Introduction to pandas

by Maxwell Margenot

Part of the Quantopian Lecture Series:

pandas is a Python library that provides a collection of powerful data structures to better help you manage data. In this lecture, we will cover how to use the Series and DataFrame objects to handle data. These objects have a strong integration with NumPy, covered elsewhere in the lecture series, allowing us to easily do the necessary statistical and mathematical calculations that we need for finance.


In [1]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

With pandas, it is easy to store, visualize, and perform calculations on your data. With only a few lines of code we can modify our data and present it in an easily-understandable way. Here we simulate some returns in NumPy, put them into a pandas DataFrame, and perform calculations to turn them into prices and plot them, all only using a few lines of code.


In [2]:
returns = pd.DataFrame(np.random.normal(1.0, 0.03, (100, 10)))
prices = returns.cumprod()
prices.plot()
plt.title('Randomly-generated Prices')
plt.xlabel('Time')
plt.ylabel('Price')
plt.legend(loc=0);


So let's have a look at how we actually build up to this point!

pandas Data Structures

Series

A pandas Series is a 1-dimensional array with labels that can contain any data type. We primarily use them for handling time series data. Creating a Series is as easy as calling pandas.Series() on a Python list or NumPy array.


In [3]:
s = pd.Series([1, 2, np.nan, 4, 5])
print s


0    1.0
1    2.0
2    NaN
3    4.0
4    5.0
dtype: float64

Every Series has a name. We can give the series a name as a parameter or we can define it afterwards by directly accessing the name attribute. In this case, we have given our time series no name so the attribute should be empty.


In [4]:
print s.name


None

This name can be directly modified with no repercussions.


In [5]:
s.name = "Toy Series"
print s.name


Toy Series

We call the collected axis labels of a Series its index. An index can either passed to a Series as a parameter or added later, similarly to its name. In the absence of an index, a Series will simply contain an index composed of integers, starting at $0$, as in the case of our "Toy Series".


In [6]:
print s.index


RangeIndex(start=0, stop=5, step=1)

pandas has a built-in function specifically for creating date indices, date_range(). We use the function here to create a new index for s.


In [7]:
new_index = pd.date_range("2016-01-01", periods=len(s), freq="D")
print new_index


DatetimeIndex(['2016-01-01', '2016-01-02', '2016-01-03', '2016-01-04',
               '2016-01-05'],
              dtype='datetime64[ns]', freq='D')

An index must be exactly the same length as the Series itself. Each index must match one-to-one with each element of the Series. Once this is satisfied, we can directly modify the Series index, as with the name, to use our new and more informative index (relatively speaking).


In [8]:
s.index = new_index
print s.index


DatetimeIndex(['2016-01-01', '2016-01-02', '2016-01-03', '2016-01-04',
               '2016-01-05'],
              dtype='datetime64[ns]', freq='D')

The index of the Series is crucial for handling time series, which we will get into a little later.

Accessing Series Elements

Series are typically accessed using the iloc[] and loc[] methods. We use iloc[] to access elements by integer index and we use loc[] to access the index of the Series.


In [9]:
print "First element of the series: ", s.iloc[0]
print "Last element of the series: ", s.iloc[len(s)-1]


First element of the series:  1.0
Last element of the series:  5.0

We can slice a Series similarly to our favorite collections, Python lists and NumPy arrays. We use the colon operator to indicate the slice.


In [10]:
s.iloc[:2]


Out[10]:
2016-01-01    1.0
2016-01-02    2.0
Freq: D, Name: Toy Series, dtype: float64

When creating a slice, we have the options of specifying a beginning, an end, and a step. The slice will begin at the start index, and take steps of size step until it passes the end index, not including the end.


In [11]:
start = 0
end = len(s) - 1
step = 1

s.iloc[start:end:step]


Out[11]:
2016-01-01    1.0
2016-01-02    2.0
2016-01-03    NaN
2016-01-04    4.0
Freq: D, Name: Toy Series, dtype: float64

We can even reverse a Series by specifying a negative step size. Similarly, we can index the start and end with a negative integer value.


In [12]:
s.iloc[::-1]


Out[12]:
2016-01-05    5.0
2016-01-04    4.0
2016-01-03    NaN
2016-01-02    2.0
2016-01-01    1.0
Freq: -1D, Name: Toy Series, dtype: float64

This returns a slice of the series that starts from the second to last element and ends at the third to last element (because the fourth to last is not included, taking steps of size $1$).


In [13]:
s.iloc[-2:-4:-1]


Out[13]:
2016-01-04    4.0
2016-01-03    NaN
Freq: -1D, Name: Toy Series, dtype: float64

We can also access a series by using the values of its index. Since we indexed s with a collection of dates (Timestamp objects) we can look at the value contained in s for a particular date.


In [14]:
s.loc['2016-01-01']


Out[14]:
1.0

Or even for a range of dates!


In [15]:
s.loc['2016-01-02':'2016-01-04']


Out[15]:
2016-01-02    2.0
2016-01-03    NaN
2016-01-04    4.0
Freq: D, Name: Toy Series, dtype: float64

With Series, we can just use the brackets ([]) to access elements, but this is not best practice. The brackets are ambiguous because they can be used to access Series (and DataFrames) using both index and integer values and the results will change based on context (especially with DataFrames).

Boolean Indexing

In addition to the above-mentioned access methods, you can filter Series using boolean arrays. Series are compatible with your standard comparators. Once compared with whatever condition you like, you get back yet another Series, this time filled with boolean values.


In [16]:
print s < 3


2016-01-01     True
2016-01-02     True
2016-01-03    False
2016-01-04    False
2016-01-05    False
Freq: D, Name: Toy Series, dtype: bool

We can pass this Series back into the original Series to filter out only the elements for which our condition is True.


In [17]:
print s.loc[s < 3]


2016-01-01    1.0
2016-01-02    2.0
Freq: D, Name: Toy Series, dtype: float64

If we so desire, we can group multiple conditions together using the logical operators &, |, and ~ (and, or, and not, respectively).


In [18]:
print s.loc[(s < 3) & (s > 1)]


2016-01-02    2.0
Freq: D, Name: Toy Series, dtype: float64

This is very convenient for getting only elements of a Series that fulfill specific criteria that we need. It gets even more convenient when we are handling DataFrames.

Indexing and Time Series

Since we use Series for handling time series, it's worth covering a little bit of how we handle the time component. For our purposes we use pandas Timestamp objects. Let's pull a full time series, complete with all the appropriate labels, by using our get_pricing() method. All data pulled with get_pricing() or using our Pipeline API will be in either Series or DataFrame format. We can modify this index however we like.


In [19]:
symbol = "CMG"
start = "2012-01-01"
end = "2016-01-01"
prices = get_pricing(symbol, start_date=start, end_date=end, fields="price")

We can display the first few elements of our series by using the head() method and specifying the number of elements that we want. The analogous method for the last few elements is tail().


In [20]:
print "\n", type(prices)
prices.head(5)


<class 'pandas.core.series.Series'>
Out[20]:
2012-01-03 00:00:00+00:00    340.9800
2012-01-04 00:00:00+00:00    348.7400
2012-01-05 00:00:00+00:00    349.9900
2012-01-06 00:00:00+00:00    348.9500
2012-01-09 00:00:00+00:00    339.5225
Name: Equity(28016 [CMG]), dtype: float64

As with our toy example, we can specify a name for our time series, if only to clarify the name the get_pricing() provides us.


In [21]:
print 'Old name: ', prices.name
prices.name = symbol
print 'New name: ', prices.name


Old name:  Equity(28016 [CMG])
New name:  CMG

Let's take a closer look at the DatetimeIndex of our prices time series.


In [22]:
print prices.index


DatetimeIndex(['2012-01-03', '2012-01-04', '2012-01-05', '2012-01-06',
               '2012-01-09', '2012-01-10', '2012-01-11', '2012-01-12',
               '2012-01-13', '2012-01-17',
               ...
               '2015-12-17', '2015-12-18', '2015-12-21', '2015-12-22',
               '2015-12-23', '2015-12-24', '2015-12-28', '2015-12-29',
               '2015-12-30', '2015-12-31'],
              dtype='datetime64[ns, UTC]', length=1006, freq=None)

Notice that this DatetimeIndex has a collection of associated information. In particular it has an associated frequency (freq) and an associated timezone (tz). The frequency indicates whether the data is daily vs monthly vs some other period while the timezone indicates what locale this index is relative to. We can modify all of this extra information!

If we resample our Series, we can adjust the frequency of our data. We currently have daily data (excluding weekends) because get_pricing() pulls only data from market days. Let's up-sample from this daily data to monthly data using the resample() method.


In [23]:
monthly_prices = prices.resample('M')
monthly_prices.head(10)


Out[23]:
2012-01-31 00:00:00+00:00    354.812125
2012-02-29 00:00:00+00:00    379.582000
2012-03-31 00:00:00+00:00    406.996164
2012-04-30 00:00:00+00:00    422.818505
2012-05-31 00:00:00+00:00    405.810177
2012-06-30 00:00:00+00:00    403.061905
2012-07-31 00:00:00+00:00    353.871424
2012-08-31 00:00:00+00:00    294.513478
2012-09-30 00:00:00+00:00    326.566316
2012-10-31 00:00:00+00:00    276.545329
Freq: M, Name: CMG, dtype: float64

The resample() method defaults to using the mean of the lower level data to create the higher level data. We can specify how else we might want the up-sampling to be calculated by specifying the how parameter.


In [24]:
monthly_prices_med = prices.resample('M', how='median')
monthly_prices_med.head(10)


Out[24]:
2012-01-31 00:00:00+00:00    355.380
2012-02-29 00:00:00+00:00    378.295
2012-03-31 00:00:00+00:00    408.850
2012-04-30 00:00:00+00:00    420.900
2012-05-31 00:00:00+00:00    405.390
2012-06-30 00:00:00+00:00    402.790
2012-07-31 00:00:00+00:00    380.370
2012-08-31 00:00:00+00:00    295.380
2012-09-30 00:00:00+00:00    332.990
2012-10-31 00:00:00+00:00    286.440
Freq: M, Name: CMG, dtype: float64

We can even specify how we want the calculation of the new period to be done. Here we create a custom_resampler() function that will return the first value of the period. In our specific case, this will return a Series where the monthly value is the first value of that month.


In [25]:
def custom_resampler(array_like):
    """ Returns the first value of the period """
    return array_like[0]

first_of_month_prices = prices.resample('M', how=custom_resampler)
first_of_month_prices.head(10)


Out[25]:
2012-01-31 00:00:00+00:00    340.98
2012-02-29 00:00:00+00:00    370.84
2012-03-31 00:00:00+00:00    394.58
2012-04-30 00:00:00+00:00    418.65
2012-05-31 00:00:00+00:00    419.78
2012-06-30 00:00:00+00:00    397.14
2012-07-31 00:00:00+00:00    382.97
2012-08-31 00:00:00+00:00    280.60
2012-09-30 00:00:00+00:00    285.91
2012-10-31 00:00:00+00:00    316.13
Freq: M, Name: CMG, dtype: float64

We can also adjust the timezone of a Series to adapt the time of real-world data. In our case, our time series is already localized to UTC, but let's say that we want to adjust the time to be 'US/Eastern'. In this case we use the tz_convert() method, since the time is already localized.


In [26]:
eastern_prices = prices.tz_convert('US/Eastern')
eastern_prices.head(10)


Out[26]:
2012-01-02 19:00:00-05:00    340.9800
2012-01-03 19:00:00-05:00    348.7400
2012-01-04 19:00:00-05:00    349.9900
2012-01-05 19:00:00-05:00    348.9500
2012-01-08 19:00:00-05:00    339.5225
2012-01-09 19:00:00-05:00    340.7000
2012-01-10 19:00:00-05:00    347.3300
2012-01-11 19:00:00-05:00    347.8300
2012-01-12 19:00:00-05:00    354.3900
2012-01-16 19:00:00-05:00    353.6100
Name: CMG, dtype: float64

In addition to the capacity for timezone and frequency management, each time series has a built-in reindex() method that we can use to realign the existing data according to a new set of index labels. If data does not exist for a particular label, the data will be filled with a placeholder value. This is typically np.nan, though we can provide a fill method.

The data that we get_pricing() only includes market days. But what if we want prices for every single calendar day? This will include holidays and weekends, times when you normally cannot trade equities. First let's create a new DatetimeIndex that contains all that we want.


In [27]:
calendar_dates = pd.date_range(start=start, end=end, freq='D', tz='UTC')
print calendar_dates


DatetimeIndex(['2012-01-01', '2012-01-02', '2012-01-03', '2012-01-04',
               '2012-01-05', '2012-01-06', '2012-01-07', '2012-01-08',
               '2012-01-09', '2012-01-10',
               ...
               '2015-12-23', '2015-12-24', '2015-12-25', '2015-12-26',
               '2015-12-27', '2015-12-28', '2015-12-29', '2015-12-30',
               '2015-12-31', '2016-01-01'],
              dtype='datetime64[ns, UTC]', length=1462, freq='D')

Now let's use this new set of dates to reindex our time series. We tell the function that the fill method that we want is ffill. This denotes "forward fill". Any NaN values will be filled by the last value listed. So the price on the weekend or on a holiday will be listed as the price on the last market day that we know about.


In [28]:
calendar_prices = prices.reindex(calendar_dates, method='ffill')
calendar_prices.head(15)


Out[28]:
2012-01-01 00:00:00+00:00         NaN
2012-01-02 00:00:00+00:00         NaN
2012-01-03 00:00:00+00:00    340.9800
2012-01-04 00:00:00+00:00    348.7400
2012-01-05 00:00:00+00:00    349.9900
2012-01-06 00:00:00+00:00    348.9500
2012-01-07 00:00:00+00:00    348.9500
2012-01-08 00:00:00+00:00    348.9500
2012-01-09 00:00:00+00:00    339.5225
2012-01-10 00:00:00+00:00    340.7000
2012-01-11 00:00:00+00:00    347.3300
2012-01-12 00:00:00+00:00    347.8300
2012-01-13 00:00:00+00:00    354.3900
2012-01-14 00:00:00+00:00    354.3900
2012-01-15 00:00:00+00:00    354.3900
Freq: D, Name: CMG, dtype: float64

You'll notice that we still have a couple of NaN values right at the beginning of our time series. This is because the first of January in 2012 was a Sunday and the second was a market holiday! Because these are the earliest data points and we don't have any information from before them, they cannot be forward-filled. We will take care of these NaN values in the next section, when we deal with missing data.

Missing Data

Whenever we deal with real data, there is a very real possibility of encountering missing values. Real data is riddled with holes and pandas provides us with ways to handle them. Sometimes resampling or reindexing can create NaN values. Fortunately, pandas provides us with ways to handle them. We have two primary means of coping with missing data. The first of these is filling in the missing data with fillna(). For example, say that we want to fill in the missing days with the mean price of all days.


In [29]:
meanfilled_prices = calendar_prices.fillna(calendar_prices.mean())
meanfilled_prices.head(10)


Out[29]:
2012-01-01 00:00:00+00:00    501.062621
2012-01-02 00:00:00+00:00    501.062621
2012-01-03 00:00:00+00:00    340.980000
2012-01-04 00:00:00+00:00    348.740000
2012-01-05 00:00:00+00:00    349.990000
2012-01-06 00:00:00+00:00    348.950000
2012-01-07 00:00:00+00:00    348.950000
2012-01-08 00:00:00+00:00    348.950000
2012-01-09 00:00:00+00:00    339.522500
2012-01-10 00:00:00+00:00    340.700000
Freq: D, Name: CMG, dtype: float64

Using fillna() is fairly easy. It is just a matter of indicating the value that you want to fill the spaces with. Unfortunately, this particular case doesn't make a whole lot of sense, for reasons discussed in the lecture on stationarity in the Lecture series. We could fill them with with $0$, simply, but that's similarly uninformative.

Rather than filling in specific values, we can use the method parameter, similarly to how the reindex() method works. We could use "backward fill", where NaNs are filled with the next filled value (instead of forward fill's last filled value) like so:


In [30]:
bfilled_prices = calendar_prices.fillna(method='bfill')
bfilled_prices.head(10)


Out[30]:
2012-01-01 00:00:00+00:00    340.9800
2012-01-02 00:00:00+00:00    340.9800
2012-01-03 00:00:00+00:00    340.9800
2012-01-04 00:00:00+00:00    348.7400
2012-01-05 00:00:00+00:00    349.9900
2012-01-06 00:00:00+00:00    348.9500
2012-01-07 00:00:00+00:00    348.9500
2012-01-08 00:00:00+00:00    348.9500
2012-01-09 00:00:00+00:00    339.5225
2012-01-10 00:00:00+00:00    340.7000
Freq: D, Name: CMG, dtype: float64

But again, this is a bad idea for the same reasons as the previous option. Both of these so-called solutions take into account future data that was not available at the time of the data points that we are trying to fill. In the case of using the mean or the median, these summary statistics are calculated by taking into account the entire time series. Backward filling is equivalent to saying that the price of a particular security today, right now, tomorrow's price. This also makes no sense. These two options are both examples of look-ahead bias, using data that would be unknown or unavailable at the desired time, and should be avoided.

Our next option is significantly more appealing. We could simply drop the missing data using the dropna() method. This is much better alternative than filling NaN values in with arbitrary numbers.


In [31]:
dropped_prices = calendar_prices.dropna()
dropped_prices.head(10)


Out[31]:
2012-01-03 00:00:00+00:00    340.9800
2012-01-04 00:00:00+00:00    348.7400
2012-01-05 00:00:00+00:00    349.9900
2012-01-06 00:00:00+00:00    348.9500
2012-01-07 00:00:00+00:00    348.9500
2012-01-08 00:00:00+00:00    348.9500
2012-01-09 00:00:00+00:00    339.5225
2012-01-10 00:00:00+00:00    340.7000
2012-01-11 00:00:00+00:00    347.3300
2012-01-12 00:00:00+00:00    347.8300
Freq: D, Name: CMG, dtype: float64

Now our time series is cleaned for the calendar year, with all of our NaN values properly handled. It is time to talk about how to actually do time series analysis with pandas data structures.

Time Series Analysis with pandas

Let's do some basic time series analysis on our original prices. Each pandas Series has a built-in plotting method.


In [32]:
prices.plot();
# We still need to add the axis labels and title ourselves
plt.title(symbol + " Prices")
plt.ylabel("Price")
plt.xlabel("Date");


As well as some built-in descriptive statistics. We can either calculate these individually or using the describe() method.


In [33]:
print "Mean: ", prices.mean()
print "Standard deviation: ", prices.std()


Mean:  501.64121332
Standard deviation:  146.700132549

In [34]:
print "Summary Statistics"
print prices.describe()


Summary Statistics
count    1006.000000
mean      501.641213
std       146.700133
min       236.240000
25%       371.605000
50%       521.130000
75%       646.810000
max       757.770000
Name: CMG, dtype: float64

We can easily modify Series with scalars using our basic mathematical operators.


In [35]:
modified_prices = prices * 2 - 10
modified_prices.head(5)


Out[35]:
2012-01-03 00:00:00+00:00    671.960
2012-01-04 00:00:00+00:00    687.480
2012-01-05 00:00:00+00:00    689.980
2012-01-06 00:00:00+00:00    687.900
2012-01-09 00:00:00+00:00    669.045
Name: CMG, dtype: float64

And we can create linear combinations of Series themselves using the basic mathematical operators. pandas will group up matching indices and perform the calculations elementwise to produce a new Series.


In [36]:
noisy_prices = prices + 5 * pd.Series(np.random.normal(0, 5, len(prices)), index=prices.index) + 20
noisy_prices.head(5)


Out[36]:
2012-01-03 00:00:00+00:00    371.013281
2012-01-04 00:00:00+00:00    357.417023
2012-01-05 00:00:00+00:00    344.953572
2012-01-06 00:00:00+00:00    407.123572
2012-01-09 00:00:00+00:00    305.081540
dtype: float64

If there are no matching indices, however, we may get an empty Series in return.


In [37]:
empty_series = prices + pd.Series(np.random.normal(0, 1, len(prices)))
empty_series.head(5)


Out[37]:
2012-01-03 00:00:00+00:00   NaN
2012-01-04 00:00:00+00:00   NaN
2012-01-05 00:00:00+00:00   NaN
2012-01-06 00:00:00+00:00   NaN
2012-01-09 00:00:00+00:00   NaN
dtype: float64

Rather than looking at a time series itself, we may want to look at its first-order differences or percent change (in order to get additive or multiplicative returns, in our particular case). Both of these are built-in methods.


In [38]:
add_returns = prices.diff()[1:]
mult_returns = prices.pct_change()[1:]

In [39]:
plt.title("Multiplicative returns of " + symbol)
plt.xlabel("Date")
plt.ylabel("Percent Returns")
mult_returns.plot();


pandas has convenient functions for calculating rolling means and standard deviations, as well!


In [40]:
rolling_mean = pd.rolling_mean(prices, 30)
rolling_mean.name = "30-day rolling mean"

In [41]:
prices.plot()
rolling_mean.plot()
plt.title(symbol + "Price")
plt.xlabel("Date")
plt.ylabel("Price")
plt.legend();



In [42]:
rolling_std = pd.rolling_std(prices, 30)
rolling_std.name = "30-day rolling volatility"

In [43]:
rolling_std.plot()
plt.title(rolling_std.name);
plt.xlabel("Date")
plt.ylabel("Standard Deviation");


Many NumPy functions will work on Series the same way that they work on 1-dimensional NumPy arrays.


In [44]:
print np.median(mult_returns)


0.000194158599839

The majority of these functions, however, are already implemented directly as Series and DataFrame methods.


In [45]:
print mult_returns.median()


0.000194158599839

In every case, using the built-in pandas method will be better than using the NumPy function on a pandas data structure due to improvements in performance. Make sure to check out the Series documentation before resorting to other calculations of common functions.

DataFrames

Many of the aspects of working with Series carry over into DataFrames. pandas DataFrames allow us to easily manage our data with their intuitive structure.

Like Series, DataFrames can hold multiple types of data, but DataFrames are 2-dimensional objects, unlike Series. Each DataFrame has an index and a columns attribute, which we will cover more in-depth when we start actually playing with an object. The index attribute is like the index of a Series, though indices in pandas have some extra features that we will unfortunately not be able to cover here. If you are interested in this, check out the pandas documentation on advanced indexing. The columns attribute is what provides the second dimension of our DataFrames, allowing us to combine named columns (all Series), into a cohesive object with the index lined-up.

We can create a DataFrame by calling pandas.DataFrame() on a dictionary or NumPy ndarray. We can also concatenate a group of pandas Series into a DataFrame using pandas.concat().


In [46]:
dict_data = {
    'a' : [1, 2, 3, 4, 5],
    'b' : ['L', 'K', 'J', 'M', 'Z'],
    'c' : np.random.normal(0, 1, 5)
}
print dict_data


{'a': [1, 2, 3, 4, 5], 'c': array([ 0.23752859, -0.49607459, -0.81027968, -0.28216034,  0.89001851]), 'b': ['L', 'K', 'J', 'M', 'Z']}

Each DataFrame has a few key attributes that we need to keep in mind. The first of these is the index attribute. We can easily include an index of Timestamp objects like we did with Series.


In [47]:
frame_data = pd.DataFrame(dict_data, index=pd.date_range('2016-01-01', periods=5))
print frame_data


            a  b         c
2016-01-01  1  L  0.237529
2016-01-02  2  K -0.496075
2016-01-03  3  J -0.810280
2016-01-04  4  M -0.282160
2016-01-05  5  Z  0.890019

As mentioned above, we can combine Series into DataFrames. Concatatenating Series like this will match elements up based on their corresponding index. As the following Series do not have an index assigned, they each default to an integer index.


In [48]:
s_1 = pd.Series([2, 4, 6, 8, 10], name='Evens')
s_2 = pd.Series([1, 3, 5, 7, 9], name="Odds")
numbers = pd.concat([s_1, s_2], axis=1)
print numbers


   Evens  Odds
0      2     1
1      4     3
2      6     5
3      8     7
4     10     9

We will use pandas.concat() again later to combine multiple DataFrames into one.

Each DataFrame also has a columns attribute. These can either be assigned when we call pandas.DataFrame or they can be modified directly like the index. Note that when we concatenated the two Series above, the column names were the names of those Series.


In [49]:
print numbers.columns


Index([u'Evens', u'Odds'], dtype='object')

To modify the columns after object creation, we need only do the following:


In [50]:
numbers.columns = ['Shmevens', 'Shmodds']
print numbers


   Shmevens  Shmodds
0         2        1
1         4        3
2         6        5
3         8        7
4        10        9

In the same vein, the index of a DataFrame can be changed after the fact.


In [51]:
print numbers.index


RangeIndex(start=0, stop=5, step=1)

In [52]:
numbers.index = pd.date_range("2016-01-01", periods=len(numbers))
print numbers


            Shmevens  Shmodds
2016-01-01         2        1
2016-01-02         4        3
2016-01-03         6        5
2016-01-04         8        7
2016-01-05        10        9

Separate from the columns and index of a DataFrame, we can also directly access the values they contain by looking at the values attribute.


In [53]:
numbers.values


Out[53]:
array([[ 2,  1],
       [ 4,  3],
       [ 6,  5],
       [ 8,  7],
       [10,  9]])

This returns a NumPy array.


In [54]:
type(numbers.values)


Out[54]:
<type 'numpy.ndarray'>

Accessing DataFrame elements

Again we see a lot of carryover from Series in how we access the elements of DataFrames. The key sticking point here is that everything has to take into account multiple dimensions now. The main way that this happens is through the access of the columns of a DataFrame, either individually or in groups. We can do this either by directly accessing the attributes or by using the methods we already are familiar with.


In [55]:
symbol = ["CMG", "MCD", "SHAK", "WFM"]
start = "2012-01-01"
end = "2016-01-01"
prices = get_pricing(symbol, start_date=start, end_date=end, fields="price")
if isinstance(symbol, list):
    prices.columns = map(lambda x: x.symbol, prices.columns)
else:
    prices.name = symbol

Here we directly access the CMG column. Note that this style of access will only work if your column name has no spaces or unfriendly characters in it.


In [56]:
prices.CMG.head()


Out[56]:
2012-01-03 00:00:00+00:00    340.9800
2012-01-04 00:00:00+00:00    348.7400
2012-01-05 00:00:00+00:00    349.9900
2012-01-06 00:00:00+00:00    348.9500
2012-01-09 00:00:00+00:00    339.5225
Name: CMG, dtype: float64

We can also use loc[] to access an individual column like so.


In [57]:
prices.loc[:, 'CMG'].head()


Out[57]:
2012-01-03 00:00:00+00:00    340.9800
2012-01-04 00:00:00+00:00    348.7400
2012-01-05 00:00:00+00:00    349.9900
2012-01-06 00:00:00+00:00    348.9500
2012-01-09 00:00:00+00:00    339.5225
Name: CMG, dtype: float64

Accessing an individual column will return a Series, regardless of how we get it.


In [58]:
print type(prices.CMG)
print type(prices.loc[:, 'CMG'])


<class 'pandas.core.series.Series'>
<class 'pandas.core.series.Series'>

Notice how we pass a tuple into the loc[] method? This is a key difference between accessing a Series and accessing a DataFrame, grounded in the fact that a DataFrame has multiple dimensions. When you pass a 2-dimensional tuple into a DataFrame, the first element of the tuple is applied to the rows and the second is applied to the columns. So, to break it down, the above line of code tells the DataFrame to return every single row of the column with label 'CMG'. Lists of columns are also supported.


In [59]:
prices.loc[:, ['CMG', 'MCD']].head()


Out[59]:
CMG MCD
2012-01-03 00:00:00+00:00 340.9800 98.81
2012-01-04 00:00:00+00:00 348.7400 99.42
2012-01-05 00:00:00+00:00 349.9900 99.83
2012-01-06 00:00:00+00:00 348.9500 100.59
2012-01-09 00:00:00+00:00 339.5225 99.62

We can also simply access the DataFrame by index value using loc[], as with Series.


In [60]:
prices.loc['2015-12-15':'2015-12-22']


Out[60]:
CMG MCD SHAK WFM
2015-12-15 00:00:00+00:00 555.6401 116.96 41.5101 32.96
2015-12-16 00:00:00+00:00 568.4200 117.84 40.1400 33.66
2015-12-17 00:00:00+00:00 554.9399 117.56 38.5300 33.38
2015-12-18 00:00:00+00:00 540.7500 116.58 39.3800 32.72
2015-12-21 00:00:00+00:00 521.2300 117.71 38.2050 32.98
2015-12-22 00:00:00+00:00 495.2001 117.71 39.7600 34.78

This plays nicely with lists of columns, too.


In [61]:
prices.loc['2015-12-15':'2015-12-22', ['CMG', 'MCD']]


Out[61]:
CMG MCD
2015-12-15 00:00:00+00:00 555.6401 116.96
2015-12-16 00:00:00+00:00 568.4200 117.84
2015-12-17 00:00:00+00:00 554.9399 117.56
2015-12-18 00:00:00+00:00 540.7500 116.58
2015-12-21 00:00:00+00:00 521.2300 117.71
2015-12-22 00:00:00+00:00 495.2001 117.71

Using iloc[] also works similarly, allowing you to access parts of the DataFrame by integer index.


In [62]:
prices.iloc[0:2, 1]


Out[62]:
2012-01-03 00:00:00+00:00    98.81
2012-01-04 00:00:00+00:00    99.42
Name: MCD, dtype: float64

In [63]:
# Access prices with integer index in
# [1, 3, 5, 7, 9, 11, 13, ..., 99]
# and in column 0 or 3
prices.iloc[[1, 3, 5] + range(7, 100, 2), [0, 3]].head(20)


Out[63]:
CMG WFM
2012-01-04 00:00:00+00:00 348.74 35.725
2012-01-06 00:00:00+00:00 348.95 36.435
2012-01-10 00:00:00+00:00 340.70 36.335
2012-01-12 00:00:00+00:00 347.83 35.935
2012-01-17 00:00:00+00:00 353.61 38.390
2012-01-19 00:00:00+00:00 358.10 38.665
2012-01-23 00:00:00+00:00 360.53 38.060
2012-01-25 00:00:00+00:00 363.28 38.575
2012-01-27 00:00:00+00:00 366.80 37.445
2012-01-31 00:00:00+00:00 367.58 37.015
2012-02-02 00:00:00+00:00 362.64 37.800
2012-02-06 00:00:00+00:00 371.65 38.205
2012-02-08 00:00:00+00:00 373.81 38.960
2012-02-10 00:00:00+00:00 376.39 40.805
2012-02-14 00:00:00+00:00 379.14 40.495
2012-02-16 00:00:00+00:00 381.91 40.300
2012-02-21 00:00:00+00:00 383.86 40.285
2012-02-23 00:00:00+00:00 386.82 40.520
2012-02-27 00:00:00+00:00 389.11 40.825
2012-02-29 00:00:00+00:00 390.47 40.370

Boolean indexing

As with Series, sometimes we want to filter a DataFrame according to a set of criteria. We do this by indexing our DataFrame with boolean values.


In [64]:
prices.loc[prices.MCD > prices.WFM].head()


Out[64]:
CMG MCD SHAK WFM
2012-01-03 00:00:00+00:00 340.9800 98.81 NaN 34.810
2012-01-04 00:00:00+00:00 348.7400 99.42 NaN 35.725
2012-01-05 00:00:00+00:00 349.9900 99.83 NaN 36.370
2012-01-06 00:00:00+00:00 348.9500 100.59 NaN 36.435
2012-01-09 00:00:00+00:00 339.5225 99.62 NaN 36.440

We can add multiple boolean conditions by using the logical operators &, |, and ~ (and, or, and not, respectively) again!


In [65]:
prices.loc[(prices.MCD > prices.WFM) & ~prices.SHAK.isnull()].head()


Out[65]:
CMG MCD SHAK WFM
2015-01-30 00:00:00+00:00 709.58 92.42 45.80 52.10
2015-02-02 00:00:00+00:00 712.55 92.49 43.50 53.15
2015-02-03 00:00:00+00:00 726.07 93.92 44.87 53.41
2015-02-04 00:00:00+00:00 676.00 94.02 41.32 53.67
2015-02-05 00:00:00+00:00 670.62 94.32 42.46 53.38

Adding, Removing Columns, Combining DataFrames/Series

It is all well and good when you already have a DataFrame filled with data, but it is also important to be able to add to the data that you have.

We add a new column simply by assigning data to a column that does not already exist. Here we use the .loc[:, 'COL_NAME'] notation and store the output of get_pricing() (which returns a pandas Series if we only pass one security) there. This is the method that we would use to add a Series to an existing DataFrame.


In [66]:
s_1 = get_pricing('TSLA', start_date=start, end_date=end, fields='price')
prices.loc[:, 'TSLA'] = s_1
prices.head(5)


Out[66]:
CMG MCD SHAK WFM TSLA
2012-01-03 00:00:00+00:00 340.9800 98.81 NaN 34.810 28.06
2012-01-04 00:00:00+00:00 348.7400 99.42 NaN 35.725 27.71
2012-01-05 00:00:00+00:00 349.9900 99.83 NaN 36.370 27.12
2012-01-06 00:00:00+00:00 348.9500 100.59 NaN 36.435 26.94
2012-01-09 00:00:00+00:00 339.5225 99.62 NaN 36.440 27.21

It is also just as easy to remove a column.


In [67]:
prices = prices.drop('TSLA', axis=1)
prices.head(5)


Out[67]:
CMG MCD SHAK WFM
2012-01-03 00:00:00+00:00 340.9800 98.81 NaN 34.810
2012-01-04 00:00:00+00:00 348.7400 99.42 NaN 35.725
2012-01-05 00:00:00+00:00 349.9900 99.83 NaN 36.370
2012-01-06 00:00:00+00:00 348.9500 100.59 NaN 36.435
2012-01-09 00:00:00+00:00 339.5225 99.62 NaN 36.440

If we instead want to combine multiple DataFrames into one, we use the pandas.concat() method.


In [68]:
df_1 = get_pricing(['SPY', 'VXX'], start_date=start, end_date=end, fields='price')
df_2 = get_pricing(['MSFT', 'AAPL', 'GOOG'], start_date=start, end_date=end, fields='price')
df_3 = pd.concat([df_1, df_2], axis=1)
df_3.head()


Out[68]:
Equity(8554 [SPY]) Equity(38054 [VXX]) Equity(5061 [MSFT]) Equity(24 [AAPL]) Equity(46631 [GOOG])
2012-01-03 00:00:00+00:00 127.59 2154.88 26.83 58.730 NaN
2012-01-04 00:00:00+00:00 127.68 2111.36 27.39 59.064 NaN
2012-01-05 00:00:00+00:00 128.06 2065.28 27.67 59.710 NaN
2012-01-06 00:00:00+00:00 127.79 2032.00 28.12 60.351 NaN
2012-01-09 00:00:00+00:00 128.00 2002.56 27.74 60.248 NaN

Missing data (again)

Bringing real-life data into a DataFrame brings us the same problems that we had with it in a Series, only this time in more dimensions. We have access to the same methods as with Series, as demonstrated below.


In [69]:
filled0_prices = prices.fillna(0)
filled0_prices.head(5)


Out[69]:
CMG MCD SHAK WFM
2012-01-03 00:00:00+00:00 340.9800 98.81 0.0 34.810
2012-01-04 00:00:00+00:00 348.7400 99.42 0.0 35.725
2012-01-05 00:00:00+00:00 349.9900 99.83 0.0 36.370
2012-01-06 00:00:00+00:00 348.9500 100.59 0.0 36.435
2012-01-09 00:00:00+00:00 339.5225 99.62 0.0 36.440

In [70]:
bfilled_prices = prices.fillna(method='bfill')
bfilled_prices.head(5)


Out[70]:
CMG MCD SHAK WFM
2012-01-03 00:00:00+00:00 340.9800 98.81 45.8 34.810
2012-01-04 00:00:00+00:00 348.7400 99.42 45.8 35.725
2012-01-05 00:00:00+00:00 349.9900 99.83 45.8 36.370
2012-01-06 00:00:00+00:00 348.9500 100.59 45.8 36.435
2012-01-09 00:00:00+00:00 339.5225 99.62 45.8 36.440

But again, the best choice in this case (since we are still using time series data, handling multiple time series at once) is still to simply drop the missing values.


In [71]:
dropped_prices = prices.dropna()
dropped_prices.head(5)


Out[71]:
CMG MCD SHAK WFM
2015-01-30 00:00:00+00:00 709.58 92.42 45.80 52.10
2015-02-02 00:00:00+00:00 712.55 92.49 43.50 53.15
2015-02-03 00:00:00+00:00 726.07 93.92 44.87 53.41
2015-02-04 00:00:00+00:00 676.00 94.02 41.32 53.67
2015-02-05 00:00:00+00:00 670.62 94.32 42.46 53.38

Time Series Analysis with pandas

Using the built-in statistics methods for DataFrames, we can perform calculations on multiple time series at once! The code to perform calculations on DataFrames here is almost exactly the same as the methods used for Series above, so don't worry about re-learning everything.

The plot() method makes another appearance here, this time with a built-in legend that corresponds to the names of the columns that you are plotting.


In [72]:
prices.plot()
plt.title("Collected Stock Prices")
plt.ylabel("Price")
plt.xlabel("Date");


The same statistical functions from our interactions with Series resurface here with the addition of the axis parameter. By specifying the axis, we tell pandas to calculate the desired function along either the rows (axis=0) or the columns (axis=1). We can easily calculate the mean of each columns like so:


In [73]:
prices.mean(axis=0)


Out[73]:
CMG     501.641213
MCD      96.621592
SHAK     53.532675
WFM      45.592710
dtype: float64

As well as the standard deviation:


In [74]:
prices.std(axis=0)


Out[74]:
CMG     146.700133
MCD       5.715712
SHAK     11.951954
WFM       7.772486
dtype: float64

Again, the describe() function will provide us with summary statistics of our data if we would rather have all of our typical statistics in a convenient visual instead of calculating them individually.


In [75]:
prices.describe()


/usr/local/lib/python2.7/dist-packages/numpy/lib/function_base.py:3834: RuntimeWarning: Invalid value encountered in percentile
  RuntimeWarning)
Out[75]:
CMG MCD SHAK WFM
count 1006.000000 1006.000000 233.000000 1006.000000
mean 501.641213 96.621592 53.532675 45.592710
std 146.700133 5.715712 11.951954 7.772486
min 236.240000 84.060000 38.205000 29.150000
25% 371.605000 93.675000 NaN 39.792500
50% 521.130000 96.304950 NaN 45.800000
75% 646.810000 99.135000 NaN 51.727500
max 757.770000 120.010000 92.470000 65.235000

We can scale and add scalars to our DataFrame, as you might suspect after dealing with Series. This again works element-wise.


In [76]:
(2 * prices - 50).head(5)


Out[76]:
CMG MCD SHAK WFM
2012-01-03 00:00:00+00:00 631.960 147.62 NaN 19.62
2012-01-04 00:00:00+00:00 647.480 148.84 NaN 21.45
2012-01-05 00:00:00+00:00 649.980 149.66 NaN 22.74
2012-01-06 00:00:00+00:00 647.900 151.18 NaN 22.87
2012-01-09 00:00:00+00:00 629.045 149.24 NaN 22.88

Here we use the pct_change() method to get a DataFrame of the multiplicative returns of the securities that we are looking at.


In [77]:
mult_returns = prices.pct_change()[1:]
mult_returns.head()


Out[77]:
CMG MCD SHAK WFM
2012-01-04 00:00:00+00:00 0.022758 0.006173 NaN 0.026286
2012-01-05 00:00:00+00:00 0.003584 0.004124 NaN 0.018055
2012-01-06 00:00:00+00:00 -0.002972 0.007613 NaN 0.001787
2012-01-09 00:00:00+00:00 -0.027017 -0.009643 NaN 0.000137
2012-01-10 00:00:00+00:00 0.003468 0.000402 NaN -0.002881

If we use our statistics methods to standardize the returns, a common procedure when examining data, then we can get a better idea of how they all move relative to each other on the same scale.


In [78]:
norm_returns = (mult_returns - mult_returns.mean(axis=0))/mult_returns.std(axis=0)
norm_returns.loc['2014-01-01':'2015-01-01'].plot();


This makes it easier to compare the motion of the different time series contained in our example.

Rolling means and standard deviations also work with DataFrames.


In [79]:
rolling_mean = pd.rolling_mean(prices, 30)
rolling_mean.columns = prices.columns

In [80]:
rolling_mean.plot()
plt.title("Rolling Mean of Prices")
plt.xlabel("Date")
plt.ylabel("Price")
plt.legend();


For a complete list of all the methods that are built into DataFrames, check out the documentation.

Next Steps

Managing data gets a lot easier when you deal with pandas, though this has been a very general introduction. There are many more tools within the package which you may discover while trying to get your data to do precisely what you want. If you would rather read more on the additional capabilities of pandas, check out the documentation.

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