# Seasonal Adjustment And X13 > Seasonal adjustment is a second, silent vintage - the published seasonally adjusted history keeps changing with no new data. TRIGGER - seasonally adjusted, SA vs NSA, "why did last year's number change", concurrent seasonal adjustment, seasonal factors, X-13ARIMA-SEATS, X-13, X-12-ARIMA, x13_arima_analysis, X13NotFoundError, "x12a and x13as not found on path", X13PATH, statsmodels seasonal_decompose, STL, ratio to moving average, annual re-adjustment, benchmark revision, "the seasonal factors were revised", residual seasonality, seasonally adjusting a series myself. SKIP for revisions to the underlying unadjusted value (real-time-macro-backtesting), for release timing (macro-release-calendar-and-embargo), for where the series live (fundamental-and-macro-data), and for general time-series decomposition and forecasting (time-series-forecasting-models). - Skill: `howard-lynn-ye/seasonal-adjustment-and-x13` (Agent Skill) - Install (CLI): `npx skillmds@latest add howard-lynn-ye/seasonal-adjustment-and-x13` - Raw SKILL.md: https://api.skillmd.com/api/skills/howard-lynn-ye/seasonal-adjustment-and-x13/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Productivity - License: MIT - Author: howard-lynn-ye (https://skillmd.com/u/howard-lynn-ye) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/howard-lynn-ye/seasonal-adjustment-and-x13 --- # Seasonal adjustment and X-13 **A seasonally adjusted number is an estimate, and the agency re-estimates it every month.** The unadjusted data for a month settles in about two months. The *published adjusted* value for that same month keeps moving for years — not because anyone collected anything, but because the seasonal factors were recomputed. `../real-time-macro-backtesting/SKILL.md` owns revisions to the *value*. This skill owns the revision that arrives with **no new information at all**, which is invisible to every diagnostic built for the first kind. Everything marked ✅ Measured is printed by `scripts/seasonal_adjustment.py` (numpy + pandas, seed 20260909, about **3 s**, no network; `statsmodels` probed inside a function). Everything marked ✅ source-verified was read at the URL given on 2026-09-09. ## 1. ✅ What the agency says it does ✅ source-verified at `bls.gov/web/empsit/cesseasadjtn.htm`, verbatim: > *"The CES program employs a **concurrent** seasonal adjustment methodology to seasonally > adjust its national estimates of employment, hours, and earnings."* > > *"Under concurrent methodology, **new seasonal factors are calculated each month using all > relevant data up to and including the current month period**."* > > *"Once a year, BLS seasonally adjusts CES series again, **replacing the most recent 5 years > of historical estimates** with newly seasonally adjusted estimates."* — using *"the U.S. Census Bureau's X-13ARIMA-SEATS application."* ✅ source-verified at `bls.gov/web/empsit/cesvininfo.htm`: *"CES estimates are subject to revisions for up to 2 months from their original publication due to ongoing receipt of sample data."* 🔑 **Put those two together and the trap states itself.** Past the two-month window the unadjusted number is settled. **Anything the published seasonally adjusted value does after that is arithmetic**, and it happens twelve times a year, and again over five years of history at each annual re-adjustment. ⚠️ The annual benchmark compounds it from the other direction: ✅ source-verified at `bls.gov/web/empsit/cesbmart.htm`, *"Twenty-one months of not seasonally adjusted CES estimates for all data types are revised based on this new March level, **prior to seasonal adjustment**"*, and the March-2025 benchmark moved the SA level by **−898,000** against −862,000 NSA. The extra 36,000 is the seasonal adjustment reacting to the new NSA history. `../real-time-macro-backtesting/SKILL.md` §1 has that table month by month. ## 2. The mechanism, in one paragraph X-11's core is ratio-to-moving-average: estimate the trend with a **centred** 2x12 moving average, form SI ratios (`data / trend`), smooth each calendar month's SI ratios across years, normalise. 🔑 **A centred filter does not exist for the last six months.** The newest factors are one-sided extrapolations; when six more months arrive they become centred, and they change. That is not a flaw in the implementation — it is why concurrent adjustment revises at all, and no filter choice removes it. `scripts/seasonal_adjustment.py` implements exactly that core in ~40 lines of numpy, so the effect is visible rather than delegated to a binary that is not installed. It is **not** a substitute for X-13: no RegARIMA pre-adjustment, no outlier detection, no trading-day or holiday regressors, no SEATS. ## 3. ✅ Measured — how far a settled month's published value moves Synthetic monthly series, 300 months, seasonal amplitude 8.2 % of level at its widest and slowly evolving, irregular noise 0.35 %. Month-on-month movement in the **published** SA value for a month `age` months back, in percent of level: | age (months) | concurrent, mean | p95 | max | projected (annual), mean | new data possible? | |---|---|---|---|---|---| | 1 | 0.0213 | 0.0538 | 0.0949 | 0.0289 | yes | | 2 | 0.0213 | 0.0538 | 0.0949 | 0.0288 | yes | | 3 | 0.0213 | 0.0538 | 0.0949 | 0.0290 | **NO** | | **6** | **0.2301** | **0.5638** | **1.0198** | 0.0174 | **NO** | | 12 | 0.0157 | 0.0389 | 0.0693 | 0.0190 | **NO** | | 24 | 0.0070 | 0.0173 | 0.0308 | 0.0098 | **NO** | ⚠️ Ages 1–3 move by an identical amount here because this simplified filter gives every month inside the un-centred tail one shared end-normaliser; X-13's asymmetric end filters differ in that detail. **The rows that carry the point are 6 and beyond.** 🚨 **The largest single rewrite lands at age 6** — the month the centred trend filter finally reaches it: **0.23 % on average and 1.02 % at worst, in one month, on a number nobody collected any new data about.** ✅ Measured over its life, a settled month's published SA value ends **0.204 %** from where it first settled (max 0.576 %) and **travels 0.668 %** getting there. On US total nonfarm's ~158 million level, 0.01 % is 15,800 jobs — so the 12-month-old row (0.0157 %) is about **25,000 jobs a month arriving from nowhere**, on a series whose mean absolute first-to-third *sample* revision is 51,000. ## 4. 🚨 Measured — the phantom signal For each of 203 months, the over-the-month change **as it was published at the time** against **as it appears in the series you download today**: | | value | |---|---| | sd of the change, as published today | 601 | | sd of the change, in real time | 1,089 | | sd of the difference (revision) | 649 | | **revision sd / published-today sd** | **1.08** | | correlation between the two | 0.860 | 🚨 **26.1 % of the variation in the change you read today was not in the change that existed at the time, and the sign differs in 20.2 % of months.** None of that is new data — every month here is at least three months old. A momentum, acceleration or surprise feature computed on today's SA history is partly reading a factor update that arrived *after* the decision it is supposed to inform. 🔑 **And the re-adjustment is not wrong — that is what makes it dangerous.** ✅ Measured against the true adjusted series: the settled concurrent estimate has RMSE **0.187 %**, the real-time one **0.305 %**. Re-adjustment genuinely improves the history. It just makes it **a different series from the one anyone traded**. ## 5. ✅ Measured — three regimes, and what each one buys | regime | RMSE vs truth, settled | RMSE, real time | rewrite of a 12-month-old value | |---|---|---|---| | **concurrent** (CES today) | **0.187 %** | 0.305 % | 0.0157 % | | projected, annual factors | 0.199 % | **0.283 %** | 0.0190 % | | **frozen at the start** | 0.424 % | 0.424 % | **0.0000 %** | 🔑 **That is the whole trade in one table: accuracy of the history against stability of the history.** Frozen factors are the least accurate on a series whose seasonality drifts, and they are the only ones that never rewrite a published value. **A backtest needs the second column.** **The practical form:** keep the **NSA vintage** series, estimate your own factors on the data available at each decision date, and never let a later factor estimate touch an earlier published value. If you must use the agency's SA series, carry its vintages (`../real-time-macro-backtesting/SKILL.md` §2 lists the sources) and say which you used. ## 6. ✅ X-13ARIMA-SEATS in Python ✅ source-verified at `census.gov/data/software/x13as.html` (page updated 2025-07-10): *"X-13ARIMA-SEATS is seasonal adjustment software produced, distributed, and maintained by the Census Bureau"*, offering *"ARIMA model-based seasonal adjustment using a version of the SEATS software"* as well as *"nonparametric adjustments from the X-11 procedure"*, distributed *"for Windows® PC and Linux/Unix platforms"*. 🚨 **`pip install statsmodels` does not install the adjustment engine.** ✅ source-verified in `statsmodels/tsa/x13.py` (statsmodels 0.15.0, read in the installed package): ```python BINARY_NAMES = ("x13as", "x12a", "x13as_ascii", "x13as_html") BINARY_NAMES += tuple(f"{name}.exe" for name in BINARY_NAMES) # windows ``` `_find_x12` searches `X13PATH`, then `X12PATH`, then an explicit `x12path=`. With none of them, ✅ Measured by running it on this machine: ``` statsmodels.tools.sm_exceptions.X13NotFoundError: x12a and x13as not found on path. Give the path, put them on PATH, or set the X12PATH or X13PATH environmental variable. ``` The wrapper writes a spec file, shells out to the Census binary and parses its output; with no binary it raises before doing any work. **Download the binary from Census and set `X13PATH`.** 🔑 That also means **X-13 is not reproducible from a `requirements.txt`** — pin the binary version in your environment notes the way you pin a package. ⚠️ **What you are likely to reach for instead, and what it is not.** `statsmodels.tsa.seasonal.seasonal_decompose` is a plain ratio-to-moving-average with a *single fixed* seasonal profile — no evolving seasonality, no outlier handling, no calendar effects. `STL` (Cleveland et al.) does allow the seasonal to evolve and is a reasonable in-house choice, but neither reproduces an agency's published SA series, and using one to "check" an official number compares two different estimators. Both are in `../../../fin-models/skills/time-series-forecasting-models/SKILL.md`'s territory as decomposition tools; the point here is that they are **your** adjustment, so they are stable and point-in-time — which for a backtest is the property that matters. ## 7. Traps - 🚨 **Treating the SA series as data rather than as an estimate.** §3–4. - 🚨 **Computing a change or a momentum feature on today's SA history.** §4: a quarter of its variation and a fifth of its signs were not there at the time. - 🚨 **Diagnosing SA revisions with a vintage tool built for value revisions.** A first-to-third revision table will show nothing: the NSA input never changed. - 🚨 **Mixing SA and NSA in one model.** A ratio, a spread or a regression between an SA and an NSA series inherits the full seasonal on one side. Check both series' units and adjustment status before every join; FRED series IDs often differ only in a suffix. - 🚨 **Residual seasonality after aggregation.** Summing or differencing independently adjusted components does not give an adjusted aggregate, and quarterly GDP has a documented history of residual seasonality. If your "adjusted" series still shows a calendar-month pattern in its residuals, it is not adjusted. - 🚨 **Assuming an agency uses concurrent adjustment.** CES does — ✅ verified. Other programmes and other countries publish projected factors, sometimes a year ahead, and some publish the factors themselves. ⚠️ Check the specific programme's technical note; do not generalise from CES. - 🚨 **Comparing your own STL/seasonal_decompose output with the official SA series and calling the difference an error.** They are different estimators. The comparison that means something is your own adjustment against *itself* at two vintages. - 🚨 **The adjustment method is a trial.** Concurrent vs projected vs frozen, X-11 vs SEATS, the seasonal filter length, whether to log. Log them in `../../../fin-core/skills/backtest-validation/scripts/trial_ledger.py`. ## ❓ Not verified Which non-CES US programmes use concurrent versus projected factors · whether BEA's GDP seasonal adjustment carries published vintages · the exact asymmetric end filters X-13 uses (this script's simplified end handling is stated as such in §3) · the current X-13ARIMA-SEATS version number (the Census page showed an update date of 2025-07-10 but no version in the text that was retrieved). ## 8. Scripts and where this sits `scripts/seasonal_adjustment.py` — the X-11 ratio-to-moving-average core with time-varying factors, the three publication regimes (concurrent / projected / frozen) as publication-date x reference-month matrices, the rewrite profile and settled-drift measures, the phantom-signal decomposition, the accuracy comparison, and the X-13 availability probe. numpy + pandas, seed 20260909, about 3 s; `statsmodels` imported inside a function and the demo degrades gracefully without it or without the Census binary. - Revisions to the unadjusted value, and the vintage A/B — `../real-time-macro-backtesting/SKILL.md`. - Why the unemployment rate barely revises and payrolls do — `../macro-regime-and-recession-indicators/SKILL.md` §4. - When each print lands — `../macro-release-calendar-and-embargo/SKILL.md`. - Feeding an adjusted or unadjusted series to a mixed-frequency factor model — `../gdp-nowcasting-dynamic-factor/SKILL.md`. - Decomposition and forecasting tools in general — `../../../fin-models/skills/time-series-forecasting-models/SKILL.md`. - Where the SA and NSA series come from — `../../../fin-core/skills/fundamental-and-macro-data/SKILL.md`.