Daily variable for inflation I was wondering if there is a way to account for daily inflation data. I have daily short-term interest rates, and I would like to convert them to real short-term interest rates. 

Can I just average the monthly CPI over the days of that month to calculate the real rate with the Fisher equation?

Any help is greatly appreciated!
The Billion Price Project offers what you want:


  Daily price indices, monthly, and annual inflation rates for Argentina
  and the US. Monthly data with annual inflation rates for Argentina,
  Brazil, China, Germany, Japan, South Africa, UK, US, 3 US sectors, and
  global aggregates (including Eurozone). Daily PPP series for Argentina
  and Australia.


However, these data, which come mostly from online transaction data, are imperfect because they end in 2015. However, I've put together some code so you can see that there is not very much high frequency price level variation for the basket of goods:

import delimited pricestats_bpp_arg_usa.csv
drop if country=="ARGENTINA"
gen date2 = date(date, "DMY")
format date2 %d 
tsset date2
twoway (tsline indexps)

tssmooth ma indexps_ma30  = indexps, window(30)
twoway (tsline indexps) (tsline indexps_ma30)
gen monthly_diff = indexps - l30.indexps
gen monthly_diff_ma = indexps_ma30 - l30.indexps_ma30
gen abs_double_diff =  abs(monthly_diff -  monthly_diff_ma)

sum indexps indexps_ma30 monthly_diff monthly_diff_ma abs_double_diff, detail
twoway (tsline monthly_diff) (tsline monthly_diff_ma)\


This generates a figure comparing the 30 day moving average price level and actual price level you can see below that there is very little difference between the smoothed and actual price level. The price level of a broad basket of prices doesn't fluctuate enough for daily inflation to be very different from assuming a constant inflation (which is roughly equivalent to using the average). 


I estimate, using the calculations above, that monthly inflation is about 11 basis point per month. Using a measure of inflation rather than the price level shows that the smoothed and raw inflation estimates are very similar. This variation could be because there is measurement error and bias from the high frequency calculation approach.

Bottom line, I would just stick with converting monthly series to an implied daily rate. Depending on if you care about business days or calendar days and how you feel about using real time data, this could be as simple as: $$ \hat{r}_{daily\ implied, t} = ( 1 + r_{monthly\ observed, t})^{1/30} -1 +\epsilon$$