seasadj

X-11 style seasonal adjustment, generalized to an arbitrary cycle length. period=7 for the day-of-week cycle of daily data, period=24 for the daily cycle of hourly data, or any other cycle length your data has — X-13ARIMA-SEATS only handles monthly and quarterly data, and this package covers the rest.

日本語版 README

Why this exists

X-13ARIMA-SEATS is the standard tool for seasonal adjustment, but its X-11 core is hard-wired for monthly (period 12) or quarterly (period 4) data. More and more real series — daily data with a weekly cycle, hourly data with a daily cycle, etc. — don't fit that mold.

This package takes the X-11 procedure apart: outlier, holiday and level-shift adjustment and forecast extension are left to X-13ARIMA-SEATS's RegARIMA pre-adjustment, which works for any cycle length and has a proven track record. The cycle-length-bound X-11 core — moving averages, automatic seasonal filter selection, extreme-value replacement — is reimplemented here, generalized to any cycle length.

Features

• Multiplicative, additive and log-additive decomposition modes
• Log-additive mode includes the Thomson & Ozaki (2002) trend bias correction
• Outlier handling via SI ratios (X-11 extreme value replacement)
• Automatic seasonal filter selection (3x3/3x5/3x9) via the moving seasonality ratio (MSR)
• Automatic Henderson moving average term selection
• Zero dependencies (standard library only)

Install

pip install seasadj

Quick start

import math
from seasadj import decompose

# a synthetic series with a 7-day seasonal cycle
data = [100 + 0.05 * i + 20 * math.sin(2 * math.pi * i / 7) for i in range(400)]

result = decompose(data, period=7)

print(result.trend[:5])      # trend-cycle component
print(result.seasonal[:5])   # seasonal component
print(result.adjusted[:5])   # seasonally adjusted series
print(result.irregular[:5])  # irregular component

decompose() returns a Decomposition with trend, seasonal, adjusted and irregular series (all plain lists), plus the original observed series and diagnostics. For multiplicative/log models, prior_adjusted ≈ trend * seasonal * irregular; for the additive model, prior_adjusted ≈ trend + seasonal + irregular.

Preparing inputs with X-13ARIMA-SEATS

decompose() expects data that has already been adjusted for holidays, outliers and level shifts (or you can pass those effects directly — see the API reference below) and, optionally, a forecast extension. The usual way to get these is a RegARIMA run in X-13ARIMA-SEATS:

• Multiplicative or log model: run X-13 without a transform (or with transform function=none for the regressors), and use its multiplicative effect estimates (values near 1.0) as holiday_effect / ao_effect / ls_effect.
• Additive model: run X-13 with transform function=none, and use its additive effect estimates (values near 0.0, the "amount to subtract") as the same arguments.

Mixing the two — e.g. passing multiplicative-style effect factors while model="additive" — will silently produce a wrong adjustment, since the additive model treats the effect arguments as amounts to subtract, not factors to divide by.

File mode (Fortran-compatible CLI)

For compatibility with the original Fortran program, seasadj also has a file-based mode that reads a working directory laid out as in_data/ + para/ and writes out_data/:

seasadj <workdir>
# or
python -m seasadj <workdir>

See docs/porting-notes.ja.md for the file formats and module-to-Fortran-source mapping (developer-facing, Japanese).

API reference

decompose(data, period, **kwargs) -> Decomposition

Argument	Default	Description
data	required	Observed values (list/tuple/np.ndarray/pd.Series of numbers)
period	required	Seasonal cycle length (2 or larger), e.g. 7 for a day-of-week cycle
first_position	1	Cycle position of data[0] (1..period)
model	"multiplicative"	"multiplicative", "additive" or "log"
forecast	None	Forecast-extension values (e.g. from X-13ARIMA-SEATS)
holiday_effect	None	Holiday prior-adjustment factor per period
holiday_regressor	None	Holiday regression variable; required if holiday_effect and forecast are both given
holiday_coef	0.0	Holiday regression coefficient
ao_effect	None	Additive-outlier prior-adjustment factor
ls_effect	None	Level-shift prior-adjustment factor
seasonal_ma	3	Initial seasonal moving average term: 3, 5 or 9 (3x3/3x5/3x9)
replace_extreme	True	Outlier replacement (X-11 extreme value replacement)
sigma	(1.5, 2.5)	(lower, upper) sigma limits for outlier replacement
ft_o	1	Running position of the first observation (rarely changed)
verbose	False	If True, print progress lines; otherwise they land in diagnostics["log"]

Raises SeasadjError on invalid input. Validation reports the first failure it finds, checking data length before checking that values are positive (relevant for the multiplicative and log models).

Decomposition

All series are plain 0-based lists. n_total = n_observed + n_forecast; index n_observed onward is the forecast-extension period.

Field	Length	Content
observed	n_observed	The input data
prior_adjusted	n_total	Data after holiday/outlier/level-shift adjustment (log model: back-transformed to the original scale)
trend	n_total	Trend-cycle component
seasonal	n_total	Seasonal component
irregular	n_total	Irregular component
adjusted	n_total	Seasonally adjusted series
holiday_effect / ao_effect / ls_effect	n_total	The effect series actually applied
n_observed / n_forecast	int	Observed / forecast-extension length
period	int	Echoes the period argument
model	str	Echoes the model argument
diagnostics	dict	h_terms, sum_ratios, swm_term, msr_ratio, msr_count, si_replaced, bias_sig, log
internals	dict	Intermediate series (TC1, SI1, w1, SI1r, S1p, S1, A1, TC2, SI2, w2, SI2r, S2p) and ft_SI1; series-edge padding (0.0 / -999.0 / weight 1.0) follows the same convention as the file-mode output

Algorithm

The X-11 procedure estimates trend-cycle, seasonal and irregular components in three passes (initial trend → intermediate estimate → final estimate), each refining the previous one's seasonal factor and Henderson-filtered trend. This package generalizes every step — the seasonal moving average, the Henderson filter term selection, the moving seasonality ratio, the extreme-value replacement — from the fixed periods of the original X-11 (12 or 4) to an arbitrary period.

References: Dagum, E. B. (1988), The X-11-ARIMA/88 Seasonal Adjustment Method; the JDemetra+ X-11 theory documentation; Thomson, P. and Ozaki, T. (2002), trend bias correction for log-additive decomposition.

Development / testing

This package is a port of an original Fortran90 implementation (Ver16_00), verified against 7 frozen golden-test cases (not distributed with this package — see docs/porting-notes.ja.md) to match bit-for-bit. The tests distributed with this package (tests/test_api.py) instead check the decomposition identity and the equivalence of the API and file-mode code paths on artificial data.

pip install -e . pytest
python -m pytest tests/ -v

Citation

If you use this package in research, please cite:

Arita, Tetsuma (2022). "Assessment of the spread of COVID-19 in seven countries using a seasonal adjustment method." Statistical Journal of the IAOS. https://doi.org/10.3233/SJI-220932

A paper describing the Ver14-16 extensions implemented in this package (extreme SI-ratio replacement, additive/log-additive modes, Thomson & Ozaki trend bias correction) is in preparation; this citation will be updated once it is available.

License / Commercial use

seasadj is licensed under the GNU Affero General Public License v3.0 or later (AGPL-3.0-or-later) — see LICENSE.

If the AGPL's terms don't work for your use case (e.g. embedding in proprietary software), or if you are interested in research collaboration or customization, inquiries are welcome — please open an issue on GitHub to get in touch.