EXPONENTIAL SMOOTHING: METHOD AND EXAMPLE - DUDAS - 2025

The exponential smoothing is a way to forecast the demand for an article for a given period. This method estimates that the demand will be equal to the average of the historical consumption in a given period, giving greater weight or weight to the values ​​that are closer in time. Additionally, for the following forecasts take into account the existing error of the current forecast.

Demand forecasting is the method of projecting customer demand for a product or service. This process is continuous, where managers use historical data to calculate what they expect the sales demand for a good or service to be.

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Information from the company's past is used by adding it to market economic data to see if sales will increase or decrease.

The results of the demand forecast are used to set goals for the sales department, trying to stay in line with the goals of the company.

Exponential smoothing method

Smoothing is a very common statistical process. Smoothed data is often found in various forms of everyday life. Every time an average is used to describe something, a smoothed number is being used.

Suppose the warmest winter on record was experienced this year. To quantify this, we start with the daily temperature data set for the winter period of each recorded historical year.

This generates a number of numbers with big “jumps”. You need a number that eliminates all these jumps from the data to make it easier to compare one winter with another.

Eliminating the jump in the data is called smoothing. In this case a simple average can be used to achieve smoothing.

Smoothing in the forecast

For forecasting demand, smoothing is also used to eliminate variations in historical demand. This allows for better identification of demand patterns, which can be used to estimate future demand.

The variations in demand is the same concept as the "jump" of the temperature data. The most common way that variations in demand history are removed is by using an average, or specifically, a moving average.

The moving average uses a predefined number of periods to calculate the average, and those periods move as time passes.

For example, if you use a four-month moving average and today is May 1, you will use the average demand for January, February, March, and April. On June 1, the demand for February, March, April and May will be used.

Weighted moving average

When using a simple average, the same importance is applied to each value in the data set. Therefore, in a four-month moving average, each month represents 25% of the moving average.

By using demand history to project future demand, it stands to reason that the most recent period has a greater impact on the forecast.

The moving average calculation can be adapted to apply different "weights" to each period to obtain the desired results.

These weights are expressed as percentages. The total of all weights for all periods must add up to 100%.

Therefore, if you want to apply 35% as the weight for the closest period in the four-month weighted average, you can subtract 35% from 100%, leaving 65% to divide between the three remaining periods.

For example, you can end up with a weighting of 15%, 20%, 30% and 35% respectively for the four months (15 + 20 + 30 + 35 = 100).

Exponential smoothing

The control input for the exponential smoothing calculation is known as the smoothing factor. Represents the weight applied to demand for the most recent period.

If 35% is used as the most recent period weight in the weighted moving average calculation, you could also choose to use 35% as the smoothing factor in the exponential smoothing calculation.

Exponential part

The difference in the exponential smoothing calculation is that instead of having to figure out how much weight to apply to each previous period, the smoothing factor is used to do that automatically.

This is the "exponential" part. If 35% is used as the smoothing factor, the demand weight for the most recent period will be 35%. The weighting of the demand from the period prior to the most recent one will be 65% of 35%.

65% comes from subtracting 35% from 100%. This equates to 22.75% weighting for that period. The demand for the next most recent period will be 65% from 65% from 35%, which is equal to 14.79%.

The previous period will be weighted as 65% of 65% of 65% of 35%, equivalent to 9.61%. This will be done for all previous periods, up to the first period.

Formula

The formula for calculating exponential smoothing is as follows: (D * S) + (P * (1-S)), where, D = most recent demand for the period.

S = smoothing factor, represented in decimal form (35% would be 0.35).

P = forecast of the most recent period, resulting from the smoothing calculation of the previous period.

Assuming that we have a smoothing factor of 0.35, we would then have: (D * 0.35) + (P * 0.65).

As you can see, the only data inputs required are the demand and the most recent period forecast.

Example

An insurance company has decided to expand its market to the largest city in the country, providing insurance for vehicles.

As an initial action, the company wants to forecast how much vehicle insurance will be bought by the inhabitants of this city.

To do this, they will use as initial data the amount of car insurance purchased in another smaller city.

The demand forecast for period 1 is 2,869 contracted vehicle insurance, but the real demand in that period was 3,200.

At the company's discretion, it assigns a smoothing factor of 0.35. The forecast demand for the next period is: P2 = (3200 * 0.35) + 2869 * (1-0.35) = 2984.85.

This same calculation was made for the entire year, obtaining the following comparative table between what was actually obtained and what was forecast for that month.

Compared to averaging techniques, exponential smoothing can predict the trend better. However, it still falls short, as shown in the graph:

It can be seen how the gray line of the forecast can be well below or above the blue line of demand, without being able to fully follow it.

References

1. Wikipedia (2019). Exponential smoothing. Taken from: es.wikipedia.org.
2. Ingenio Empresa (2016). How to use simple exponential smoothing to forecast demand. Taken from: ingenioempresa.com.
3. Dave Piasecki (2019). Exponential Smoothing Explained. Taken from: inventoryops.com.
4. Study (2019). Demand Forecasting Techniques: Moving Average & Exponential Smoothing. Taken from: study.com.
5. Cityu (2019). Exponential Smoothing Methods. Taken from: personal.cb.cityu.edu.hk.