Calculate seasonal indices from time series data, interpret an index as a percentage above or below the seasonal average, deseasonalise data by dividing by the index, and reseasonalise a forecast by multiplying by the index

What this dot point is asking

VCAA wants you to quantify and remove a repeating seasonal pattern from a time series. You calculate a seasonal index for each season (each quarter, month or day), interpret it as a percentage above or below the seasonal average, deseasonalise the raw data by dividing by the index, and later reseasonalise a forecast by multiplying by the index. This lets you fit a trend line to data with the seasonal wobble removed and then put the season back for a realistic forecast.

Calculating seasonal indices

For each cycle (for example each year of quarterly data), divide each season's value by that cycle's seasonal average (the mean of the four quarters). Average these ratios across all cycles for each season. If the resulting indices do not sum to the number of seasons, scale them so they do.

Interpreting a seasonal index

An index above $1$ means the season is above the yearly average; below $1$ means below it. Convert to a percentage by subtracting $1$: an index of $1.15$ is $15\%$ above average, an index of $0.92$ is $8\%$ below average.

Deseasonalising and reseasonalising

To strip out the seasonal effect, divide each actual value by its seasonal index:

To put the season back, for example when forecasting from a deseasonalised trend line, multiply:

Averaging indices across several cycles

When data covers more than one year, you compute a seasonal index for each season in each cycle, then average the matching seasons across the cycles to get one stable index per season. For example, with three years of quarterly data you would find three Q1 indices and average them for the final Q1 index, and similarly for Q2, Q3 and Q4. Averaging across cycles smooths out the irregular variation in any single year, so the resulting indices describe the typical seasonal pattern rather than one year's noise. After averaging, check the sum: the four quarterly indices must total $4$ (so the average is $1$); if they do not, rescale.

Rescaling indices that do not sum correctly

If the calculated indices do not sum to the number of seasons, multiply every index by a correction factor equal to (number of seasons) divided by (current sum). For quarterly data, if the four indices sum to $3.92$, the correction factor is $4 / 3.92 = 1.0204$, and each index is multiplied by this. After rescaling, confirm the new sum is exactly the number of seasons. This step is easy to forget under exam pressure but is genuinely assessed, because indices that do not average to $1$ would systematically bias every deseasonalised value.

The full forecasting workflow

Seasonal indices rarely stand alone; they are one stage of a forecasting pipeline. The standard sequence is: deseasonalise the raw series by dividing each value by its seasonal index, fit a least-squares trend line to the deseasonalised data with time numbered $1, 2, 3, \dots$, substitute the future time number to forecast the deseasonalised value, then reseasonalise by multiplying by the relevant season's index. Each stage carries marks, so set out the deseasonalised value, the trend-line forecast and the reseasonalised final answer as separate, clearly labelled lines. The single most common error is stopping at the deseasonalised forecast and forgetting to put the season back.

Why this matters for the exams

Seasonal index questions are a recurring written-response feature and reward careful direction: divide to deseasonalise, multiply to reseasonalise. Markers also check the interpretation sentence, so state the percentage above or below average. This dot point combines with the trend line from time series work: you deseasonalise, fit the trend, forecast, then reseasonalise for the final answer.