.. currentmodule:: pandas
.. _timeseries:

.. ipython:: python
   :suppress:

   from datetime import datetime
   import numpy as np
   np.random.seed(123456)
   from pandas import *
   randn = np.random.randn
   randint = np.random.randint
   np.set_printoptions(precision=4, suppress=True)
   from dateutil.relativedelta import relativedelta
   from pandas.tseries.api import *
   from pandas.tseries.offsets import *

********************************
Time Series / Date functionality
********************************

pandas has proven very successful as a tool for working with time series data,
especially in the financial data analysis space. With the 0.8 release, we have
further improved the time series API in pandas by leaps and bounds. Using the
new NumPy ``datetime64`` dtype, we have consolidated a large number of features
from other Python libraries like ``scikits.timeseries`` as well as created
a tremendous amount of new functionality for manipulating time series data.

In working with time series data, we will frequently seek to:

  - generate sequences of fixed-frequency dates and time spans
  - conform or convert time series to a particular frequency
  - compute "relative" dates based on various non-standard time increments
    (e.g. 5 business days before the last business day of the year), or "roll"
    dates forward or backward

pandas provides a relatively compact and self-contained set of tools for
performing the above tasks.

Create a range of dates:

.. ipython:: python

   # 72 hours starting with midnight Jan 1st, 2011
   rng = date_range('1/1/2011', periods=72, freq='H')
   rng[:5]

Index pandas objects with dates:

.. ipython:: python

   ts = Series(randn(len(rng)), index=rng)
   ts.head()

Change frequency and fill gaps:

.. ipython:: python

   # to 45 minute frequency and forward fill
   converted = ts.asfreq('45Min', method='pad')
   converted.head()

Resample:

.. ipython:: python

   # Daily means
   ts.resample('D', how='mean')


.. _timeseries.representation:

Time Stamps vs. Time Spans
--------------------------

Time-stamped data is the most basic type of timeseries data that associates
values with points in time. For pandas objects it means using the points in
time to create the index

.. ipython:: python

   dates = [datetime(2012, 5, 1), datetime(2012, 5, 2), datetime(2012, 5, 3)]
   ts = Series(np.random.randn(3), dates)

   type(ts.index)

   ts

However, in many cases it is more natural to associate things like change
variables with a time span instead.

For example:

.. ipython:: python

   periods = PeriodIndex([Period('2012-01'), Period('2012-02'),
                          Period('2012-03')])

   ts = Series(np.random.randn(3), periods)

   type(ts.index)

   ts

Starting with 0.8, pandas allows you to capture both representations and
convert between them. Under the hood, pandas represents timestamps using
instances of ``Timestamp`` and sequences of timestamps using instances of
``DatetimeIndex``. For regular time spans, pandas uses ``Period`` objects for
scalar values and ``PeriodIndex`` for sequences of spans. Better support for
irregular intervals with arbitrary start and end points are forth-coming in
future releases.

.. _timeseries.daterange:

Generating Ranges of Timestamps
-------------------------------

To generate an index with time stamps, you can use either the DatetimeIndex or
Index constructor and pass in a list of datetime objects:

.. ipython:: python

   dates = [datetime(2012, 5, 1), datetime(2012, 5, 2), datetime(2012, 5, 3)]
   index = DatetimeIndex(dates)
   index # Note the frequency information

   index = Index(dates)
   index # Automatically converted to DatetimeIndex

Practically, this becomes very cumbersome because we often need a very long
index with a large number of timestamps. If we need timestamps on a regular
frequency, we can use the pandas functions ``date_range`` and ``bdate_range``
to create timestamp indexes.

.. ipython:: python

   index = date_range('2000-1-1', periods=1000, freq='M')
   index

   index = bdate_range('2012-1-1', periods=250)
   index

Convenience functions like ``date_range`` and ``bdate_range`` utilizes a
variety of frequency aliases. The default frequency for ``date_range`` is a
**calendar day** while the default for ``bdate_range`` is a **business day**

.. ipython:: python

   start = datetime(2011, 1, 1)
   end = datetime(2012, 1, 1)

   rng = date_range(start, end)
   rng

   rng = bdate_range(start, end)
   rng

``date_range`` and ``bdate_range`` makes it easy to generate a range of dates
using various combinations of its parameters like ``start``, ``end``,
``periods``, and ``freq``:

.. ipython:: python

   date_range(start, end, freq='BM')

   date_range(start, end, freq='W')

   bdate_range(end=end, periods=20)

   bdate_range(start=start, periods=20)

The start and end dates are strictly inclusive. So it will not generate any
dates outside of those dates if specified.

.. _timeseries.datetimeindex:

DatetimeIndex
~~~~~~~~~~~~~

One of the main uses for ``DatetimeIndex`` is as an index for pandas objects.
The ``DatetimeIndex`` class contains many timeseries related optimizations:

  - A large range of dates for various offsets are pre-computed and cached
    under the hood in order to make generating subsequent date ranges very fast
    (just have to grab a slice)
  - Fast shifting using the ``shift`` and ``tshift`` method on pandas objects
  - Unioning of overlapping DatetimeIndex objects with the same frequency is
    very fast (important for fast data alignment)
  - Quick access to date fields via properties such as ``year``, ``month``, etc.
  - Regularization functions like ``snap`` and very fast ``asof`` logic

``DatetimeIndex`` can be used like a regular index and offers all of its
intelligent functionality like selection, slicing, etc.

.. ipython:: python

   rng = date_range(start, end, freq='BM')
   ts = Series(randn(len(rng)), index=rng)
   ts.index
   ts[:5].index
   ts[::2].index

You can pass in dates and strings that parses to dates as indexing parameters:

.. ipython:: python

   ts['1/31/2011']

   ts[datetime(2011, 12, 25):]

   ts['10/31/2011':'12/31/2011']

A ``truncate`` convenience function is provided that is equivalent to slicing:

.. ipython:: python

   ts.truncate(before='10/31/2011', after='12/31/2011')

To provide convenience for accessing longer time series, you can also pass in
the year or year and month as strings:

.. ipython:: python

   ts['2011']

   ts['2011-6']

Even complicated fancy indexing that breaks the DatetimeIndex's frequency
regularity will result in a ``DatetimeIndex`` (but frequency is lost):

.. ipython:: python

   ts[[0, 2, 6]].index

DatetimeIndex objects has all the basic functionality of regular Index objects
and a smorgasbord of advanced timeseries-specific methods for easy frequency
processing.

.. seealso::
    :ref:`Reindexing methods <basics.reindexing>`

.. note::

    While pandas does not force you to have a sorted date index, some of these
    methods may have unexpected or incorrect behavior if the dates are
    unsorted. So please be careful.


.. _timeseries.offsets:

DateOffset objects
------------------

In the preceding examples, we created DatetimeIndex objects at various
frequencies by passing in frequency strings like 'M', 'W', and 'BM to the
``freq`` keyword. Under the hood, these frequency strings are being translated
into an instance of pandas ``DateOffset``, which represents a regular
frequency increment. Specific offset logic like "month", "business day", or
"one hour" is represented in its various subclasses.

.. csv-table::
    :header: "Class name", "Description"
    :widths: 15, 65

    DateOffset, "Generic offset class, defaults to 1 calendar day"
    BDay, "business day (weekday)"
    Week, "one week, optionally anchored on a day of the week"
    WeekOfMonth, "the x-th day of the y-th week of each month"
    MonthEnd, "calendar month end"
    MonthBegin, "calendar month begin"
    BMonthEnd, "business month end"
    BMonthBegin, "business month begin"
    QuarterEnd, "calendar quarter end"
    QuarterBegin, "calendar quarter begin"
    BQuarterEnd, "business quarter end"
    BQuarterBegin, "business quarter begin"
    YearEnd, "calendar year end"
    YearBegin, "calendar year begin"
    BYearEnd, "business year end"
    BYearBegin, "business year begin"
    Hour, "one hour"
    Minute, "one minute"
    Second, "one second"
    Milli, "one millisecond"
    Micro, "one microsecond"


The basic ``DateOffset`` takes the same arguments as
``dateutil.relativedelta``, which works like:

.. ipython:: python

   d = datetime(2008, 8, 18)
   d + relativedelta(months=4, days=5)

We could have done the same thing with ``DateOffset``:

.. ipython:: python

   from pandas.tseries.offsets import *
   d + DateOffset(months=4, days=5)

The key features of a ``DateOffset`` object are:

  - it can be added / subtracted to/from a datetime object to obtain a
    shifted date
  - it can be multiplied by an integer (positive or negative) so that the
    increment will be applied multiple times
  - it has ``rollforward`` and ``rollback`` methods for moving a date forward
    or backward to the next or previous "offset date"

Subclasses of ``DateOffset`` define the ``apply`` function which dictates
custom date increment logic, such as adding business days:

.. code-block:: python

    class BDay(DateOffset):
	"""DateOffset increments between business days"""
        def apply(self, other):
            ...

.. ipython:: python

   d - 5 * BDay()
   d + BMonthEnd()

The ``rollforward`` and ``rollback`` methods do exactly what you would expect:

.. ipython:: python

   d
   offset = BMonthEnd()
   offset.rollforward(d)
   offset.rollback(d)

It's definitely worth exploring the ``pandas.tseries.offsets`` module and the
various docstrings for the classes.

Parametric offsets
~~~~~~~~~~~~~~~~~~

Some of the offsets can be "parameterized" when created to result in different
behavior. For example, the ``Week`` offset for generating weekly data accepts a
``weekday`` parameter which results in the generated dates always lying on a
particular day of the week:

.. ipython:: python

   d + Week()
   d + Week(weekday=4)
   (d + Week(weekday=4)).weekday()

Another example is parameterizing ``YearEnd`` with the specific ending month:

.. ipython:: python

   d + YearEnd()
   d + YearEnd(month=6)

.. _timeseries.alias:

Offset Aliases
~~~~~~~~~~~~~~

A number of string aliases are given to useful common time series
frequencies. We will refer to these aliases as *offset aliases*
(referred to as *time rules* prior to v0.8.0).

.. csv-table::
    :header: "Alias", "Description"
    :widths: 15, 100

    "B", "business day frequency"
    "D", "calendar day frequency"
    "W", "weekly frequency"
    "M", "month end frequency"
    "BM", "business month end frequency"
    "MS", "month start frequency"
    "BMS", "business month start frequency"
    "Q", "quarter end frequency"
    "BQ", "business quarter endfrequency"
    "QS", "quarter start frequency"
    "BQS", "business quarter start frequency"
    "A", "year end frequency"
    "BA", "business year end frequency"
    "AS", "year start frequency"
    "BAS", "business year start frequency"
    "H", "hourly frequency"
    "T", "minutely frequency"
    "S", "secondly frequency"
    "L", "milliseonds"
    "U", "microseconds"

Combining Aliases
~~~~~~~~~~~~~~~~~

As we have seen previously, the alias and the offset instance are fungible in
most functions:

.. ipython:: python

   date_range(start, periods=5, freq='B')

   date_range(start, periods=5, freq=BDay())

You can combine together day and intraday offsets:

.. ipython:: python

   date_range(start, periods=10, freq='2h20min')

   date_range(start, periods=10, freq='1D10U')

Anchored Offsets
~~~~~~~~~~~~~~~~

For some frequencies you can specify an anchoring suffix:

.. csv-table::
    :header: "Alias", "Description"
    :widths: 15, 100

    "W\-SUN", "weekly frequency (sundays). Same as 'W'"
    "W\-MON", "weekly frequency (mondays)"
    "W\-TUE", "weekly frequency (tuesdays)"
    "W\-WED", "weekly frequency (wednesdays)"
    "W\-THU", "weekly frequency (thursdays)"
    "W\-FRI", "weekly frequency (fridays)"
    "W\-SAT", "weekly frequency (saturdays)"
    "(B)Q(S)\-DEC", "quarterly frequency, year ends in December. Same as 'Q'"
    "(B)Q(S)\-JAN", "quarterly frequency, year ends in January"
    "(B)Q(S)\-FEB", "quarterly frequency, year ends in February"
    "(B)Q(S)\-MAR", "quarterly frequency, year ends in March"
    "(B)Q(S)\-APR", "quarterly frequency, year ends in April"
    "(B)Q(S)\-MAY", "quarterly frequency, year ends in May"
    "(B)Q(S)\-JUN", "quarterly frequency, year ends in June"
    "(B)Q(S)\-JUL", "quarterly frequency, year ends in July"
    "(B)Q(S)\-AUG", "quarterly frequency, year ends in August"
    "(B)Q(S)\-SEP", "quarterly frequency, year ends in September"
    "(B)Q(S)\-OCT", "quarterly frequency, year ends in October"
    "(B)Q(S)\-NOV", "quarterly frequency, year ends in November"
    "(B)A(S)\-DEC", "annual frequency, anchored end of December. Same as 'A'"
    "(B)A(S)\-JAN", "annual frequency, anchored end of January"
    "(B)A(S)\-FEB", "annual frequency, anchored end of February"
    "(B)A(S)\-MAR", "annual frequency, anchored end of March"
    "(B)A(S)\-APR", "annual frequency, anchored end of April"
    "(B)A(S)\-MAY", "annual frequency, anchored end of May"
    "(B)A(S)\-JUN", "annual frequency, anchored end of June"
    "(B)A(S)\-JUL", "annual frequency, anchored end of July"
    "(B)A(S)\-AUG", "annual frequency, anchored end of August"
    "(B)A(S)\-SEP", "annual frequency, anchored end of September"
    "(B)A(S)\-OCT", "annual frequency, anchored end of October"
    "(B)A(S)\-NOV", "annual frequency, anchored end of November"

These can be used as arguments to ``date_range``, ``bdate_range``, constructors
for ``DatetimeIndex``, as well as various other timeseries-related functions
in pandas.

Legacy Aliases
~~~~~~~~~~~~~~
Note that prior to v0.8.0, time rules had a slightly different look. Pandas
will continue to support the legacy time rules for the time being but it is
strongly recommended that you switch to using the new offset aliases.

.. csv-table::
    :header: "Legacy Time Rule", "Offset Alias"
    :widths: 15, 65

    "WEEKDAY", "B"
    "EOM", "BM"
    "W\@MON", "W\-MON"
    "W\@TUE", "W\-TUE"
    "W\@WED", "W\-WED"
    "W\@THU", "W\-THU"
    "W\@FRI", "W\-FRI"
    "W\@SAT", "W\-SAT"
    "W\@SUN", "W\-SUN"
    "Q\@JAN", "BQ\-JAN"
    "Q\@FEB", "BQ\-FEB"
    "Q\@MAR", "BQ\-MAR"
    "A\@JAN", "BA\-JAN"
    "A\@FEB", "BA\-FEB"
    "A\@MAR", "BA\-MAR"
    "A\@APR", "BA\-APR"
    "A\@MAY", "BA\-MAY"
    "A\@JUN", "BA\-JUN"
    "A\@JUL", "BA\-JUL"
    "A\@AUG", "BA\-AUG"
    "A\@SEP", "BA\-SEP"
    "A\@OCT", "BA\-OCT"
    "A\@NOV", "BA\-NOV"
    "A\@DEC", "BA\-DEC"
    "min", "T"
    "ms", "L"
    "us": "U"

As you can see, legacy quarterly and annual frequencies are business quarter
and business year ends. Please also note the legacy time rule for milliseconds
``ms`` versus the new offset alias for month start ``MS``. This means that
offset alias parsing is case sensitive.

.. _timeseries.advanced_datetime:

Time series-related instance methods
------------------------------------

Shifting / lagging
~~~~~~~~~~~~~~~~~~

One may want to *shift* or *lag* the values in a TimeSeries back and forward in
time. The method for this is ``shift``, which is available on all of the pandas
objects. In DataFrame, ``shift`` will currently only shift along the ``index``
and in Panel along the ``major_axis``.

.. ipython:: python

   ts = ts[:5]
   ts.shift(1)

The shift method accepts an ``freq`` argument which can accept a
``DateOffset`` class or other ``timedelta``-like object or also a :ref:`offset alias <timeseries.alias>`:

.. ipython:: python

   ts.shift(5, freq=datetools.bday)
   ts.shift(5, freq='BM')

Rather than changing the alignment of the data and the index, ``DataFrame`` and
``TimeSeries`` objects also have a ``tshift`` convenience method that changes
all the dates in the index by a specified number of offsets:

.. ipython:: python

   ts.tshift(5, freq='D')

Note that with ``tshift``, the leading entry is no longer NaN because the data
is not being realigned.

Frequency conversion
~~~~~~~~~~~~~~~~~~~~

The primary function for changing frequencies is the ``asfreq`` function.
For a ``DatetimeIndex``, this is basically just a thin, but convenient wrapper
around ``reindex`` which generates a ``date_range`` and calls ``reindex``.

.. ipython:: python

   dr = date_range('1/1/2010', periods=3, freq=3 * datetools.bday)
   ts = Series(randn(3), index=dr)
   ts
   ts.asfreq(BDay())

``asfreq`` provides a further convenience so you can specify an interpolation
method for any gaps that may appear after the frequency conversion

.. ipython:: python

   ts.asfreq(BDay(), method='pad')

Filling forward / backward
~~~~~~~~~~~~~~~~~~~~~~~~~~

Related to ``asfreq`` and ``reindex`` is the ``fillna`` function documented in
the :ref:`missing data section <missing_data.fillna>`.

.. _timeseries.resampling:

Up- and downsampling
--------------------

With 0.8, pandas introduces simple, powerful, and efficient functionality for
performing resampling operations during frequency conversion (e.g., converting
secondly data into 5-minutely data). This is extremely common in, but not
limited to, financial applications.

.. ipython:: python

   rng = date_range('1/1/2012', periods=100, freq='S')

   ts = Series(randint(0, 500, len(rng)), index=rng)

   ts.resample('5Min', how='sum')

The ``resample`` function is very flexible and allows you to specify many
different parameters to control the frequency conversion and resampling
operation.

The ``how`` parameter can be a function name or numpy array function that takes
and array and produces an aggregated values:

.. ipython:: python

   ts.resample('5Min') # default is mean

   ts.resample('5Min', how='ohlc')

   ts.resample('5Min', how=np.max)

Any function available via :ref:`dispatching <groupby.dispatch>` can be given to
the ``how`` parameter by name, including ``sum``, ``mean``, ``std``, ``max``,
``min``, ``median``, ``first``, ``last``, ``ohlc``.

For downsampling, ``closed`` can be set to 'left' or 'right' to specify which
end of the interval is closed:

.. ipython:: python

   ts.resample('5Min', closed='right')

   ts.resample('5Min', closed='left')

For upsampling, the ``fill_method`` and ``limit`` parameters can be specified
to interpolate over the gaps that are created:

.. ipython:: python

   # from secondly to every 250 milliseconds

   ts[:2].resample('250L')

   ts[:2].resample('250L', fill_method='pad')

   ts[:2].resample('250L', fill_method='pad', limit=2)

Parameters like ``label`` and ``loffset`` are used to manipulate the resulting
labels. ``label`` specifies whether the result is labeled with the beginning or
the end of the interval. ``loffset`` performs a time adjustment on the output
labels.

.. ipython:: python

   ts.resample('5Min') # by default label='right'

   ts.resample('5Min', label='left')

   ts.resample('5Min', label='left', loffset='1s')

The ``axis`` parameter can be set to 0 or 1 and allows you to resample the
specified axis for a DataFrame.

``kind`` can be set to 'timestamp' or 'period' to convert the resulting index
to/from time-stamp and time-span representations. By default ``resample``
retains the input representation.

``convention`` can be set to 'start' or 'end' when resampling period data
(detail below). It specifies how low frequency periods are converted to higher
frequency periods.

Note that 0.8 marks a watershed in the timeseries functionality in pandas. In
previous versions, resampling had to be done using a combination of
``date_range``, ``groupby`` with ``asof``, and then calling an aggregation
function on the grouped object. This was not nearly convenient or performant as
the new pandas timeseries API.

.. _timeseries.periods:

Time Span Representation
------------------------

Regular intervals of time are represented by ``Period`` objects in pandas while
sequences of ``Period`` objects are collected in a ``PeriodIndex``, which can
be created with the convenience function ``period_range``.

Period
~~~~~~
A ``Period`` represents a span of time (e.g., a day, a month, a quarter, etc).
It can be created using a frequency alias:

.. ipython:: python

   Period('2012', freq='A-DEC')

   Period('2012-1-1', freq='D')

   Period('2012-1-1 19:00', freq='H')

Unlike time stamped data, pandas does not support frequencies at multiples of
DateOffsets (e.g., '3Min') for periods.

Adding and subtracting integers from periods shifts the period by its own
frequency.

.. ipython:: python

   p = Period('2012', freq='A-DEC')

   p + 1

   p - 3

Taking the difference of ``Period`` instances with the same frequency will
return the number of frequency units between them:

.. ipython:: python

   Period('2012', freq='A-DEC') - Period(2002', freq='A-DEC')

PeriodIndex and period_range
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Regular sequences of ``Period`` objects can be collected in a ``PeriodIndex``,
which can be constructed using the ``period_range`` convenience function:

.. ipython:: python

   prng = period_range('1/1/2011', '1/1/2012', freq='M')
   prng

The ``PeriodIndex`` constructor can also be used directly:

.. ipython:: python

   PeriodIndex(['2011-1', '2011-2', '2011-3'], freq='M')

Just like ``DatetimeIndex``, a ``PeriodIndex`` can also be used to index pandas
objects:

.. ipython:: python

   Series(randn(len(prng)), prng)

Frequency Conversion and Resampling with PeriodIndex
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The frequency of Periods and PeriodIndex can be converted via the ``asfreq``
method. Let's start with the fiscal year 2011, ending in December:

.. ipython:: python

   p = Period('2011', freq='A-DEC')
   p

We can convert it to a monthly frequency. Using the ``how`` parameter, we can
specify whether to return the starting or ending month:

.. ipython:: python

   p.asfreq('M', how='start')

   p.asfreq('M', how='end')

The shorthands 's' and 'e' are provided for convenience:

.. ipython:: python

   p.asfreq('M', 's')
   p.asfreq('M', 'e')

Converting to a "super-period" (e.g., annual frequency is a super-period of
quarterly frequency) automatically returns the super-period that includes the
input period:

.. ipython:: python

   p = Period('2011-12', freq='M')

   p.asfreq('A-NOV')

Note that since we converted to an annual frequency that ends the year in
November, the monthly period of December 2011 is actually in the 2012 A-NOV
period.

.. _timeseries.quarterly:

Period conversions with anchored frequencies are particularly useful for
working with various quarterly data common to economics, business, and other
fields. Many organizations define quarters relative to the month in which their
fiscal year start and ends. Thus, first quarter of 2011 could start in 2010 or
a few months into 2011. Via anchored frequencies, pandas works all quarterly
frequencies ``Q-JAN`` through ``Q-DEC``.

``Q-DEC`` define regular calendar quarters:

.. ipython:: python

   p = Period('2012Q1', freq='Q-DEC')

   p.asfreq('D', 's')

   p.asfreq('D', 'e')

``Q-MAR`` defines fiscal year end in March:

.. ipython:: python

   p = Period('2011Q4', freq='Q-MAR')

   p.asfreq('D', 's')

   p.asfreq('D', 'e')

.. _timeseries.interchange:

Converting between Representations
----------------------------------

Timestamped data can be converted to PeriodIndex-ed data using ``to_period``
and vice-versa using ``to_timestamp``:

.. ipython:: python

   rng = date_range('1/1/2012', periods=5, freq='M')

   ts = Series(randn(len(rng)), index=rng)

   ts

   ps = ts.to_period()

   ps

   ps.to_timestamp()

Remember that 's' and 'e' can be used to return the timestamps at the start or
end of the period:

.. ipython:: python

   ps.to_timestamp('D', how='s')

Converting between period and timestamp enables some convenient arithmetic
functions to be used. In the following example, we convert a quarterly
frequency with year ending in November to 9am of the end of the month following
the quarter end:

.. ipython:: python

   prng = period_range('1990Q1', '2000Q4', freq='Q-NOV')

   ts = Series(randn(len(prng)), prng)

   ts.index = (prng.asfreq('M', 'e') + 1).asfreq('H', 's') + 9

   ts.head()

.. _timeseries.timezone:

Time Zone Handling
------------------

Using ``pytz``, pandas provides rich support for working with timestamps in
different time zones. By default, pandas objects are time zone unaware:

.. ipython:: python

   rng = date_range('3/6/2012 00:00', periods=15, freq='D')
   print(rng.tz)

To supply the time zone, you can use the ``tz`` keyword to ``date_range`` and
other functions:

.. ipython:: python

   rng_utc = date_range('3/6/2012 00:00', periods=10, freq='D', tz='UTC')
   print(rng_utc.tz)

Timestamps, like Python's ``datetime.datetime`` object can be either time zone
naive or time zone aware. Naive time series and DatetimeIndex objects can be
*localized* using ``tz_localize``:

.. ipython:: python

   ts = Series(randn(len(rng)), rng)

   ts_utc = ts.tz_localize('UTC')
   ts_utc

You can use the ``tz_convert`` method to convert pandas objects to convert
tz-aware data to another time zone:

.. ipython:: python

   ts_utc.tz_convert('US/Eastern')

Under the hood, all timestamps are stored in UTC. Scalar values from a
``DatetimeIndex`` with a time zone will have their fields (day, hour, minute)
localized to the time zone. However, timestamps with the same UTC value are
still considered to be equal even if they are in different time zones:

.. ipython:: python

   rng_eastern = rng_utc.tz_convert('US/Eastern')
   rng_berlin = rng_utc.tz_convert('Europe/Berlin')

   rng_eastern[5]
   rng_berlin[5]
   rng_eastern[5] == rng_berlin[5]

Like Series, DataFrame, and DatetimeIndex, Timestamps can be converted to other
time zones using ``tz_convert``:

.. ipython:: python

   rng_eastern[5]
   rng_berlin[5]
   rng_eastern[5].tz_convert('Europe/Berlin')

Localization of Timestamps functions just like DatetimeIndex and TimeSeries:

.. ipython:: python

   rng[5]
   rng[5].tz_localize('Asia/Shanghai')


Operations between TimeSeries in difficult time zones will yield UTC
TimeSeries, aligning the data on the UTC timestamps:

.. ipython:: python

   eastern = ts_utc.tz_convert('US/Eastern')
   berlin = ts_utc.tz_convert('Europe/Berlin')
   result = eastern + berlin
   result
   result.index
