X-13ARIMA-SEATS Seasonal Adjustment
Also known as: X-13ARIMA-SEATS, X-12-ARIMA, Census X-13, Mevsimsel Düzeltme X-13
X-13ARIMA-SEATS is the standard seasonal adjustment program produced by the U.S. Census Bureau, combining RegARIMA pre-adjustment with either the classical X-11 filter or the model-based SEATS signal-extraction algorithm. It is the official tool used by national statistical agencies worldwide — including Eurostat and the U.S. Bureau of Labor Statistics — to remove recurring calendar and seasonal patterns from monthly or quarterly economic time series such as GDP, employment, and retail sales.
Key highlights
- Industry-standard methodology endorsed by Eurostat, IMF, and national statistical offices, ensuring cross-country comparability
- Combines model-based SEATS extraction with the proven X-11 filter, offering two complementary decomposition philosophies in one package
- Automatic outlier detection and trading-day correction via RegARIMA reduce contamination of seasonal estimates by calendar and shock effects
- Rich built-in diagnostics — M-statistics, spectral analysis, sliding spans — provide formal evidence of adjustment quality
Intuition
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How it works
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When to use it
Apply X-13ARIMA-SEATS when you have a monthly or quarterly economic time series of at least four to five years and need to isolate the underlying trend or business-cycle signal from predictable seasonal fluctuations. The series should exhibit stable or evolving seasonality; if seasonality is absent, adjustment adds no value. The method assumes the decomposition model (additive or multiplicative) is correctly specified and that structural breaks are identified as outliers or level-shift regressors. When seasonality is highly nonlinear or the series is daily or weekly, STL decomposition or state-space models may be more appropriate alternatives.
Strengths & limitations
- Industry-standard methodology endorsed by Eurostat, IMF, and national statistical offices, ensuring cross-country comparability
- Combines model-based SEATS extraction with the proven X-11 filter, offering two complementary decomposition philosophies in one package
- Automatic outlier detection and trading-day correction via RegARIMA reduce contamination of seasonal estimates by calendar and shock effects
- Rich built-in diagnostics — M-statistics, spectral analysis, sliding spans — provide formal evidence of adjustment quality
- Designed primarily for monthly and quarterly data; application to other frequencies requires non-standard configurations
- Requires a reasonably long history (typically 5+ years) to estimate stable seasonal factors
- Model selection and outlier specification can be sensitive to analyst choices, producing different adjusted series across software implementations
- Revised seasonal factors when new data arrive, meaning published seasonally adjusted figures are subject to backward revisions
Common pitfalls
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Applications
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Frequently asked
Should I use the X-11 filter or SEATS for my series?
X-11 is more robust when the series deviates from ARIMA assumptions or contains heavy outlier contamination, because its moving averages are non-parametric. SEATS is preferable when an ARIMA model fits well, as it yields theoretically optimal estimates with minimum revision variance. In practice, both usually give similar results; examine the diagnostics for each and prefer the one with fewer residual-seasonality flags.
How many years of data do I need before running X-13ARIMA-SEATS?
The U.S. Census Bureau recommends a minimum of three years, but five or more years of monthly data (or four-plus years of quarterly data) are needed to estimate seasonal factors reliably and to obtain meaningful sliding-span stability statistics. With shorter series, seasonal estimates are unstable and diagnostics unreliable.
What does the Q statistic tell me and what is a passing value?
The Q statistic is a weighted average of the eleven M-statistics that assess different aspects of adjustment quality — residual seasonality, moving seasonality, irregular-to-trend ratios, and more. A Q value below 1.0 is considered acceptable by Census Bureau guidelines. Values between 1.0 and 1.5 indicate caution; values above 1.5 suggest the adjustment is unsatisfactory and the model specification should be revisited.
Sources
- 1.Findley, D. F., Monsell, B. C., Bell, W. R., Otto, M. C., & Chen, B.-C. (1998). New capabilities and methods of the X-12-ARIMA seasonal adjustment program. Journal of Business & Economic Statistics, 16(2), 127–152.
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Cite this page
ScholarGate. (2026, June 2). X-13ARIMA-SEATS. ScholarGate. https://scholargate.app/econometrics/x13-arima-seats