# Converting quarterly growth rate forecasts to yearly growth rate forecasts

I'm generating forecasts on a quarterly basis, focusing on metrics like the GDP growth rate for Brazil. These forecasts are presented as growth rates.

For example, the forecast for 2020Q1 represents the growth rate for the first quarter of 2020 relative to the first quarter of 2019, while 2020Q4 represents the forecasted growth rate for the fourth quarter of 2020 relative to the fourth quarter of 2019.

Once I've completed the quarterly forecasts, I want to convert them into annual forecasts.

Currently, the approach I'm using to calculate the yearly growth rate is by first converting the quarterly growth rate to quarterly absolute numbers.

Then I use the latest historical absolute number to calculate the first forecasted quarterly absolute number, then iteratively calculate all the subsequent quarterly absolute numbers.

Once I have all the quarterly absolute numbers, I derive the yearly absolute numbers and then calculate the yearly growth rate.

Are there any common pitfalls to avoid or best practices to follow when converting growth rate forecasts from quarterly to yearly forecasts? I'm considering a simple method like taking the average of the quarters for each year, but this approach doesn't take into account potential seasonality factors found within the quarterly forecasts.

Any tips and advice would be greatly appreciated.

• It depends on what your "the growth rate for the first quarter of 2020" represents: (a) the % change in GDP from 2019Q4 to 2020Q1, or (b) that compounded to an annual rate, or (c) the % change in GDP from 2019Q1 to 2020Q1. It also depends on what growth rate you want for the year 2020: (d) the % change in quarterly GDP from 2019Q4 to 2020Q4 or (e) the % change in annual GDP from 2019 to 2020. The clearest approach may be to translate your % change forecasts into forecasts of actual GDP, then do suitable summation, division and subtraction to get the forecast % change you are interested in. Commented May 10 at 11:15
• Going from (a) to (e) only really works at the actual GDP level. Going from (a) to (d) has a shortcut: just combine the four quarterly figures (close to summation, but more accurately compounded). Going from (b) to (d) or (e) requires you to undo the compounding at an annual rate to find (a) as an intermediate step, though (b) to (d) may be close to the average of the four forecasts. Going from (c) to (d) is trivial as it is already in your forecasts for Q4, while going from (c) to (e) would again benefit from using forecasts of GDP levels though near the average of the four forecasts. Commented May 10 at 11:25
• Using approximations is also an issue in years with dramatic quarterly changes: 2020 saw a Covid-recession followed by a bounce back. And you may also want to check whether you are working with seasonally adjusted numbers or not. Commented May 10 at 11:39
• @Henry, your comments make for a nice answer. Why not post them as such? Commented May 10 at 12:15

It depends on what your "the growth rate for the first quarter of 2020" represents:

(a) the % change in GDP from 2019Q4 to 2020Q1, or

(b) that compounded to an annual rate, or

(c) the % change in GDP from 2019Q1 to 2020Q1.

It also depends on what growth rate you want for the year 2020:

(d) the % change in quarterly GDP from 2019Q4 to 2020Q4 or

(e) the % change in annual GDP from 2019 to 2020.

The clearest approach may be to translate your % change forecasts into forecasts of actual GDP levels, then do suitable summation, division and subtraction to get the forecast % change you are interested in.

• Going from (a) to (d) has a shortcut: just combine the four quarterly figures (close to summation, but more accurately compounded).
• Going from (a) to (e) only really works at the actual GDP level.
• Going from (b) to (d) or (e) requires you to undo the compounding at an annual rate to find (a) as an intermediate step,
• though (b) to (d) may be close to the average of the four forecasts.
• Going from (c) to (d) is trivial as it is already in your forecasts for Q4.
• Going from (c) to (e) would again benefit from using forecasts of GDP levels though near the average of the four forecasts.

Using approximations is also an issue in years with dramatic quarterly changes: 2020 saw a Covid-recession followed by a bounce back. And you may also want to check whether you are working with seasonally adjusted numbers or not.

• it seems the current approach is the clearest approach you're suggesting. I'm translating the quarterly growth into actuals, then sum the quarterly actuals into the respective years, then calculate the yearly growth. Commented May 15 at 14:01