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12 exam-style questions with model answers, plus 16 quick multi-choice questions — every question on the site for this standard, grouped by the 4 pages of notes they come from.
Write a full answer before you reveal the model one — that comparison is where the marks come from. Every block links back to the notes that teach it.
Explain the difference between the trend, seasonal and irregular components of a time series.
A time series of monthly residential electricity demand for a New Zealand city shows a repeating annual pattern with peaks in June and July and troughs in January and February, and a slow upward trend across ten years. Describe these features and explain them in context.
A student is investigating quarterly sales for a New Zealand ice cream manufacturer over eight years. The seasonal swing between the Q1 peak and Q3 trough was about $180 000 in the first year and about $310 000 in the final year, while average quarterly sales roughly doubled over the period. The student fits an additive model. Evaluate this choice.
Explain why a 4-point moving average is used for quarterly data, and why it must be centred.
A student uses a 3-point moving average on quarterly data and finds the resulting trend still shows a regular zigzag. Explain what has gone wrong and what the consequence is.
A student's series of monthly hospital admissions shows a clear 12-month seasonal pattern, but also a sharp one-off spike in a single month caused by a major storm. She fits a centred 12-point moving average and notes the trend rises noticeably around that month. Discuss how she should handle this.
Three quarterly seasonal effects from an additive model are +5 200, −2 800 and −6 100. Find the fourth, and explain what a seasonal effect of +5 200 means.
A student's report says 'the Q4 seasonal effect is 12 400.' Explain what is missing from this statement and rewrite it properly for a series measuring quarterly retail sales in dollars.
A student deseasonalises a quarterly series of employment figures and finds the deseasonalised plot still shows a clear repeating pattern, with every Q1 sitting above the neighbouring points. Discuss what this indicates and how she should respond.
A trend is projected to be 8 400 units for the next quarter, whose seasonal effect is −1 250. Calculate the forecast and state one assumption it relies on.
A student forecasts quarterly café sales three years ahead from a five-year series. Explain why this forecast should not be relied on.
A student forecasting quarterly building consents in a region produces a figure and writes: 'The forecast for Q1 2025 is 842 consents. This assumes the trend continues and the seasonal pattern stays the same.' Evaluate this and explain how it could be improved to Excellence standard.