Statistical Methods
Rebuild an index from successive percentage changes
Define the task
Check which value serves as the denominator for each reported percentage. Chaining is appropriate when each change is relative to the immediately preceding level of the same quantity. Percentage-point changes and changes from a fixed baseline require different arithmetic. Keep a record of rebasing, definition changes and missing periods.
Carry out the check
Set the starting index to 100 and convert each change to a multiplier by adding the percentage divided by 100 to one. Multiply the previous index by the new multiplier in sequence. Display intermediate levels so a reviewer can locate the first disagreement. Rounding published changes may prevent an exact match to the final published level.
Worked hypothetical example
For a hypothetical activity index, a rise of 20% followed by a fall of 20% produces levels 120 and 96. The cumulative change is a loss of 4%. Starting from 96 would require an increase of about 4.167% to return to 100. A percentage change from a zero base is undefined. A missing change cannot silently be treated as zero.
Method checked 10 November 2026 against R documentation: Cumulative Sums, Products, and Extremes.