time series analysis using four period centred moving average to forecast sales

Marketing Analysis – Sales Forecasting (Cambridge IGCSE / A‑Level)

1. Objective

Show how a four‑period centred moving average (CMA) can be used to smooth a sales time‑series, estimate the underlying trend and produce a short‑term forecast. The note also links the technique to the wider marketing‑analysis framework required by syllabus 8.1 & 8.2.

2. Syllabus 8.1 – Core Marketing Concepts (Brief Coverage)

2.1 8.1.1 – Role of Marketing & Marketing Objectives

• Marketing creates, communicates and delivers value to customers, helping the organisation achieve its corporate goals.
• Typical objectives: increase market share, achieve a target sales volume, improve profitability, enhance brand image.
• Sales forecasts provide the quantitative basis for setting realistic, measurable objectives.

2.2 8.1.2 – Demand & Supply

• Demand determinants: price (price elasticity), consumer income, tastes & preferences, price of related goods (substitutes & complements), advertising.
• Supply determinants: production capacity, input costs, technology, government regulations.
• Forecasts must consider how changes in these factors could shift the demand curve or constrain supply.

2.3 8.1.3 – Markets (Type, Share, Growth)

Market Type	Definition	Example
Consumer (B2C)	Products bought by individuals for personal use	Smartphones, clothing
Industrial (B2B)	Products bought by organisations for production or operation	Machinery, raw materials
Local / National / International	Geographic scope of the market	Local bakery vs global fast‑food chain

Market‑share calculation (example):
If a company sells 12 000 units in a market where total sales are 60 000 units, market share = 12 000 ÷ 60 000 × 100 % = 20 %.

2.4 8.1.4 – Mass vs. Niche Marketing

Aspect	Mass Marketing	Niche Marketing
Target	Broad, undifferentiated audience	Specific, well‑defined segment
Product	Standardised, low‑cost	Specialised, often premium
Promotion	Wide‑reach media (TV, radio)	Targeted media, direct marketing
Risk	High competition, price wars	Limited market size, dependence on segment

2.5 8.1.5 – Market Segmentation

• Geographic: region, climate, urban/rural.
• Demographic: age, gender, income, education.
• Psychographic: lifestyle, values, personality.
• Behavioural: usage rate, loyalty, occasion.

Illustration: A sports‑wear brand may target 18‑30‑year‑old urban males (demographic) who value fitness and buy clothing for weekly gym sessions (behavioural).

2.6 8.1.6 – Customer‑Relationship Marketing (CRM)

• Goal: build long‑term, profitable relationships with customers.
• Key activities: loyalty programmes, personalised communication, after‑sales service.
• Benefits: higher repeat purchase rates, lower acquisition costs, richer data for forecasting.

3. Data Collection & Sampling (Primary & Secondary Research)

Before any quantitative analysis, verify that the data set is appropriate for the chosen method.

3.1 Sources of Data

• Primary data: sales registers, point‑of‑sale (POS) systems, customer surveys.
• Secondary data: industry reports, trade‑association statistics, government publications.

3.2 Sampling Checklist

1. Define the target population (e.g., all retail outlets selling the product).
2. Choose a sampling method (simple random, stratified by region, cluster).
3. Determine an adequate sample size (≥ 30 observations for basic analysis; use a confidence‑level calculator for more precision).
4. Validate data – check for missing values, outliers or recording errors.

4. Time‑Series Analysis Using a Four‑Period Centred Moving Average

4.1 Procedure Overview

1. Arrange the sales data chronologically (monthly, quarterly, etc.).
2. Compute the 4‑period simple moving averages (MA):
     MA_t = (Y_t + Y_t+1 + Y_t+2 + Y_t+3) ÷ 4
3. Because the period number is even, centre each MA by averaging two successive MAs:
     CMA_t+½ = (MA_t + MA_t+1) ÷ 2
4. The CMA series represents the smoothed **trend component**.
5. Extend the trend to the required future period(s). Two common approaches:
   • Assume the most recent change (Δ) continues.
   • Fit a simple linear regression to the CMA values and extrapolate.
6. If seasonality or irregular factors are known, add them to the trend forecast to obtain the final sales forecast.

4.2 Illustrative Example (Monthly Sales – £ 000)

Month	Sales (Yt)
Jan	48
Feb	52
Mar	55
Apr	60
May	58
Jun	63
Jul	66
Aug	70
Sep	68
Oct	73
Nov	75
Dec	78

Step 1 – 4‑Period Simple Moving Averages

Start‑Month	MAt (£ k)
Jan‑Apr	53.75
Feb‑May	56.25
Mar‑Jun	59.00
Apr‑Jul	61.75
May‑Aug	64.25
Jun‑Sep	66.75
Jul‑Oct	69.25
Aug‑Nov	71.50
Sep‑Dec	73.50

Step 2 – Centre the Moving Averages

Centred Period	CMAt+½ (£ k)
Feb‑Mar	55.00
Mar‑Apr	57.62
Apr‑May	60.38
May‑Jun	63.00
Jun‑Jul	65.50
Jul‑Aug	68.38
Aug‑Sep	70.38
Sep‑Oct	72.38
Oct‑Nov	74.38

Step 3 – Estimate the Trend Component

Recent change (Δ) = CMA_Oct‑Nov – CMA_Sep‑Oct = 74.38 – 72.38 = 2.00 £k per month.

Step 4 – Forecast the Next Period

Assuming the same increase continues:

• CMA_Dec‑Jan = 74.38 + 2.00 = 76.38 £k (centred on Jan).
• Because the CMA is centred, the forecast for **January (next year)** is 76.4 £k (rounded).

Forecast: £ 76.4 k sales in January of the following year.

5. Interpretation for Business Decision‑Making

• The upward trend of roughly £2 k per month indicates growing demand – review production capacity, inventory policies and raw‑material orders.
• If the forecast exceeds current stock levels, consider a temporary price promotion or increased distribution to avoid stock‑outs.
• Monitor actual sales against the forecast; persistent deviation may signal the need to incorporate seasonality or adopt a more sophisticated method (e.g., exponential smoothing).

6. Limitations of the Four‑Period CMA Method

• Does **not capture seasonality** – a separate seasonal index is required for products with strong seasonal patterns.
• Assumes a **linear trend**; accelerating or decelerating growth will bias the forecast.
• Relies only on historical data; unexpected market events (new competitor, regulatory change) are not reflected.
• Best suited for short‑term forecasts (1–3 periods ahead); longer horizons need more advanced techniques.

7. Integration into a Marketing Plan (Syllabus 8.2)

Once a reliable forecast is produced, it informs each element of the marketing mix and the budgeting process.

4 Ps	How the Forecast is Used
Product	Decide on line extensions, capacity expansion, or product‑life‑cycle timing.
Price	Set price levels that balance projected demand with desired margin; anticipate price‑elasticity effects.
Place (Distribution)	Adjust warehousing, logistics and channel coverage to meet the forecasted volume.
Promotion	Allocate advertising and sales‑force budgets proportionally to the expected sales lift.

Forecasts also underpin **marketing objectives** (e.g., “increase market share by 5 % in the next 12 months”) and the **budgeting process** (linking projected revenue to promotional spend).

8. Extending the Technique to International Markets (Syllabus 8.2.3)

• Apply the four‑period CMA separately to each geographic market (e.g., UK, Germany, Japan) after converting sales to a common currency.
• Account for differing seasonal patterns – opposite summer/winter cycles in hemispheres may require separate seasonal indices.
• Consider data availability: some markets may rely more heavily on secondary industry reports.
• If growth rates differ markedly, calculate separate trend estimates and compare them to guide entry strategies (direct investment, joint venture, exporting).

9. Quick Reference – Key Points to Remember

• Even‑period moving averages must be centred by averaging two successive MAs.
• The centred moving average isolates the trend component, removing short‑term random fluctuations.
• Forecasts are extensions of the identified trend; always verify the underlying assumptions (linearity, no seasonality).
• Combine quantitative forecasts with qualitative insights (Delphi, expert opinion) for a robust marketing plan.
• Link the forecast to the 4 Ps, budgeting, and international‑market decisions to demonstrate full syllabus integration.