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Create 1-column dataframe from multi-index pandas series

I have a multi-index series like this:

Year  Month
2012  1        444
      2        222
      3        333
      4        1101

which I want to turn into:

Date      Value
2012-01   444
2012-02   222
2012-03   333
2012-04   1101

to plot a line.

I have tried both series.unstack(level=0) and series.unstack(level=1) , but this creates a matrix

In[1]: series.unstack(level=0)
Out[1]: 
Year   2012  2013  2014  2015  2016  2017   2018
Month                                          
1      444  ...   ...   ...   ...   ...    ...
2      222  ...   ...   ...   ...   ...    ...
3      333  ...   ...   ...   ...   ...    ...
4      1101 ...   ...   ...   ...   ...    ...

What am I missing?

Use Index.to_frame with to_datetime working if also added Day column, and reasign back:

s.index = pd.to_datetime(s.index.to_frame().assign(Day=1))
print (s)
2012-01-01     444
2012-02-01     222
2012-03-01     333
2012-04-01    1101
Name: a, dtype: int64

For one column DataFrame use Series.to_frame :

df1 = s.to_frame('Value')
print (df1)
            Value
2012-01-01    444
2012-02-01    222
2012-03-01    333
2012-04-01   1101

If need PeriodIndex add Series.dt.to_period :

s.index = pd.to_datetime(s.index.to_frame().assign(Day=1)).dt.to_period('m')
print (s)
2012-01     444
2012-02     222
2012-03     333
2012-04    1101
Freq: M, Name: a, dtype: int64

df2 = s.to_frame('Value')
print (df2)
         Value
2012-01    444
2012-02    222
2012-03    333
2012-04   1101
idx = pd.PeriodIndex(
    year=s.index.get_level_values(0).tolist(), 
    month=s.index.get_level_values(1).tolist(), 
    freq='M', 
    name='Date'
)
s2 = pd.Series(s.values, index=idx, name=s.name)
s2.plot()

You could also use a list comprehension with f-strings to create a DatetimeIndex.

idx = pd.to_datetime([f'{year}-{month}' for year, month in s.index])

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