Get rolling average of a Pandas DataFrame with hourly values, while taking into account cyclical nature of days

Lets say I have a dataframe with a multiindex, constructed as follows:

import numpy as np
import pandas as pd

ids = ['a', 'b', 'c']
hours = np.arange(24)
data = np.random.random((len(ids),len(hours)))

df = pd.concat([pd.DataFrame(index = [[id]*len(hours), hours], data = {'value':data[ind]}) for ind, id in enumerate(ids)])
df.index.names = ['ID', 'hour']

Which looks like this:

            value
ID hour          
a  0     0.020479
   1     0.059987
   2     0.053100
   3     0.406198
   4     0.452231
          ...
c  19    0.150493
   20    0.617098
   21    0.377062
   22    0.196807
   23    0.954401

What I want to do is get a new 24-hour timeseries for each station, but calculated with a 5-hour rolling average.

I know I can do something like df.rolling(5, center = True, on = 'hour'), but the problem with this is that it doesn't take into account the fact that the hours are cyclical - i.e., the rolling average for hour 0 should be the average of hours 22, 23, 0, 1, and 2.

What is a good way to do this?

Thanks!

If you want to take into account the cycle, use np.pad and np.convolve:

import pandas as pd
import numpy as np

# A more comprehensive example
mi = pd.MultiIndex.from_product([['a'], np.arange(1, 25)], names=['ID', 'hour'])
df = pd.DataFrame({'value': np.arange(1, 25)}, index=mi)

def cycling_ma(x):
    return np.convolve(np.pad(x, 2, mode='wrap'), np.ones(5)/5, mode='valid')

df['ma'] = df.groupby('ID')['value'].transform(cycling_ma)

Output:

>>> df
         value    ma
ID hour
a  1         1  10.6  # (23 + 24 + 1 + 2 + 3) / 5 (23 and 24 -> pad from end)
   2         2   6.8
   3         3   3.0
   4         4   4.0
   5         5   5.0
   6         6   6.0
   7         7   7.0
   8         8   8.0
   9         9   9.0
   10       10  10.0
   11       11  11.0
   12       12  12.0
   13       13  13.0
   14       14  14.0
   15       15  15.0
   16       16  16.0
   17       17  17.0
   18       18  18.0
   19       19  19.0
   20       20  20.0
   21       21  21.0
   22       22  22.0
   23       23  18.2
   24       24  14.4  # (22 + 23 + 24 + 1 + 2) / 5 (1 and 2 -> pad from begin)

Reference: How to calculate rolling / moving average using python + NumPy / SciPy?

Here is a way using np.roll()

df.join(
    df.groupby('ID',group_keys=False).apply(
        lambda x: pd.DataFrame([np.roll(x['value'],2 - i)[:5].mean() for i in range(x.shape[0])],
                               index = x.index,
                               columns = ['ma'])))

Output:

         value    ma
ID hour             
a  1         1  10.6
   2         2   6.8
   3         3   3.0
   4         4   4.0
   5         5   5.0
   6         6   6.0
   7         7   7.0
   8         8   8.0
   9         9   9.0
   10       10  10.0
   11       11  11.0
   12       12  12.0
   13       13  13.0
   14       14  14.0
   15       15  15.0
   16       16  16.0
   17       17  17.0
   18       18  18.0
   19       19  19.0
   20       20  20.0
   21       21  21.0
   22       22  22.0
   23       23  18.2
   24       24  14.4