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Seasonally Adjusted Data Versus Seasonally Adjusted Annual Rates

Article Quant Q&A · Author: eykanal
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Summary

Seasonally adjusted (SA) data remove recurring seasonal patterns from a time series. Seasonally adjusted annual rate (SAAR) data do that as well, then express the measurement as an annualized amount or pace. For a monthly level, the annualized figure scales the adjusted value to represent a full year; for reported growth, annualization conveys what the rate would imply if it continued across the year.

The explanation uses a hypothetical monthly average of 100 to illustrate annual scaling and quarterly real GDP growth to clarify annualized growth rates. A quarterly GDP figure reported as 3% SAAR describes the pace implied by repeating that quarter's growth for four quarters, rather than growth actually realized in that quarter. These definitions help distinguish seasonal adjustment from annualization. The examples are illustrative, and the document does not discuss the particular adjustment methods, compounding conventions, or how to interpret SAAR for every type of series.

Key ideas

  • Seasonal adjustment removes recurring patterns associated with the time of year or other periodic cycles.
  • SAAR combines seasonal adjustment with scaling to an annual amount or growth pace.
  • An annualized quarterly growth figure describes the result implied by repeating the quarter's pace across a year.
  • Reported SAAR growth should not be read as the actual change within the reporting quarter.

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# What's the difference between SA and SAAR?


# What's the difference between SA and SAAR?












I've only recently begun working in the quantitative finance field, and I've noticed that some time series I'm given are labeled "seasonally adjusted", and some labeled with "seasonally adjusted annual rate". What's the difference between these two data transforms?

## Answer by Dirk Eddelbuettel (score 3, accepted)

https://quant.stackexchange.com/a/2423

Seasonal adjustments per se are a topic in and by itself, see for example this Wikipedia page.

As for the added "AR", imagine an event with an unconditional average of '100' (to pick a base) when measure monthly. So the annual average is 1200, and similarly, a 'SAAR' series accounts for both recurring seasonal patterns (quarterly, monthly, weekly, daily, intra-daily, ...) and also scales the measurements to an annual total.

This wasn't really a quant finance question, maybe try the Stats sister site next time around.

## Answer by Joshua Ulrich (score 2)

https://quant.stackexchange.com/a/2424

A SAAR series is expressed as if period-over-period growth were to occur for an entire year. Real GDP is reported this way. A report of 3% GDP growth in a quarter does not mean GDP grew 3% in that quarter. It means GDP would be 3% higher in one year if this quarter's growth were to occur over 4 consecutive quarters.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.