Demand Analytics / Study 01 of 07

Seasonal Demand Modeling

Identifying the recurring annual demand curve

Question: Can a compact recurring annual curve support forward forecasting without assuming every year has the same demand level?
Method: Recurring annual demand curve; chronological comparison of seasonal specifications.
Evidence: 2024 development selected the full adaptive architecture (MAE 5.22). No seasonality-only holdout lift is reported.
Decision: Retain seasonality as the backbone; adapt its level using recent demand.

Business Question

Can a compact recurring annual curve support forward forecasting without assuming every year has the same demand level?

Why It Matters

A yearly average misses the spring ramp and seasonal decline. A separate estimate for every week can overfit when only two annual cycles are available for development.

Data / Method

The target is weekly New Customers: 104 development observations from 2023–2024 and 52 untouched holdout weeks from 2025. Month controls and Fourier harmonics were compared chronologically.

Analysis

The retained 52-week seasonal curve

Seasonal factor S(w) · fixed historical week buckets

Seasonal factor S(w)

Reconstructed directly from the published frozen Fourier coefficients. This is the seasonal factor on the New Customers + 1 scale, not the final weekly forecast.

View chart data

Week	Seasonal factor S(w)
1	1.06
2	1.19
3	1.37
4	1.63
5	1.99
6	2.46
7	3.08
8	3.85
9	4.81
10	5.96
11	7.27
12	8.70
13	10.18
14	11.64
15	12.98
16	14.14
17	15.04
18	15.68
19	16.06
20	16.20
21	16.16
22	15.99
23	15.73
24	15.44
25	15.12
26	14.81
27	14.49
28	14.15
29	13.78
30	13.35
31	12.82
32	12.19
33	11.42
34	10.54
35	9.55
36	8.48
37	7.39
38	6.32
39	5.31
40	4.40
41	3.60
42	2.94
43	2.39
44	1.96
45	1.63
46	1.38
47	1.20
48	1.07
49	0.99
50	0.95
51	0.95
52	0.98

The smooth annual shape shows a low-demand offseason, a ramp into higher demand, a broad high-demand period, and decline. These are descriptions of the fitted curve, not separately estimated calendar regimes.

2 harmonics

Four sine/cosine terms + intercept

Category controls

Separate effects for months or weeks

Method detail

Two harmonics supply four seasonal terms—one sine and one cosine at each frequency—plus an intercept. The seasonal factor is S(w) = exp(η(w)).

η(w) = 1.66650229 + 0.32560289 sin(2πw/52) − 1.35700057 cos(2πw/52) + 0.07409782 sin(4πw/52) − 0.32840420 cos(4πw/52)

Results

Development benchmark used to select the final architecture

2024 rolling-origin development MAE · weekly New Customers · full architectures, not the seasonal component alone

Adaptive seasonal K2 + six-week trend

5.22

Seasonal month mean

5.44

Recent four-week mean

5.51

Recent six-week mean

6.38

Same week prior year

6.98

Interpretation

Seasonality is necessary but not sufficient. Its role is to supply the recurring shape; the adaptive layers determine how high or low the current year is running.

Limitations

Only two complete annual cycles informed development. The 5.22 MAE belongs to the full adaptive seasonal architecture, not the Fourier curve alone.

How this fits into the forecasting system

Retained component: the seasonal backbone feeds normalization, adaptive level, and the final forecast.

Next: Environmental Demand Signals

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