statistics - How to find average monthly annualized growth rate for time series in R?

Question

I am trying to find the average monthly annualized growth rate for a continuous data set that contains monthly data. I can find the annualized growth rate using the formula gt = ((1 + (current month - previous month)/previous month))^12) - 1. However, I am unsure how to find the average monthly annualized version of this growth rate. Am I missing something obvious? Any help would be much appreciated.

question from:https://stackoverflow.com/questions/65904299/how-to-find-average-monthly-annualized-growth-rate-for-time-series-in-r

Answer 1

The periods used should all be of equal length, do not mix periods of different duration, so I think monthly annualized is no sens.

First of all, you should calculate the simple percentage growth of each year by using this formula

[GR = (ending value - ending value) - 1]

Then calculate the AAGR by this formula

[ AAGR = (GR1 + GR2 + ... +GRn) / N ] 

For example, we have:

Beginning value = $100,000
End of year 1 value = $120,000
End of year 2 value = $135,000
End of year 3 value = $160,000
End of year 4 value = $200,000

?
Thus, the growth rates for each of the years are as follows:

Year 1 growth = $120,000 / $100,000 - 1 = 20%
Year 2 growth = $135,000 / $120,000 - 1 = 12.5%
Year 3 growth = $160,000 / $135,000 - 1 = 18.5%
Year 4 growth = $200,000 / $160,000 - 1 = 25%

AAGR = (20%+12.5%+18.5%+25%) / 4 = 19%