Forecast Solutions

Seasonal Forecasting

The challenge in seasonal forecasting is to best reflect in the demand forecast those changes in demand that occur across the year in a regular annual cycle.  When there is marked or extreme seasonality in the demand pattern, the effectiveness in dealing with it will have great impact on forecast accuracy. 

The other side of the coin in seasonal forecasting is that it's important not to build seasonality into the forecast if it does not really exist, because that would adversely affect forecast accuracy. So when the existence of seasonality is ambiguous it is important to make the best possible decision as to whether or not to include seasonality in the forecast. Various statistical tests can help in this.

It is important to understand the way that seasonality is dealt with in any proprietary forecasting software that is used.

Forecast Solutions can provide an ad hoc service to test examples of your company's sales history for seasonality and create a forecast, plus we can advise on forecasting software

Contact us by email at or telephone 01844 291942.

Calculation Methods for Seasonality

Perhaps the simplest way to take seasonality into account is to make the forecast on a 'same as last year' basis.  This is not usually a good way to proceed because last year's sales may be abnormal for a number of possible reasons. Popular approaches include the 'percent of year' approach or the creation of additive seasonal factors or multiplicative seasonal indices.

In terms of calculating multiplicative seasonal indices there are a number of different methods.  Simple approaches include seasonal averaging and the ratio to centred moving average method, both mentioned below.  Other methods include fourier analysis, where sine and cosine waves are combined in order to represent the seasonal pattern.

Seasonal Average Method

This is a really simple method that can be used even when there are only two years of available history.  First, the average sales is calculated for each season e.g. each calendar month.  This gives the average for January, the average for February, etc. The grand average is then calculated as the average of the seasonal averages. Finally, the seasonal indices are created by dividing each seasonal average by the grand average. The indices will average 1.00.  This easy method is good when the sales history is stationery i.e. has not been subject to large changes in the underlying level of demand over time.  If there have been major changes, one option is to de-trend the historical data in some way before finalising the indices.  Alternatively, if three years or more of history is available it is better to employ the Ratio to Moving Average method, described below.

Ratio to Moving Average Method

The ratio to moving average method for calculation of multiplicative seasonal indices is a simple calculation that can easily be set up in Excel or other software. The following example for monthly data:

  1. Create a series for the centred annual moving average (CMA) e.g. start by putting the monthly average for 2013 against June 2013, etc.

  2. Calculate another series as the ratio of sales in a given month to the CMA at that month i.e. ratio = sales / CMA.

  3. Calculate the seasonal indices as the average the ratios per seasonal month e.g. the seasonal index for March is the average of the ratios for Mar-13, Mar-14, Mar-15 and Mar-16.  Adjust the indices if necessary to make the seasonal indices add to 12.00

Strictly speaking the centre of a 12 month calendar is not June or July, but in the middle of the two.  To be exact about it, the CMA can be calculated based on June, then, separately, based on July and an average of the two calculated.  For most monthly data the refinement makes little difference, but it would be important to carry it out if dealing with quarterly data.

The only downside of the Ratio to Moving Average method is that it requires a minimum of three years of sales history.

Data Cleansing and Data Volatility

It is a good idea to cleanse the sales history before carrying out a seasonal calculation, otherwise the inclusion of abnormal data is likely to distort the seasonal analysis and may lead to inaccurate forecasting.  This can sometimes be a difficult task as it is easy to confuse abnormal data with seasonality and normal volatility.  Some specialist software offers tools for identifying and correcting 'outliers' (abnormal data), but a manual approach may be better if time is available.

Seasonality in Weekly Forecasting

Seasonal analysis of weekly data is often more difficult than with monthly data.  It becomes less likely that annual events will take place in the same calendar period, so may necessitate cleansing those instances, such as bank holidays, from the sales history and adding future instances to the forecast as planned events.

The volatility of weekly information is inevitably greater than with months.  The result is often that a set of weekly seasonal indices may display a ragged effect due to the increased volatility.  A number of approaches are possible to smooth out the weekly indices, such as the following:

  • group seasonal indices (calculate the seasonal pattern at a group level, then assign the indices to each member of the group)

  • seasonal simplification (aggregate the history to 4 wk periods, calculate the 4 wk indices and assign to each week of the period)

  • seasonal smoothing (apply a 5 week centred moving average to the seasonal indices to smooth them out)

  • use sophisticated forecasting methods such as TBATS that incorporate fourier analysis in the seasonal calculation (using trigonometric sine and cosine waves)

At Forecast Solutions we can test examples of your company's sales history for seasonality, calculate a set of seasonal indices and create a forecast.  And we can advise on forecasting software.  Contact us by telephone or email.