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'Tis be the season for SAAR

Given today's news on GDP, I thought it would be timely to discuss that curious barnacle known as the seasonally adjusted annual rate (SAAR). Or as the pirates call it, SAARRR!

What exactly is SAAR?

First, we be adjusting for the seasons. Let's say we are following a particular set of data over time (a time series). The data's change can be understood as comprising three parts: (1) the trend cycle, which reflects the long-term tendency of the data (the economy has grown at such and such average rate over the past 20 years); (2) the irregular component, which reflects short-term fluctuations (the outbreak of Sars, or as the pirates call it, SARRRS!); and (3) the seasonal component, which shows systematic variations (stock market volumes go down during holiday weeks).

The seasonal component can be further decomposed into seasonality effects, which are regular variations such as higher visitor arrivals in August and December; and calendar effects, which change from year to year because of moving holidays, such as the Chinese New Year, and an inconstant number of trading days in each month every year.

Seasonally adjusted data seeks to remove the seasonal component and leave only the trend cycle and irregular component in the data. Singapore, as of 2006, was using the X12-Arima procedure developed by the US Census Bureau. It is actually possible to download the X12-Arima software for free to play around with.

To derive SAAR, the seasonally adjusted quarterly growth rate is then annualised by assuming that the economy grows at the same rate for the rest of the year. In mathematical terms, the annualised rate is equal to (1 + the seasonally adjusted quarterly growth rate)^4 - 1.

SAAR in the context of GDP is only used to compare quarter-on-quarter growth. That's because seasonal adjustments are irrelevant in year-on-year comparisons, and because quarter-on-quarter comparisons are meaningless if seasonality remains in the data.

There are a couple of dated but still relevant and good reports talking about Saar by the Department of Statistics, one on annualising and another on seasonal adjustments. Worth the visit.