What kind of interpolating should I use?

[Steven Zhao]

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

[Nick Cox]

This sounds like an insoluble problem to me. If you assume a relationship between the daily variable and the monthly variable then just about 29/30 of your values will be interpolated or rather estimated. You will no longer have two variables but two versions of one variable that are strongly correlated and at best there will be weird artefacts and at best you'll just discover the correlation you assumed in the first place.

Much depends on whether the monthly variable is a snapshot at the beginning of the month or some kind of overall average or representative value that refers to the whole month. If the latter, then it seems to me that the only defensible action is to spread the values for the first day of each month to all days in the same month.

This is a delicate point on which researchers may disagree and so different views might be expressed