What Formulas are Used to Calculate Growth Rates?

What Formulas are Used to Calculate Growth Rates?

Note that because FRED uses levels and rounded data as published by the source, calculations of percentage changes and/or growth rates in some series may not be identical to those in the original releases.

The following formulas are used:

Change:  

 

Change from Year Ago: 

 

Percent Change:  
Percent Change from Year Ago: 

 

Compounded Annual Rate of Change: 

 

Continuously Compounded Rate of Change: 

 

Continuously Compounded Annual Rate of Change: 

 

Natural Log: 

Notes:

 is the value of series x at time period t.

'n_obs_per_yr' is the number of observations per year. The number of observations per year differs by frequency:

Daily, 260 (no values on weekends)
Annual, 1
Monthly, 12
Quarterly, 4
Biweekly, 26
Weekly,52

'ln' represents the natural logarithm.