Unit 4: Time series and reporting
Business Analytics for Decision Making notes · PTU syllabus (MBA 201-26)
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Unit summary
Many business series move with trends and seasons, and analysis is only useful when it reaches decision-makers clearly. This unit covers the components and methods of time series analysis, trend analysis by least squares, integration of predictive and descriptive models for forecasting and performance measurement, and the preparation and presentation of analytical reports and managerial recommendations.
After this unit you can
- Explain the components of a time series and methods of analysis
- Fit trends using the method of least squares
- Integrate descriptive and predictive models for forecasting and performance measurement
- Prepare and present analytical reports with recommendations
PTU syllabus topics
- Components and methods of time series
- trend analysis using least squares
- integration of predictive and descriptive models for forecasting and performance measurement
- preparation and presentation of analytical reports and managerial recommendations
Trend (T)
Long-run direction
Seasonal (S)
Regular yearly pattern
Cyclical (C)
Business-cycle swings
Irregular (I)
Random shocks
Models
Additive Y = T + S + C + I; multiplicative Y = T × S × C × I
Topic 1
Components and methods of time series analysis
Secular trend (T)
Long-term movement
Seasonal variation (S)
Regular within-year patterns
Cyclical variation (C)
Business cycles over years
Irregular variation (I)
Random, unpredictable events
- Models: additive Y = T + S + C + I; multiplicative Y = T × S × C × I.
- Measuring trend: freehand, semi-averages, moving averages, least squares.
Trend equation
Yc = a + bX
With X coded so ΣX = 0
a = ΣY ÷ n; b = ΣXY ÷ ΣX²
Example
Sales (₹ lakh) 2021–2025: 10, 12, 15, 16, 22; X = −2, −1, 0, 1, 2. ΣY = 75 → a = 15; ΣXY = −20 − 12 + 0 + 16 + 44 = 28; ΣX² = 10 → b = 2.8. Trend for 2026 (X = 3) = 15 + 8.4 = ₹23.4 lakh.
Topic 2
Moving averages and seasonal indices
Simple moving average
Average of the latest n periods
Exponential smoothing
Ft+1 = α At + (1 − α) Ft
Seasonal index (ratio to moving average)
Actual ÷ centred moving average × 100, averaged by season
Example
With α = 0.3, last forecast 500 and actual 540, the next forecast = 0.3 × 540 + 0.7 × 500 = 512.
- Deseasonalised data = actual ÷ seasonal index × 100 — shows the underlying trend.
- SPSS: Analyze → Forecasting → Create Traditional Models (Expert Modeler chooses exponential smoothing or ARIMA); Seasonal Decomposition is under Analyze → Forecasting.
Topic 3
Trend analysis by least squares
Straight line
Yc = a + bX
Normal equations
ΣY = na + bΣX; ΣXY = aΣX + bΣX²
With ΣX = 0
a = ΣY ÷ n; b = ΣXY ÷ ΣX²
Even number of years
Code X as −5, −3, −1, 1, 3, 5 (half-year units)
- Merits: objective, gives a trend value for every year and enables forecasting. Limitations: assumes a linear trend; adding data changes all values.
Topic 4
Integrating predictive and descriptive models
- Descriptive models establish the baseline — KPIs, segment profiles, seasonality.
- Predictive models forecast outcomes — demand, churn, default.
- 1Describe current performance
Dashboards and KPIs
- 2Diagnose drivers
Correlation, segmentation
- 3Predict
Forecast or classification models
- 4Prescribe
Targets, budgets, actions
- 5Monitor
Actual vs forecast, variance and model refresh
Example
A retail chain uses seasonal indices (descriptive) with a regression on promotions and price (predictive) to set monthly store targets, then tracks forecast vs actual on a Power BI dashboard.
Topic 5
Analytical reports and managerial recommendations
- 1
Executive summary
Key findings and recommendations first
- 2
Business problem and objectives
- 3
Data and methods
Sources, sample, tools, assumptions
- 4
Findings
Tables and charts with interpretation
- 5
Recommendations
Specific, actionable, with expected impact
- 6
Limitations and next steps
- 7
Appendix
Detailed output
- Presenting to managers: lead with the answer, translate statistics into business terms ("a ₹10 price cut raises volume by 6%"), one message per chart, quantify uncertainty, link to decisions and KPIs.
- Ethics: honest reporting of limitations, no cherry-picking or misleading charts, data privacy (DPDP Act 2023).
Key terms
- Secular trend
- Long-term movement of a time series
- Seasonal index
- Average seasonal effect expressed as a percentage
- Exponential smoothing
- Weighted average forecasting giving more weight to recent data
- Least squares
- Method minimising the sum of squared deviations
- Executive summary
- Brief overview of findings and recommendations
Quick revision
- Components T, S, C, I; additive and multiplicative models.
- Moving averages, exponential smoothing, seasonal indices.
- Least squares trend: Yc = a + bX, coding of X.
- Descriptive + predictive → prescriptive → monitor.
- Report structure; presenting insights; ethics.
Important exam questions
Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).
Short-answer questions
- Q1.Name the components of a time series.
- Q2.Distinguish additive and multiplicative models.
- Q3.What is exponential smoothing?
- Q4.State the normal equations for a straight-line trend.
- Q5.What is a seasonal index?
- Q6.What should an executive summary contain?
Long-answer questions
- Q1.Explain the components of a time series and methods of measuring trend.
- Q2.Fit a straight-line trend by least squares and forecast the next year (numerical).
- Q3.Discuss how descriptive and predictive models are integrated for forecasting and performance measurement.
- Q4.Explain how to prepare and present an analytical report with managerial recommendations.
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