APO DP – Forecast Model Parameters: Second-Order Exponential Smoothing (Holt Model)

This document reviews the impact of the parameters of the Second-Order Exponential Smoothing. The explanation follows a graphical approach without going into the heavy mathematics behind them.

This Forecasting model introduces a new statistical concept: Trend (Beta). It also uses the parameter Alpha, which was already introduced in the previous document:

APO DP – Forecast Model Parameters: First-Order Exponential Smoothing

1. Model Selection: Sales pattern

If you want to select a model manually, then you must analyze the historical data to determine whether a distinct pattern exists according to which you can manually select a model for the system.

Trend pattern:

If your historical data represents a suspected trend behavior, you can then select the second-order exponential smoothing (Holt Model).

Suppose that you have the following sales pattern, the constant forecast is clearly not appropriate here:

a = 0.3

We need to incorporate the significant trend Pattern, for this we use Beta.

Simple exponential smoothing does not do well when there is a trend in the data. In such situations, it could be useful to apply a second-order exponential smoothing Model (Holt Model). The basic idea behind double exponential smoothing (Holt Model) is to introduce a term to take into account the possibility of a series exhibiting some form of trend.

2. Forecast Model Parameters: Second-Order Exponential Smoothing – Holt Model

The 2nd order exponential smoothing model without the seasonal pattern is also called Holt Model. In the opposite, models with Seasonal patterns and no tred are called Winters.

Model Parameters:

Alpha factor:

The system uses the alpha factor for smoothing the basic value. If you do not specify an alpha factor, the system will automatically use the alpha factor 0.3.

Beta factor:

The system uses the beta factor for smoothing the trend.

In the following forecasting graphs you will see the impact of Beta (with a constant alpha = 0.3):

b = 0.1 / a = 0.3  -> (MAPE = 16.39)

b = 0.2 / a = 0.3  -> (MAPE = 15.45)

b = 0.3 / a = 0.3  -> (MAPE = 15.37)

b = 0.4 / a = 0.3  -> (MAPE = 15.86)

b = 0.5 / a = 0.3  -> (MAPE = 16.48) 

b = 0.6 / a = 0.3  -> (MAPE = 17.03)

b = 0.7 / a = 0.3  -> (MAPE = 17.51)

b = 0.8 / a = 0.3  -> (MAPE = 17.91)

b = 0.9 / a = 0.3  -> (MAPE = 18.31)

The choice of Beta is very important: the following table contains the monthly forecasting quantity of the different b beta factors for alpha = 0.3:

Note that the forecast got with beta 0.1 is 2 times bigger than the forecast got with beta 0.9.

Conclusion: 0.3 is a good compromise

• b (beta) close to 0: use a longer horizon to forecast the trend.
• b (beta) close to 1: will probably use only the last few values to estimate the trend.