## Tuesday, 2 August 2011

### Daily CPI Formula

Daily CPI Formula

Updated on 6-9-11

A Daily Consumer Price Index (DCPI) is a lagged daily interpolation of the CPI based on the formula used to calculate the Chile´s Unidad de Fomento. In practice, a DCPI is used to inflation–adjust monetary items, to update historical variable items and to measure constant items in units of constant purchasing power under Constant Item Purchasing Power Accounting. The UF is the most successful monetized daily indexed unit of account.

A Daily Consumer Price Index is calculated and published daily. The monthly published CPI for the first day of any month is only available round–about the tenth of the next month: up to 41 days later.

The DCPI is a lagged daily interpolation of the consumer price index. The formula for calculating the DCPI is based on Chile´s Unidad de Fomento published daily by the Central Bank of Chile.

The above formula applies to the UF in Chile where the CPI for the current calendar month used to be available on the 10th of the next calendar month. The general case formula can be stated as follows:

On day t
DI t = DI t-1  x  (1 + π) to the power 1/d

where π is the inflation rate for the calendar month preceding the calendar month in which t falls if t is on or between the day the CPI for the previous calendar month is published and the last day of the month (and d is the number of days in the calendar month in which t falls), and π is the inflation rate for the second calendar month before the calendar month in which t falls if t is on or between day one and the day of publication of the CPI of the previous calendar month (and d is the number of days in the calendar month before the calendar month in which t falls).

Since the inflation rate for a calendar month is computed using the CPI for that month and for the preceding month, the DIs within a given calendar month will depend on the CPI for each of the three preceding months (e.g., the July DIs will depend before the day the June CPI is published on the CPI for April and May, and starting with the day the June CPI is publised on the CPI for May and June).