Seasonal false alarms in customer churn and decline early-warning systems: adjacent-window labels confound seasonality with decline, and a year-over-year correction

Md Rezwanul Islam; Wael Mohammed

stat.APAug 17, 2026

Seasonal false alarms in customer churn and decline early-warning systems: adjacent-window labels confound seasonality with decline, and a year-over-year correction

Authors: Md Rezwanul Islam, Wael Mohammed

Organizations: Field Nation LLC, Minneapolis, MN, USA

Abstract

Customer decline early-warning systems feed account-manager action lists, and every flagged account consumes intervention capacity. In a deployed business-to-business marketplace system, one action-list slot in three went to flags that dissolve under a seasonally aligned label. The standard target in non-contractual churn prediction compares an entity's next k months of activity with its trailing k months. The two windows cover different calendar months, so for seasonal entities the threshold-ratio construction confounds seasonality with decline, and the event rate depends on the label's anchor calendar month. We formalize the mechanism and measure it on three public panels and the production panel (the public arms pre-specified). Of the adjacent-window decay events, 37--69% on the public panels and 28--50% in production have no counterpart under a seasonally aligned definition. Pooling anchors, the standard remedy, balances the training mixture but corrects no individual label. Measured alternatives repair the curve only partially or change the detection horizon. Aligning the baseline to the same k calendar months one year prior -- advice practitioners already state, here formalized, measured, and costed -- flattens the curve at the source. With the classifier held fixed, production holdout ROC-AUC rises from 0.767 to 0.864 for decline (different targets; the gap closes on synthetic ground truth and a production hindsight referee). The served action list shrinks by a third, 119 to 79 accounts. The measured price is extra history, a blind spot to decline-then-stabilization, and a stricter cut under sustained growth.

Figures & tables

Figure 1: Decay-event rate by anchor calendar month, pooled across years, for the adjacent-window label (red) and the year-over-year-aligned label (blue), on the joint set where both are defined. The dotted red line in the right panel is the adjacent label on its full valid set, which covers all twelve anchor months; its joint set spans seven anchors in a single observed year. Production panel omitted (proprietary); its curves are described in the text.

Panel	Entities	Obs.	Ratio	CV adj/yoy	$P_{b}$	Disagr. %
Prod., all buyers	2,001	51,509	1.3	0.090 / 0.020	$>$ 0.999	28 [26,29]
Prod., material cohort	496	18,597	2.4	0.284 / 0.054	$>$ 0.999	50 [45,54]
M5 store–items	2,000	84,742	2.1	0.249 / 0.047	$>$ 0.999	37 [34,39]
Tourism regions	274	47,503	2.4	0.195 / 0.090	$>$ 0.999	69 [65,72]
Retail II customers	298	1,444	4.5	0.366 / 0.246	0.998	37 [29,45]
M5 store–departments	70	3,290	no decay events occur			—

Table 1: The artifact and its correction across panels, every row under the unified protocol of Section 4.2 . Ratio is the max/min of the pooled anchor-month rates of the adjacent label on the joint set (twelve observed anchor months everywhere except Retail II: seven, in a single observed year); CV is the coefficient of variation across those rates;

P_{b}

is the entity-cluster bootstrap probability (1,000 draws) that the adjacent label’s CV exceeds the aligned label’s; Disagr. is the share of adjacent decay events with no aligned event, with 95% cluster-bootstrap intervals. Ratios use unrounded rates. Material cohort: the deployed $100K materiality floor applied to the full panel.

Figure 2: Synthetic amplitude sweep, 400 entities per amplitude (peak-to-trough swing

(1{+}a)/(1{-}a)

), 72 months,

k=6

\theta=0.5

. (a) False decay-event rate on the clean cohort. (b) Recall of injected

-60\%

level shifts: at seasonal amplitudes the adjacent label also misses genuine declines.

Label	History	FP syn	Recall syn	CV M5	CV tour	CV prod
Adjacent	12	9.2%	0.82	0.235	0.195	0.267
Deseason. (pooled idx)	18	9.5%	0.83	0.216	0.186	0.121
Deseason. (per-entity)	30	0.0%	0.90	0.158	0.084	0.107
Annual windows ( $k=12$ )	24	0.0%	0.95	0.070	0.050	0.056
Year-over-year aligned	18	0.0%	0.91	0.047	0.090	0.054

Table 2: Remedy arms under the unified engine (

k=6

\theta=0.5

unless stated). History is the months of data needed before the first label. Synthetic columns are ground truth (clean-cohort false-positive rate; recall of injected

-60\%

steps); panel columns are the anchor-month rate-curve CV on each arm’s own valid rows, which is why the adjacent row’s CVs differ slightly from Table 1 . The

k=12

arm detects a different event (annual decline) over a window twice as long, which is why its recall exceeds the others’.

Direction	Label	ROC-AUC	PR-AUC
Decay	adjacent-window	0.767	0.253
Decay	year-over-year aligned	0.864	0.367
Growth	adjacent-window	0.736	0.430
Growth	year-over-year aligned	0.857	0.743

Table 3: Production holdout comparison with features, learner, and temporal holdout held fixed; only the label definition changes.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 3: The construction and the confound in one picture. A purely seasonal entity (no trend, no decline) anchored just after its peak: the adjacent baseline (red span) covers the high season and the outcome window (grey span) the low season, so the label fires “decay” on seasonality alone; the year-over-year baseline (blue span) covers the same calendar months one year earlier and reads parity.

Figure 4: Aligned-label disagreement share of adjacent-window decay events, by seasonal-strength tercile of the entity.

Panel	Cell	CV adj/yoy	$P_{b}$	Disagr. %
M5 store–items	$\theta=0.4$	0.25 / 0.08	$>$ 0.999	33 [30, 35]
M5 store–items	$\theta=0.6$	0.24 / 0.03	$>$ 0.999	38 [36, 39]
M5 store–items	$k=3$	0.33 / 0.05	$>$ 0.999	37 [35, 39]
Tourism regions	$\theta=0.4$	0.22 / 0.09	$>$ 0.999	71 [68, 75]
Tourism regions	$\theta=0.6$	0.20 / 0.07	$>$ 0.999	66 [63, 69]
Tourism regions	$k=3$	0.16 / 0.08	$>$ 0.999	60 [57, 62]

Appendix

Table 4: Public-panel sensitivity cells (the main result is

k=6

\theta=0.5

; each row varies one element). CV pairs are adjacent/aligned;

P_{b}

is the entity-cluster bootstrap probability (1,000 draws) that the adjacent CV exceeds the aligned CV; Disagr. is the share of adjacent decay events with no aligned counterpart, with 95% cluster-bootstrap intervals.

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