I have a daily dataset with global aggregate numbers of an index and a monthly index of countries specifically. As the changes in the daily ones are very sporadic and volatile I can't use linear interpolation, which my supervisor agreed on. So I am trying to find a way to interpolate the country specific monthly figures to daily figures based on the global aggregate daily figure changes. I am taking the assumption that both are extremely correlated to validate this approach. How should I approach this and through which stata commands as I am not familiar with different interpolation methods and their pros and cons.

Example of the dataset for the first month where GPRD = is daily variable and GPRC_DEU the monthly
date GPRD GPRC_DEU
01/01/2022 62.95 1.26
02/01/2022 37.86
03/01/2022 55.74
04/01/2022 93.54
05/01/2022 95.46
06/01/2022 73.92
07/01/2022 119.16
08/01/2022 38.28
09/01/2022 63.70
10/01/2022 135.54
11/01/2022 192.97
12/01/2022 81.38
13/01/2022 177.09
14/01/2022 134.17
15/01/2022 71.06
16/01/2022 45.75
17/01/2022 115.06
18/01/2022 144.46
19/01/2022 155.56
20/01/2022 138.22
21/01/2022 194.31
22/01/2022 145.81
23/01/2022 106.86
24/01/2022 184.03
25/01/2022 296.21
26/01/2022 271.75
27/01/2022 267.22
28/01/2022 189.41
29/01/2022 217.44
30/01/2022 63.53
31/01/2022 149.44
01/02/2022 192.65 2.62
Many thanks!

Steven