimeIndex objects representing individual points in time, pandas also includes data structures representing durations (e.g., 125 seconds) and periods (e.g., the month of November 2018). For more about these data structures, there is a nice summary here . In this tutorial we will use DatetimeIndexes, the most common data structure for pandas time series.
Creating a time series DataFrame
To work with time series data in pandas, we use a DatetimeIndex as the index for our DataFrame (or Series). Let’s see how to do this with our OPSD data set. First, we use the read_csv()
function to read the data into a DataFrame, and then display its shape.
opsd_daily = pd.read_csv('opsd_germany_daily.csv') opsd_daily.shape
(4383, 5)
The DataFrame has 4383 rows, covering the period from January 1, 2006 through December 31, 2017. To see what the data looks like, let’s use the head()
and tail()
methods to display the first three and last three rows.
opsd_daily.head(3)
Date  Consumption  Wind  Solar  Wind+Solar  

0  20060101  1069.184  NaN  NaN  NaN 
1  20060102  1380.521  NaN  NaN  NaN 
2  20060103  1442.533  NaN  NaN  NaN 
opsd_daily.tail(3)
Date  Consumption  Wind  Solar  Wind+Solar  

4380  20171229  1295.08753  584.277  29.854  614.131 
4381  20171230  1215.44897  721.247  7.467  728.714 
4382  20171231  1107.11488  721.176  19.980  741.156 
Next, let’s check out the data types of each column.
opsd_daily.dtypes
Date object Consumption float64 Wind float64 Solar float64 Wind+Solar float64 dtype: object
We can see that the Date
column is object
data type, indicating that pandas is treating it as text. To convert it to date/time values, we use to_datetime()
.
opsd_daily['Date'] = pd.to_datetime(opsd_daily['Date']) opsd_daily.dtypes
Date datetime64[ns] Consumption float64 Wind float64 Solar float64 Wind+Solar float64 dtype: object
Now that the Date
column is the correct data type, let’s set it as the DataFrame’s index.
opsd_daily = opsd_daily.set_index('Date') opsd_daily.head(3)
Consumption  Wind  Solar  Wind+Solar  

Date  
20060101  1069.184  NaN  NaN  NaN 
20060102  1380.521  NaN  NaN  NaN 
20060103  1442.533  NaN  NaN  NaN 
opsd_daily.index
DatetimeIndex(['20060101', '20060102', '20060103', '20060104', '20060105', '20060106', '20060107', '20060108', '20060109', '20060110', ... '20171222', '20171223', '20171224', '20171225', '20171226', '20171227', '20171228', '20171229', '20171230', '20171231'], dtype='datetime64[ns]', name='Date', length=4383, freq=None)
Alternatively, we can consolidate the above steps into a single line, using the index_col
and parse_dates
parameters of the read_csv()
function. This is often a useful shortcut.
opsd_daily = pd.read_csv('opsd_germany_daily.csv', index_col=0, parse_dates=True)
Now that our DataFrame’s index is a DatetimeIndex, we can use all of pandas’ powerful timebased indexing to wrangle and analyze our data, as we shall see in the following sections.
Another useful aspect of the DatetimeIndex is that the individual date/time components are all available as attributes such as year
, month
, day
, and so on. Let’s add a few more columns to opsd_daily
, containing the year, month, and weekday name.
# Add columns with year, month, and weekday name opsd_daily['Year'] = opsd_daily.index.year opsd_daily['Month'] = opsd_daily.index.month opsd_daily['Weekday Name'] = opsd_daily.index.weekday_name # Display a random sampling of 5 rows opsd_daily.sample(5, random_state=0)
Consumption  Wind  Solar  Wind+Solar  Year  Month  Weekday Name  

Date  
20080823  1152.011  NaN  NaN  NaN  2008  8  Saturday 
20130808  1291.984  79.666  93.371  173.037  2013  8  Thursday 
20090827  1281.057  NaN  NaN  NaN  2009  8  Thursday 
20151002  1391.050  81.229  160.641  241.870  2015  10  Friday 
20090602  1201.522  NaN  NaN  NaN  2009  6  Tuesday 
Timebased indexing
One of the most powerful and convenient features of pandas time series is timebased indexing — using dates and times to intuitively organize and access our data. With timebased indexing, we can use date/time formatted strings to select data in our DataFrame with the loc
accessor. The indexing works similar to standard labelbased indexing with loc
, but with a few additional features.
For example, we can select data for a single day using a string such as '20170810'
.
opsd_daily.loc['20170810']
Consumption 1351.49 Wind 100.274 Solar 71.16 Wind+Solar 171.434 Year 2017 Month 8 Weekday Name Thursday Name: 20170810 00:00:00, dtype: object
We can also select a slice of days, such as '20140120':'20140122'
. As with regular labelbased indexing with loc
, the slice is inclusive of both endpoints.
opsd_daily.loc['20140120':'20140122']
Consumption  Wind  Solar  Wind+Solar  Year  Month  Weekday Name  

Date  
20140120  1590.687  78.647  6.371  85.018  2014  1  Monday 
20140121  1624.806  15.643  5.835  21.478  2014  1  Tuesday 
20140122  1625.155  60.259  11.992  72.251  2014  1  Wednesday 
Another very handy feature of pandas time series is partialstring indexing , where we can select all date/times which partially match a given string. For example, we can select the entire year 2006 with opsd_daily.loc['2006']
, or the entire month of February 2012 with opsd_daily.loc['201202']
.
opsd_daily.loc['201202']
Consumption  Wind  Solar  Wind+Solar  Year  Month  Weekday Name  

Date  
20120201  1511.866  199.607  43.502  243.109  2012  2  Wednesday 
20120202  1563.407  73.469  44.675  118.144  2012  2  Thursday 
20120203  1563.631  36.352  46.510  82.862  2012  2  Friday 
20120204  1372.614  20.551  45.225  65.776  2012  2  Saturday 
20120205  1279.432  55.522  54.572  110.094  2012  2  Sunday 
20120206  1574.766  34.896  55.389  90.285  2012  2  Monday 
20120207  1615.078  100.312  19.867  120.179  2012  2  Tuesday 
20120208  1613.774  93.763  36.930  130.693  2012  2  Wednesday 
20120209  1591.532  132.219  19.042  151.261  2012  2  Thursday 
20120210  1581.287  52.122  34.873  86.995  2012  2  Friday 
20120211  1377.404  32.375  44.629  77.004  2012  2  Saturday 
20120212  1264.254  62.659  45.176  107.835  2012  2  Sunday 
20120213  1561.987  25.984  11.287  37.271  2012  2  Monday 
20120214  1550.366  146.495  9.610  156.105  2012  2  Tuesday 
20120215  1476.037  413.367  18.877  432.244  2012  2  Wednesday 
20120216  1504.119  130.247  38.176  168.423  2012  2  Thursday 
20120217  1438.857  196.515  17.328  213.843  2012  2  Friday 
20120218  1236.069  237.889  26.248  264.137  2012  2  Saturday 
20120219  1107.431  272.655  30.382  303.037  2012  2  Sunday 
20120220  1401.873  160.315  53.794  214.109  2012  2  Monday 
20120221  1434.533  281.909  57.984  339.893  2012  2  Tuesday 
20120222  1453.507  287.635  74.904  362.539  2012  2  Wednesday 
20120223  1427.402  353.510  18.927  372.437  2012  2  Thursday 
20120224  1373.800  382.777  29.281  412.058  2012  2  Friday 
20120225  1133.184  302.102  42.667  344.769  2012  2  Saturday 
20120226  1086.743  95.234  37.214  132.448  2012  2  Sunday 
20120227  1436.095  86.956  43.099  130.055  2012  2  Monday 
20120228  1408.211  231.923  16.190  248.113  2012  2  Tuesday 
20120229  1434.062  77.024  30.360  107.384  2012  2  Wednesday 
Visualizing time series data
With pandas and matplotlib, we can easily visualize our time series data. In this section, we’ll cover a few examples and some useful customizations for our time series plots. First, let’s import matplotlib.
import matplotlib.pyplot as plt # Display figures inline in Jupyter notebook %matplotlib inline
We’ll use seaborn styling for our plots, and let’s adjust the default figure size to an appropriate shape for time series plots.
import seaborn as sns # Use seaborn style defaults and set the default figure size sns.set(rc={'figure.figsize':(11, 4)})
Let’s create a line plot of the full time series of Germany’s daily electricity consumption, using the DataFrame’s plot()
method.
opsd_daily['Consumption'].plot(linewidth=0.5);
We can see that the plot()
method has chosen pretty good tick locations (every two years) and labels (the years) for the xaxis, which is helpful. However, with so many data points, the line plot is crowded and hard to read. Let’s plot the data as dots instead, and also look at the Solar
and Wind
time series.
cols_plot = ['Consumption', 'Solar', 'Wind'] axes = opsd_daily[cols_plot].plot(marker='.', alpha=0.5, linestyle='None', figsize=(11, 9), subplots=True) for ax in axes: ax.set_ylabel('Daily Totals (GWh)')
We can already see some interesting patterns emerge:
 Electricity consumption is highest in winter, presumably due to electric heating and increased lighting usage, and lowest in summer.
 Electricity consumption appears to split into two clusters — one with oscillations centered roughly around 1400 GWh, and another with fewer and more scattered data points, centered roughly around 1150 GWh. We might guess that these clusters correspond with weekdays and weekends, and we will investigate this further shortly.
 Solar power production is highest in summer, when sunlight is most abundant, and lowest in winter.
 Wind power production is highest in winter, presumably due to stronger winds and more frequent storms, and lowest in summer.
 There appears to be a strong increasing trend in wind power production over the years.
All three time series clearly exhibit periodicity—often referred to as seasonality in time series analysis—in which a pattern repeats again and again at regular time intervals. The Consumption
, Solar
, and Wind
time series oscillate between high and low values on a yearly time scale, corresponding with the seasonal changes in weather over the year. However, seasonality in general does not have to correspond with the meteorological seasons. For example, retail sales data often exhibits yearly seasonality with increased sales in November and December, leading up to the holidays.
Seasonality can also occur on other time scales. The plot above suggests there may be some weekly seasonality in Germany’s electricity consumption, corresponding with weekdays and weekends. Let’s plot the time series in a single year to investigate further.
ax = opsd_daily.loc['2017', 'Consumption'].plot() ax.set_ylabel('Daily Consumption (GWh)');
Now we can clearly see the weekly oscillations. Another interesting feature that becomes apparent at this level of granularity is the drastic decrease in electricity consumption in early January and late December, during the holidays.
Let’s zoom in further and look at just January and February.
ax = opsd_daily.loc['201701':'201702', 'Consumption'].plot(marker='o', linestyle='') ax.set_ylabel('Daily Consumption (GWh)');
As we suspected, consumption is highest on weekdays and lowest on weekends.
Customizing time series plots
To better visualize the weekly seasonality in electricity consumption in the plot above, it would be nice to have vertical gridlines on a weekly time scale (instead of on the first day of each month). We can customize our plot with matplotlib.dates , so let’s import that module.
import matplotlib.dates as mdates
Because date/time ticks are handled a bit differently in matplotlib.dates compared with the DataFrame’s plot()
method, let’s create the plot directly in matplotlib. Then we use mdates.WeekdayLocator()
and mdates.MONDAY
to set the xaxis ticks to the first Monday of each week. We also use mdates.DateFormatter()
to improve the formatting of the tick labels, using the format codes we saw earlier.
fig, ax = plt.subplots() ax.plot(opsd_daily.loc['201701':'201702', 'Consumption'], marker='o', linestyle='') ax.set_ylabel('Daily Consumption (GWh)') ax.set_title('JanFeb 2017 Electricity Consumption') # Set xaxis major ticks to weekly interval, on Mondays ax.xaxis.set_major_locator(mdates.WeekdayLocator(byweekday=mdates.MONDAY)) # Format xtick labels as 3letter month name and day number ax.xaxis.set_major_formatter(mdates.DateFormatter('%b %d'));
Now we have vertical gridlines and nicely formatted tick labels on each Monday, so we can easily tell which days are weekdays and weekends.
There are many other ways to visualize time series, depending on what patterns you’re trying to explore — scatter plots, heatmaps, histograms, and so on. We’ll see other visualization examples in the following sections, including visualizations of time series data that has been transformed in some way, such as aggregated or smoothed data.
Seasonality
Next, let’s further explore the seasonality of our data with box plots , using seaborn’s boxplot()
function to group the data by different time periods and display the distributions for each group. We’ll first group the data by month, to visualize yearly seasonality.
fig, axes = plt.subplots(3, 1, figsize=(11, 10), sharex=True) for name, ax in zip(['Consumption', 'Solar', 'Wind'], axes): sns.boxplot(data=opsd_daily, x='Month', y=name, ax=ax) ax.set_ylabel('GWh') ax.set_title(name) # Remove the automatic xaxis label from all but the bottom subplot if ax != axes[1]: ax.set_xlabel('')
These box plots confirm the yearly seasonality that we saw in earlier plots and provide some additional insights:
 Although electricity consumption is generally higher in winter and lower in summer, the median and lower two quartiles are lower in December and January compared to November and February, likely due to businesses being closed over the holidays. We saw this in the time series for the year 2017, and the box plot confirms that this is consistent pattern throughout the years.
 While solar and wind power production both exhibit a yearly seasonality, the wind power distributions have many more outliers, reflecting the effects of occasional extreme wind speeds associated with storms and other transient weather conditions.
Next, let’s group the electricity consumption time series by day of the week, to explore weekly seasonality.
sns.boxplot(data=opsd_daily, x='Weekday Name', y='Consumption');
As expected, electricity consumption is significantly higher on weekdays than on weekends. The low outliers on weekdays are presumably during holidays.
This section has provided a brief introduction to time series seasonality. As we will see later, applying a rolling window to the data can also help to visualize seasonality on different time scales. Other techniques for analyzing seasonality include autocorrelation plots , which plot the correlation coefficients of the time series with itself at different time lags.
Time series with strong seasonality can often be well represented with models that decompose the signal into seasonality and a longterm trend, and these models can be used to forecast future values of the time series. A simple example of such a model is classical seasonal decomposition , as demonstrated in this tutorial . A more sophisticated example is as Facebook’s Prophet model , which uses curve fitting to decompose the time series, taking into account seasonality on multiple time scales, holiday effects, abrupt changepoints, and longterm trends, as demonstrated in this tutorial .
Frequencies
When the data points of a time series are uniformly spaced in time (e.g., hourly, daily, monthly, etc.), the time series can be associated with a frequency in pandas. For example, let’s use the date_range()
function to create a sequence of uniformly spaced dates from 19980310
through 19980315
at daily frequency.
pd.date_range('19980310', '19980315', freq='D')
DatetimeIndex(['19980310', '19980311', '19980312', '19980313', '19980314', '19980315'], dtype='datetime64[ns]', freq='D')
The resulting DatetimeIndex has an attribute freq
with a value of 'D'
, indicating daily frequency. Available frequencies in pandas include hourly ( 'H'
), calendar daily ( 'D'
), business daily ( 'B'
), weekly ( 'W'
), monthly ( 'M'
), quarterly ( 'Q'
), annual ( 'A'
), and many others . Frequencies can also be specified as multiples of any of the base frequencies, for example '5D'
for every five days.
As another example, let’s create a date range at hourly frequency, specifying the start date and number of periods, instead of the start date and end date.
pd.date_range('20040920', periods=8, freq='H')
DatetimeIndex(['20040920 00:00:00', '20040920 01:00:00', '20040920 02:00:00', '20040920 03:00:00', '20040920 04:00:00', '20040920 05:00:00', '20040920 06:00:00', '20040920 07:00:00'], dtype='datetime64[ns]', freq='H')
Now let’s take another look at the DatetimeIndex of our opsd_daily
time series.
opsd_daily.index
DatetimeIndex(['20060101', '20060102', '20060103', '20060104', '20060105', '20060106', '20060107', '20060108', '20060109', '20060110', ... '20171222', '20171223', '20171224', '20171225', '20171226', '20171227', '20171228', '20171229', '20171230', '20171231'], dtype='datetime64[ns]', name='Date', length=4383, freq=None)
We can see that it has no frequency ( freq=None
). This makes sense, since the index was created from a sequence of dates in our CSV file, without explicitly specifying any frequency for the time series.
If we know that our data should be at a specific frequency, we can use the DataFrame’s asfreq()
method to assign a frequency. If any date/times are missing in the data, new rows will be added for those date/times, which are either empty ( NaN
), or filled according to a specified data filling method such as forward filling or interpolation.
To see how this works, let’s create a new DataFrame which contains only the Consumption
data for Feb 3, 6, and 8, 2013.
# To select an arbitrary sequence of date/time values from a pandas time series, # we need to use a DatetimeIndex, rather than simply a list of date/time strings times_sample = pd.to_datetime(['20130203', '20130206', '20130208']) # Select the specified dates and just the Consumption column consum_sample = opsd_daily.loc[times_sample, ['Consumption']].copy() consum_sample
Consumption  

20130203  1109.639 
20130206  1451.449 
20130208  1433.098 
Now we use the asfreq()
method to convert the DataFrame to daily frequency, with a column for unfilled data, and a column for forward filled data.
# Convert the data to daily frequency, without filling any missings consum_freq = consum_sample.asfreq('D') # Create a column with missings forward filled consum_freq['Consumption  Forward Fill'] = consum_sample.asfreq('D', method='ffill') consum_freq
Consumption  Consumption – Forward Fill  

20130203  1109.639  1109.639 
20130204  NaN  1109.639 
20130205  NaN  1109.639 
20130206  1451.449  1451.449 
20130207  NaN  1451.449 
20130208  1433.098  1433.098 
In the Consumption
column, we have the original data, with a value of NaN
for any date that was missing in our consum_sample
DataFrame. In the Consumption  Forward Fill
column, the missings have been forward filled, meaning that the last value repeats through the missing rows until the next nonmissing value occurs.
If you’re doing any time series analysis which requires uniformly spaced data without any missings, you’ll want to use asfreq()
to convert your time series to the specified frequency and fill any missings with an appropriate method.
Resampling
It is often useful to resample our time series data to a lower or higher frequency. Resampling to a lower frequency ( downsampling ) usually involves an aggregation operation — for example, computing monthly sales totals from daily data. The daily OPSD data we’re working with in this tutorial was downsampled from the original hourly time series . Resampling to a higher frequency ( upsampling ) is less common and often involves interpolation or other data filling method — for example, interpolating hourly weather data to 10 minute intervals for input to a scientific model.
We will focus here on downsampling, exploring how it can help us analyze our OPSD data on various time scales. We use the DataFrame’s resample()
method, which splits the DatetimeIndex into time bins and groups the data by time bin. The resample()
method returns a Resampler object , similar to a pandas GroupBy object . We can then apply an aggregation method such as mean()
, median()
, sum()
, etc., to the data group for each time bin.
For example, let’s resample the data to a weekly mean time series.
# Specify the data columns we want to include (i.e. exclude Year, Month, Weekday Name) data_columns = ['Consumption', 'Wind', 'Solar', 'Wind+Solar'] # Resample to weekly frequency, aggregating with mean opsd_weekly_mean = opsd_daily[data_columns].resample('W').mean() opsd_weekly_mean.head(3)
Consumption  Wind  Solar  Wind+Solar  

Date  
20060101  1069.184000  NaN  NaN  NaN 
20060108  1381.300143  NaN  NaN  NaN 
20060115  1486.730286  NaN  NaN  NaN 
The first row above, labelled 20060101
, contains the mean of all the data contained in the time bin 20060101
through 20060107
. The second row, labelled 20060108
, contains the mean data for the 20060108
through 20060114
time bin, and so on. By default, each row of the downsampled time series is labelled with the left edge of the time bin.
By construction, our weekly time series has 1/7 as many data points as the daily time series. We can confirm this by comparing the number of rows of the two DataFrames.
print(opsd_daily.shape[0]) print(opsd_weekly_mean.shape[0])
Let’s plot the daily and weekly Solar
time series together over a single sixmonth period to compare them.
# Start and end of the date range to extract start, end = '201701', '201706' # Plot daily and weekly resampled time series together fig, ax = plt.subplots() ax.plot(opsd_daily.loc[start:end, 'Solar'], marker='.', linestyle='', linewidth=0.5, label='Daily') ax.plot(opsd_weekly_mean.loc[start:end, 'Solar'], marker='o', markersize=8, linestyle='', label='Weekly Mean Resample') ax.set_ylabel('Solar Production (GWh)') ax.legend();
We can see that the weekly mean time series is smoother than the daily time series because higher frequency variability has been averaged out in the resampling.
Now let’s resample the data to monthly frequency, aggregating with sum totals instead of the mean. Unlike aggregating with mean()
, which sets the output to NaN
for any period with all missing data, the default behavior of sum()
will return output of 0
as the sum of missing data. We use the min_count
parameter to change this behavior.
# Compute the monthly sums, setting the value to NaN for any month which has # fewer than 28 days of data opsd_monthly = opsd_daily[data_columns].resample('M').sum(min_count=28) opsd_monthly.head(3)
Consumption  Wind  Solar  Wind+Solar  

Date  
20060131  45304.704  NaN  NaN  NaN 
20060228  41078.993  NaN  NaN  NaN 
20060331  43978.124  NaN  NaN  NaN 
You might notice that the monthly resampled data is labelled with the end of each month (the right bin edge), whereas the weekly resampled data is labelled with the left bin edge. By default, resampled data is labelled with the right bin edge for monthly, quarterly, and annual frequencies, and with the left bin edge for all other frequencies. This behavior and various other options can be adjusted using the parameters listed in the resample()
documentation.
Now let’s explore the monthly time series by plotting the electricity consumption as a line plot, and the wind and solar power production together as a stacked area plot.
fig, ax = plt.subplots() ax.plot(opsd_monthly['Consumption'], color='black', label='Consumption') opsd_monthly[['Wind', 'Solar']].plot.area(ax=ax, linewidth=0) ax.xaxis.set_major_locator(mdates.YearLocator()) ax.legend() ax.set_ylabel('Monthly Total (GWh)');
At this monthly time scale, we can clearly see the yearly seasonality in each time series, and it is also evident that electricity consumption has been fairly stable over time, while wind power production has been growing steadily, with wind + solar power comprising an increasing share of the electricity consumed.
Let’s explore this further by resampling to annual frequency and computing the ratio of Wind+Solar
to Consumption
for each year.
# Compute the annual sums, setting the value to NaN for any year which has # fewer than 360 days of data opsd_annual = opsd_daily[data_columns].resample('A').sum(min_count=360) # The default index of the resampled DataFrame is the last day of each year, # ('20061231', '20071231', etc.) so to make life easier, set the index # to the year component opsd_annual = opsd_annual.set_index(opsd_annual.index.year) opsd_annual.index.name = 'Year' # Compute the ratio of Wind+Solar to Consumption opsd_annual['Wind+Solar/Consumption'] = opsd_annual['Wind+Solar'] / opsd_annual['Consumption'] opsd_annual.tail(3)
Consumption  Wind  Solar  Wind+Solar  Wind+Solar/Consumption  

Year  
2015  505264.56300  77468.994  34907.138  112376.132  0.222410 
2016  505927.35400  77008.126  34562.824  111570.950  0.220528 
2017  504736.36939  102667.365  35882.643  138550.008  0.274500 
Finally, let’s plot the wind + solar share of annual electricity consumption as a bar chart.
# Plot from 2012 onwards, because there is no solar production data in earlier years ax = opsd_annual.loc[2012:, 'Wind+Solar/Consumption'].plot.bar(color='C0') ax.set_ylabel('Fraction') ax.set_ylim(0, 0.3) ax.set_title('Wind + Solar Share of Annual Electricity Consumption') plt.xticks(rotation=0);
We can see that wind + solar production as a share of annual electricity consumption has been increasing from about 15% in 2012 to about 27% in 2017.
Rolling windows
Rolling windowoperations are another important transformation for time series data. Similar to downsampling, rolling windows split the data into time windows and and the data in each window is aggregated with a function such as mean()
, median()
, sum()
, etc. However, unlike downsampling, where the time bins do not overlap and the output is at a lower frequency than the input, rolling windows overlap and “roll” along at the same frequency as the data, so the transformed time series is at the same frequency as the original time series.
By default, all data points within a window are equally weighted in the aggregation, but this can be changed by specifying window types such as Gaussian, triangular, and others . We’ll stick with the standard equally weighted window here.
Let’s use the rolling()
method to compute the 7day rolling mean of our daily data. We use the center=True
argument to label each window at its midpoint, so the rolling windows are:

20060101
to20060107
— labelled as20060104

20060102
to20060108
— labelled as20060105

20060103
to20060109
— labelled as20060106
 and so on…
# Compute the centered 7day rolling mean opsd_7d = opsd_daily[data_columns].rolling(7, center=True).mean() opsd_7d.head(10)
Consumption  Wind  Solar  Wind+Solar  

Date  
20060101  NaN  NaN  NaN  NaN 
20060102  NaN  NaN  NaN  NaN 
20060103  NaN  NaN  NaN  NaN 
20060104  1361.471429  NaN  NaN  NaN 
20060105  1381.300143  NaN  NaN  NaN 
20060106  1402.557571  NaN  NaN  NaN 
20060107  1421.754429  NaN  NaN  NaN 
20060108  1438.891429  NaN  NaN  NaN 
20060109  1449.769857  NaN  NaN  NaN 
20060110  1469.994857  NaN  NaN  NaN 
We can see that the first nonmissing rolling mean value is on 20060104
, because this is the midpoint of the first rolling window.
To visualize the differences between rolling mean and resampling, let’s update our earlier plot of JanuaryJune 2017 solar power production to include the 7day rolling mean along with the weekly mean resampled time series and the original daily data.
# Start and end of the date range to extract start, end = '201701', '201706' # Plot daily, weekly resampled, and 7day rolling mean time series together fig, ax = plt.subplots() ax.plot(opsd_daily.loc[start:end, 'Solar'], marker='.', linestyle='', linewidth=0.5, label='Daily') ax.plot(opsd_weekly_mean.loc[start:end, 'Solar'], marker='o', markersize=8, linestyle='', label='Weekly Mean Resample') ax.plot(opsd_7d.loc[start:end, 'Solar'], marker='.', linestyle='', label='7d Rolling Mean') ax.set_ylabel('Solar Production (GWh)') ax.legend();
We can see that data points in the rolling mean time series have the same spacing as the daily data, but the curve is smoother because higher frequency variability has been averaged out. In the rolling mean time series, the peaks and troughs tend to align closely with the peaks and troughs of the daily time series. In contrast, the peaks and troughs in the weekly resampled time series are less closely aligned with the daily time series, since the resampled time series is at a coarser granularity.
Trends
Time series data often exhibit some slow, gradual variability in addition to higher frequency variability such as seasonality and noise. An easy way to visualize these trends is with rolling means at different time scales.
A rolling mean tends to smooth a time series by averaging out variations at frequencies much higher than the window size and averaging out any seasonality on a time scale equal to the window size. This allows lowerfrequency variations in the data to be explored. Since our electricity consumption time series has weekly and yearly seasonality, let’s look at rolling means on those two time scales.
We’ve already computed 7day rolling means, so now let’s compute the 365day rolling mean of our OPSD data.
# The min_periods=360 argument accounts for a few isolated missing days in the # wind and solar production time series opsd_365d = opsd_daily[data_columns].rolling(window=365, center=True, min_periods=360).mean()
Let’s plot the 7day and 365day rolling mean electricity consumption, along with the daily time series.
# Plot daily, 7day rolling mean, and 365day rolling mean time series fig, ax = plt.subplots() ax.plot(opsd_daily['Consumption'], marker='.', markersize=2, color='0.6', linestyle='None', label='Daily') ax.plot(opsd_7d['Consumption'], linewidth=2, label='7d Rolling Mean') ax.plot(opsd_365d['Consumption'], color='0.2', linewidth=3, label='Trend (365d Rolling Mean)') # Set xticks to yearly interval and add legend and labels ax.xaxis.set_major_locator(mdates.YearLocator()) ax.legend() ax.set_xlabel('Year') ax.set_ylabel('Consumption (GWh)') ax.set_title('Trends in Electricity Consumption');
We can see that the 7day rolling mean has smoothed out all the weekly seasonality, while preserving the yearly seasonality. The 7day rolling mean reveals that while electricity consumption is typically higher in winter and lower in summer, there is a dramatic decrease for a few weeks every winter at the end of December and beginning of January, during the holidays.
Looking at the 365day rolling mean time series, we can see that the longterm trend in electricity consumption is pretty flat, with a couple of periods of anomalously low consumption around 2009 and 20122013.
Now let’s look at trends in wind and solar production.
# Plot 365day rolling mean time series of wind and solar power fig, ax = plt.subplots() for nm in ['Wind', 'Solar', 'Wind+Solar']: ax.plot(opsd_365d[nm], label=nm) # Set xticks to yearly interval, adjust yaxis limits, add legend and labels ax.xaxis.set_major_locator(mdates.YearLocator()) ax.set_ylim(0, 400) ax.legend() ax.set_ylabel('Production (GWh)') ax.set_title('Trends in Electricity Production (365d Rolling Means)');
We can see a small increasing trend in solar power production and a large increasing trend in wind power production, as Germany continues to expand its capacity in those sectors.
Summary and further reading
We’ve learned how to wrangle, analyze, and visualize our time series data in pandas using techniques such as timebased indexing, resampling, and rolling windows. Applying these techniques to our OPSD data set, we’ve gained insights on seasonality, trends, and other interesting features of electricity consumption and production in Germany.
Other potentially useful topics we haven’t covered include time zone handling and time shifts . If you’d like to learn more about working with time series data in pandas, you can check out this section of the Python Data Science Handbook , this blog post , and of course the official documentation . If you’re interested in forecasting and machine learning with time series data, we’ll be covering those topics in a future blog post, so stay tuned!
原文 : Dataquest Blog