Sinewave

A sine wave has three main features: the amplitude, which is how far it rises and falls from its middle level; the period, which is the time taken to complete one full cycle; and the phase, which fixes where in the cycle it starts. Once these are known, the whole wave is known.

Its shape is symmetrical and smooth, with no sudden jumps. Many business patterns repeat in a roughly regular way.

A holiday retailer sells more every December, an ice cream seller peaks every summer, and a utility's electricity demand follows the seasons. Modelling these patterns with a sine wave gives a simple way to separate the regular cycle from the underlying trend.

Forecasters often combine a trend line with a sine term to describe seasonal sales. The trend shows long-term growth or decline, while the wave adds the repeating rise and fall around it.

This is a reasonable approximation when the seasonal pattern is smooth, though real data usually has irregular bumps as well. In market analysis, some traders use an indicator called the sine wave indicator, developed by the engineer John Ehlers, to detect cycles in prices.

It plots two lines that cross at suspected turning points. Many analysts are sceptical, because market cycles are not constant, and the signals work best when prices are cycling rather than trending.

Finance staff are most likely to meet the idea when building budgets and cash flow forecasts with seasonality. Knowing the amplitude of the seasonal swing tells you how much working capital you need at the peak.

It also shows how thin your cash cushion will be at the low point. A practical check is to compare the fitted wave with last year's actual figures month by month.

If the differences are small and random, the model is doing its job, but if they follow a pattern, a second cycle or a trend term is probably missing. Updating the amplitude each year keeps the forecast in line with the business as it grows.