Seasonal Adjustment

Seasonal adjustment is a statistical method that strips predictable, calendar-related swings out of economic data. Retail sales jump before the year-end holidays, construction slows in winter, farm and tourism jobs peak in summer, and spending patterns shift around festivals such as Ramadan, Diwali and the Lunar New Year. Without adjustment, these regular movements would hide the changes that matter to policymakers and analysts: whether the economy is actually growing faster or slower than usual.

Most headline statistics are published in seasonally adjusted form, including monthly unemployment and payroll figures, quarterly GDP and many consumer price index series. National statistics offices, such as the US Census Bureau, the Bureau of Labor Statistics, the UK Office for National Statistics and Eurostat, carry out the work, usually alongside a non-adjusted version for users who need the raw numbers.

Imagine an ice-cream stall whose sales double every July and fall by half every January. If the owner compared July with June, she would think business was booming; comparing January with December, she would panic. Neither comparison tells her whether the stall is doing better than last year.

Seasonal adjustment works out the normal July lift and the normal January dip from several years of records, then takes them out. What is left shows whether this July was a good July, not just a hot month. Statistics offices do the same for national data, so that a rise in jobs or spending means more than "it is that time of year again".

Statisticians treat an observed series as a combination of parts. A common multiplicative form is:

• $Y_t$ is the observed value in period $t$.
• $T_t$ is the trend-cycle, the slow-moving path of the series.
• $S_t$ is the seasonal factor, the typical effect of that month or quarter.
• $I_t$ is the irregular part, random noise and one-off events.

The seasonally adjusted figure is the observed value divided by the seasonal factor. For example, if a country's retail sales were 120 billion in December and the estimated December seasonal factor is 1.20 (sales are normally 20% above an average month), the adjusted figure is $120 \div 1.20 = 100$ billion. If November's adjusted figure was 101 billion, the December rise in raw sales actually hides a small underlying fall.

Before estimating seasonal factors, statisticians make calendar adjustments for the number of working days, leap years and moving holidays such as Easter, Ramadan or the Lunar New Year, whose dates change from year to year. They also identify outliers, such as strikes or natural disasters, so that these do not distort the seasonal pattern.

Two families of methods dominate official practice. X-13ARIMA-SEATS, developed and maintained by the US Census Bureau, fits a time-series model (an ARIMA model) to extend the series and then applies either the long-established X-11 filters or the SEATS decomposition. TRAMO-SEATS, developed at the Bank of Spain, takes a model-based approach. In Europe, the European Statistical System and the European System of Central Banks recommend JDemetra+, open-source software developed by the National Bank of Belgium with the Deutsche Bundesbank and Eurostat that implements both methods. Eurostat publishes ESS Guidelines on Seasonal Adjustment to keep practice consistent across member countries. These are standard tools of econometrics and time-series statistics.

Central banks such as the Federal Reserve and the European Central Bank set monetary policy partly on monthly data for jobs, inflation and spending, and financial markets react within seconds to releases such as US payrolls. Mistaking a seasonal swing for a real change could lead to wrong decisions on interest rates. Seasonal adjustment also allows month-on-month comparisons, which reveal turning points in the business cycle faster than year-on-year changes. Analysts watching leading indicators and real-time indicators rely on adjusted figures to separate signal from routine, and so do economists confirming a turn with lagging indicators such as the labour market data.

• Revisions. Seasonal factors are re-estimated as new data arrive, so adjusted figures for recent months change, sometimes noticeably.
• Residual seasonality. In the mid-2010s, analysts noted that first-quarter US GDP growth was repeatedly weak even after adjustment, which led the Bureau of Economic Analysis to revise its methods.
• Shocks. Large, sudden events such as a recession or the 2020 pandemic lockdowns can be mistaken for changes in seasonal patterns. Statistics offices treated many 2020 observations as outliers to protect later estimates.
• Changing seasons. Shifts in behaviour, such as the growth of online "Black Friday" sales or changing holiday dates, mean seasonal patterns themselves evolve.
• Short or new series. Daily and weekly data, and series with few years of history, are hard to adjust reliably.

Some users therefore look at both adjusted and unadjusted data, and at year-on-year changes, which remove most seasonal effects without any modelling. Statistical economic models estimated on adjusted data also inherit any errors in the adjustment, which is one reason forecasters test their results on raw data as well.

• US Census Bureau: X-13ARIMA-SEATS Seasonal Adjustment Program
• Eurostat: ESS Guidelines on Seasonal Adjustment (2015 edition)