Exponential Smoothing: A Weighted Moving Average Approach to Forecasting

In this section, the speaker introduces exponential smoothing as a more advanced approach to forecasting. Exponential smoothing is a weighted moving average method that adjusts forecasts based on previous forecast errors.

Introduction to Exponential Smoothing

• Exponential smoothing is a weighted moving average approach to forecasting.

• It is a more advanced technique compared to naive, simple moving average, and weighted moving average methods.

• The forecast in time t is calculated using the forecast in time t-1 (last forecast) plus a smoothing parameter (alpha) multiplied by the difference between the actual sales in time t-1 and the last forecast.

Understanding Alpha and Weighting of Data

• The smoothing parameter (alpha) determines how much weight is given to recent data.

• A higher alpha value gives more weight to recent sales data, making the forecast more responsive to recent changes.

• A lower alpha value gives more weight to historical data, resulting in a smoother forecast.

Applying Exponential Smoothing

• To apply exponential smoothing, you need an initial forecast or level.

• The formula for calculating the forecast at each period involves using the previous forecast and adjusting it based on the difference between actual sales and the last forecast, multiplied by alpha.

• By iteratively applying this formula for each period, you can generate forecasts for future periods.

Example Calculation with Different Alpha Values

For example:

• Given actual sales data for weeks 1 to 6: 20, 22, 18, 21, 22

• Assuming an initial forecast of 20 for week 1

• Using alpha values of 0.1 and 0.3:

With alpha = 0.1:

• Week 2 Forecast = Previous Forecast + (Alpha * (Actual - Previous Forecast))

• Week 2 Forecast = 20 + (0.1 * (22 - 20)) = 20

• Week 3 Forecast = Previous Forecast + (Alpha * (Actual - Previous Forecast))

• Week 3 Forecast = 20 + (0.1 * (18 - 20)) = 20.2

• Week 4 Forecast = Previous Forecast + (Alpha * (Actual - Previous Forecast))

• Week 4 Forecast = 20.2 + (0.1 * (21 - 20.2)) = 19.98

• Week 5 Forecast = Previous Forecast + (Alpha * (Actual - Previous Forecast))

• Week 5 Forecast = 19.98 + (0.1 * (22 - 19.98)) = 20.1

• Week 6 Forecast = Previous Forecast + (Alpha * (Actual - Previous Forecast))

• Week 6 Forecast = 20.1 + (0.1 * (22 - 20.1)) = 20.3

With alpha = .03:

• Repeat the same calculations as above, but with alpha equal to .03.

Conclusion

Exponential smoothing is a weighted moving average approach that adjusts forecasts based on previous forecast errors and the smoothing parameter alpha.

By choosing different values for alpha, you can control the responsiveness of the forecast to recent sales data.

Higher alpha values give more weight to recent data, while lower alpha values give more weight to historical data, resulting in a smoother forecast.

It is important to keep track of which period you are forecasting and use the appropriate numbers in the calculations.