Is It Seasonal or Structural? Retail Sales Trend Decomposition

UrbanMart's February 2026 sales (₹4,75,000) dropped 14.9% from January (₹5,58,000). The CEO is alarmed. The store manager says it's just the post-holiday seasonal dip. The regional analyst must decompose 3 years of monthly sales data using manual moving averages — before opening any spreadsheet — to determine who is right.

# Aplly.xyz Case Study Submission

## Title
Is It Seasonal or Structural? Retail Sales Trend Decomposition

## Type
Data Analytics

## Difficulty
Intermediate

## Estimated Time
75 minutes

## Overview
UrbanMart's February 2026 sales (₹4,75,000) dropped 14.9% from January (₹5,58,000). The CEO is alarmed. The store manager says it's just the post-holiday seasonal dip. The regional analyst must decompose 3 years of monthly sales data using manual moving averages — before opening any spreadsheet — to determine who is right.

## Case Details

Function Focus: Manual trend-cycle decomposition, moving-average calculation, seasonal index derivation, year-over-year comparison

Scenario:
UrbanMart's CEO saw the February numbers and emailed: "We're down 15% in a single month — what's going wrong?" The store manager replied: "Feb is always low after the holiday spike. Nothing to worry about." The regional analyst has 26 months of sales data (all of 2024 and 2025, plus Jan-Feb 2026). She must produce a one-page decomposition that separates trend from seasonality — by hand, with arithmetic shown — so the CEO gets a data-driven answer by end of day.

Dataset Structure:
- 26 months of monthly sales (₹'000s): Jan 2024 through Feb 2026
- No external market data or footfall counters — just the revenue line

Tasks:
1. Compute the year-over-year growth rate for Feb 2026 vs Feb 2025 — this is the simplest check the CEO would ask for
2. Calculate a 3-month centered moving average for the last 5 months (Oct 2025 through Feb 2026) to isolate short-term trend direction — do this manually, writing out each average
3. For each February in the dataset (2024, 2025, 2026), compute the seasonal ratio as: Feb sales ÷ average of the 12 months centered on that Feb (approximate using the calendar year average where a centered average is impractical)
4. Compare the Feb 2026 seasonal ratio against the Feb 2024 and Feb 2025 ratios — is Feb 2026 within normal seasonal range or is it an outlier?
5. Only after submitting your manual decomposition, re-run the analysis using a spreadsheet or AI tool and note any discrepancy in your conclusion

Expected Output:
A one-page memo containing: YoY growth calculation, 3-month moving averages table, seasonal ratios for each February, a clear conclusion ("seasonal" or "structural"), and a post-hoc note on any difference between the manual and tool-assisted analysis.

Evaluation Criteria:
Correct arithmetic on moving averages and ratios, proper interpretation of seasonal ratio consistency, quality of the conclusion (not just a number but a reasoned judgment), and honest discrepancy reporting between manual and tool-assisted results.

## Data Sources

| Year | Month | Sales (₹'000s) |
|---|---|---|
| 2024 | Jan | 4,80,000 |
| 2024 | Feb | 3,95,000 |
| 2024 | Mar | 4,10,000 |
| 2024 | Apr | 4,40,000 |
| 2024 | May | 4,65,000 |
| 2024 | Jun | 4,50,000 |
| 2024 | Jul | 4,75,000 |
| 2024 | Aug | 4,90,000 |
| 2024 | Sep | 5,10,000 |
| 2024 | Oct | 5,30,000 |
| 2024 | Nov | 5,65,000 |
| 2024 | Dec | 6,10,000 |
| 2025 | Jan | 5,20,000 |
| 2025 | Feb | 4,30,000 |
| 2025 | Mar | 4,50,000 |
| 2025 | Apr | 4,80,000 |
| 2025 | May | 5,05,000 |
| 2025 | Jun | 4,90,000 |
| 2025 | Jul | 5,15,000 |
| 2025 | Aug | 5,30,000 |
| 2025 | Sep | 5,50,000 |
| 2025 | Oct | 5,72,000 |
| 2025 | Nov | 6,08,000 |
| 2025 | Dec | 6,55,000 |
| 2026 | Jan | 5,58,000 |
| 2026 | Feb | 4,75,000 |

## Solution Frameworks
Time-series decomposition (trend-cycle vs seasonal), moving-average smoothing, seasonal index calculation, year-over-year analysis

## Solver Guidance & Tutorials
Link to: "Manual Time-Series Decomposition for Business Decisions" tutorial

## What You'll Learn
- Separating seasonal patterns from genuine trend changes without software
- Computing and interpreting moving averages by hand
- Using seasonal ratios to benchmark current performance
- Avoiding panic decisions from month-over-month comparisons that ignore seasonality

## Tags
seasonal decomposition, retail analytics, time series, trend analysis, business decision-making

## Registration Links
- Register as Solver
- Register as Evaluator

| Year | Month | Sales (₹'000s) |
|---|---|---|
| 2024 | Jan | 4,80,000 |
| 2024 | Feb | 3,95,000 |
| 2024 | Mar | 4,10,000 |
| 2024 | Apr | 4,40,000 |
| 2024 | May | 4,65,000 |
| 2024 | Jun | 4,50,000 |
| 2024 | Jul | 4,75,000 |
| 2024 | Aug | 4,90,000 |
| 2024 | Sep | 5,10,000 |
| 2024 | Oct | 5,30,000 |
| 2024 | Nov | 5,65,000 |
| 2024 | Dec | 6,10,000 |
| 2025 | Jan | 5,20,000 |
| 2025 | Feb | 4,30,000 |
| 2025 | Mar | 4,50,000 |
| 2025 | Apr | 4,80,000 |
| 2025 | May | 5,05,000 |
| 2025 | Jun | 4,90,000 |
| 2025 | Jul | 5,15,000 |
| 2025 | Aug | 5,30,000 |
| 2025 | Sep | 5,50,000 |
| 2025 | Oct | 5,72,000 |
| 2025 | Nov | 6,08,000 |
| 2025 | Dec | 6,55,000 |
| 2026 | Jan | 5,58,000 |
| 2026 | Feb | 4,75,000 |

Time-series decomposition (trend-cycle vs seasonal), moving-average smoothing, seasonal index calculation, year-over-year analysis