Clean way to convert quarterly periods to datetime in pandas

Use slicing by last 4 values with first 2 and convert to datetimes:

df['date'] = pd.to_datetime(df['Quarter'].str[-4:] + df['Quarter'].str[:2])

String operations in pandas are slow, so if no missing values is possible use list comprehension:

#python 3.6+ 
df['date'] = pd.to_datetime([f'{x[-4:]}{x[:2]}' for x in df['Quarter']])
#python bellow
#df['date'] = pd.to_datetime(['{}{}'.format(x[-4:], x[:2]) for x in df['Quarter']])
print (df)
   Quarter       date
0  Q3 1996 1996-07-01
1  Q4 1996 1996-10-01
2  Q1 1997 1997-01-01

You can (and should) use pd.PeriodIndex as a first step, then convert to timestamp using PeriodIndex.to_timestamp:

qs = df['Quarter'].str.replace(r'(Q\d) (\d+)', r'\2-\1')
qs

0    1996-Q3
1    1996-Q4
2    1997-Q1
Name: Quarter, dtype: object

df['date'] = pd.PeriodIndex(qs, freq='Q').to_timestamp()
df

   Quarter       date
0  Q3 1996 1996-07-01
1  Q4 1996 1996-10-01
2  Q1 1997 1997-01-01

The initial replace step is necessary as PeriodIndex expects your periods in the %Y-%q format.

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Another option is to use pd.to_datetime after performing string replacement in the same way as before.

df['date'] = pd.to_datetime(
    df['Quarter'].str.replace(r'(Q\d) (\d+)', r'\2-\1'), errors='coerce')
df

   Quarter       date
0  Q3 1996 1996-07-01
1  Q4 1996 1996-10-01
2  Q1 1997 1997-01-01

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If performance is important, you can split and join, but you can do it cleanly:

df['date'] = pd.to_datetime([
    '-'.join(x.split()[::-1]) for x in df['Quarter']])

df

   Quarter       date
0  Q3 1996 1996-07-01
1  Q4 1996 1996-10-01
2  Q1 1997 1997-01-01

Given a quarter format like 2018-Q1, one can use the built in pd.to_datetime function. As a general answer would have to deal with the plethora of ways one can store a quarter-year observation (e.g. 2018:1, 2018:Q1, 20181, Q1:2018, etc.), coercing the data into the format supra is outside of my answer's scope.

But given a formatted series:

formatted_series = formatted_series_supplier() ...
df['date'] = pd.to_datetime(formatted_series)

For example:

>>> pd.to_datetime(pd.Series(['2018-Q1']))
0   2018-01-01
dtype: datetime64[ns]

And if you're dealing with regulatory data, which almost always reflects the end of the quarter rather than it's start (i.e. instead of 2019-01-01, you want 2019-03-31), you can use offsets like below:

df['date'] = df['date'] + pd.offsets.QuarterEnd(0)

Using the example from above, removing the intermediate result,

>>> pd.to_datetime(pd.Series(['2018-Q1'])) + pd.offsets.QuarterEnd(0)
0   2018-03-31
dtype: datetime64[ns]

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Note that the 0 parameter must be provided to QuarterEnd if you want correct indexing within the same quarter for the end date. Otherwise, you'll get something like this:

>>> pd.to_datetime('2018-03-31') + pd.offsets.QuarterEnd()
Timestamp('2018-06-30 00:00:00')