Forecast Solutions

Seasonal Forecasting with Seasonal Indices or Factors

In forecasting seasonality the aim is to best reflect in the forecast those changes in demand that occur across the year in a regular annual cycle.  This can be acheived by using additive seasonal factors based on plus or minus adjustments or multiplicative seasonal indices.  Seasonal indices have the benefit that they can be applied across a number of products if they logically should exhibit the same seasonal pattern.

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 genuinely exist, because that would adversely affect forecast accuracy. So, for those products where the existence of seasonality is not clear and obvious, it is important to make the best possible decision as to whether or not to include seasonality in the forecast. There are statistical tests that can help in this.

It is important to understand the way that seasonality is dealt with in any proprietary forecasting software that is used.  Common issues include whether or not the software tests for the significance of seasonality, how intermittent demand or extreme seasonality are treated, and if seasonal indices created at a product group level can be applied to individual products.

Forecast Solutions can provide an ad hoc service to test examples of your company's sales history for seasonality and to create a forecast, plus we can advise on suitable forecasting methods.  We can assess your current forecasting process and make recommendations for improvement. 

Contact us by email at or telephone 01844 291942.

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. One traditional method is the 'percent of year' approach, based on averages over several years, but of course the forecasting has to start with a full year forecast.  Other more satisfactory methods involve the creation of additive seasonal factors or seasonal indices.

Calculation of Seasonal Indices

If we are working with monthly data that is defined in 4wk, 4wk, 5 wk accounting months it is often helpful to first de-weight the historical data, for example to base it on a standard 4 wk period, so dividing the history for the 5 wk months by 1.25.  If this is done we have to remember to re-apply the weightings when calculating the final forecast.  This process can potentially be skipped if the business has always used the same accounting month pattern and will continue as such in the foreseeable future.  However, skipping it will force a seasonal analysis to be undertaken even if there is no valid seasonality and this may compromise forecast accuracy.

Period weightings may not be necessary if the months are simply calendar months. 

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 in the form of curves.

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 steps refer to seasonal index calculation in monthly data:

  1. Create a series for the centred annual moving average (CAMA) e.g. start by putting the monthly average for 2017 against June or July 2017 .

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

  3. Calculate the seasonal indices as the average of the ratios for each 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 them average exactly 1.00.

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 CAMA can be calculated based on June, then, separately, based on July and an average of the two calculated.  For most monthly data this refinement makes very little difference, but it would be important to carry outsomething like this if dealing with quarterly data.  The only downside of this 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 index 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), or flagging certain time periods to be excluded from the analysis, but a manual approach may be better if management time is available.

 Weekly Forecasting

Forecasting seasonality with of weekly data is often more difficult than with monthly data.  It becomes less likely that annual events, such as bank holidays, will take place in the same calendar period.  This necessitates data cleansing of past events from the sales history and event planning over the forecast horizon.

The fact of the matter is that there are not exactly 52 weeks per year, which is inconvenient when we want to calculate 52 seasonal indices and use them in forecasting.  In fact, if we take leap years into account, there are on average 52.18 weeks per year. 

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.  It helps if the seasonal indices can be calculated at a logical grouped level and then assigned to each member of the group.  Additionally, a number of approaches are possible to smooth out the weekly seasonal indices:

  • Seasonal simplification: If accounting months are defined on a 4wk/4wk/5wk basis, calculate calculate the monthly indices and assign to each week of the month.  Or aggregate the data to 4wk periods, calculate 13 period indices and assign to each week of the period.

  • Seasonal Smoothing: Apply a 3 wk or 5 wk centred moving average to the seasonal indices to smooth them out.  Repeat if necessary.

  • Consider using sophisticated forecasting methods, for example TBATS that uses fourier analysis in the seasonal calculation (using trigonometric sine and cosine waves).