In this week’s What-if Wednesday post, Arkieva Supply Chain Optimization Consultant – Abhishek Shah – shares the results of a what-if demand forecast simulation using the gamma multiplicative forecast parameter of the Winters forecasting method.

In the previous blog, we experimented with Beta – the trend parameter of Holt-Winters Multiplicative method – to see how the forecast gets affected as the weight changes from 0.05 to 0.8.

This week we are going to run similar tests with Gamma, the seasonal parameter. We will use the same historical data set for our analysis. Similar to Alpha and Beta, Gamma values range from 0 to 1; and larger Gamma means more weight on recent historical seasonality.

For our analysis, we will keep the alpha and beta values at 0.05 each and will vary the Gamma values from 0.05 to 0.8 to evaluate how the forecast changes. You can see the numbers at the end of the post.

The first chart below shows historically observed values from the last three years and the subsequent graphs represent forecasts using a Gamma value of 0.05, 0.1, 0.2, 0.4, and 0.8.

## Statistical Forecasting Method: Holt-Winters Multiplicative Gamma Parameter Simulation Results

The overall behavior of the forecast with changing gamma is similar to what we saw with the additive method in the previous blog. There is little change in the seasonality of the forecast when Gamma values range from 0.05 to 0.4 but we notice that there is an uptick in the month of Mar’17 and Aug’17 as Gamma goes up to 0.8 which clearly indicates the influence of last one-year history (Mar’16). Also, just like the alpha and beta values in the multiplicative method, the seasonal changes, as we change gamma parameter from 0.05 to 0.8, are proportional to the level and not constant. You can compare the forecast from the previous method here.

[ Read Also: What-if Wednesday: Forecast Parameter Simulation &#8211; Beta Multiplicative Method ]

### What-if Scenario Forecast Numbers

 Month History Month ForecastG.05 ForecastG.1 ForecastG.2 ForecastG.4 ForecastG.8 Dec-13 62,719 Dec-16 41,248 41,326 41,462 41,789 43,721 Jan-14 60,312 Jan-17 39,915 40,318 41,014 42,065 43,612 Feb-14 38,119 Feb-17 37,090 36,554 35,774 35,195 36,506 Mar-14 51,926 Mar-17 41,412 41,927 43,009 45,346 50,492 Apr-14 64,856 Apr-17 43,968 44,038 44,132 44,227 44,827 May-14 67,589 May-17 43,173 43,292 43,325 42,689 39,633 Jun-14 57,151 Jun-17 41,235 41,089 40,847 40,557 40,791 Jul-14 53,502 Jul-17 41,233 41,417 41,747 42,192 41,778 Aug-14 47,696 Aug-17 41,134 41,181 41,425 42,389 45,259 Sep-14 49,189 Sep-17 42,343 42,458 42,842 44,109 47,811 Oct-14 62,103 Oct-17 43,111 43,498 44,186 45,268 46,822 Nov-14 45,289 Nov-17 40,362 40,228 40,077 40,108 40,530 Dec-14 38,105 Dec-17 39,785 39,872 40,033 40,414 42,397 Jan-15 45,149 Jan-18 38,784 39,164 39,830 40,865 42,477 Feb-15 38,361 Feb-18 36,398 35,922 35,233 34,749 36,061 Mar-15 46,655 Mar-18 40,473 40,953 41,967 44,174 49,117 Apr-15 44,090 Apr-18 42,916 42,994 43,112 43,270 43,992 May-15 51,350 May-18 42,303 42,424 42,484 41,968 39,291 Jun-15 40,574 Jun-18 40,641 40,519 40,323 40,110 40,441 Jul-15 52,236 Jul-18 40,717 40,894 41,217 41,675 41,420 Aug-15 44,306 Aug-18 40,695 40,747 40,989 41,917 44,685 Sep-15 43,866 Sep-18 41,842 41,957 42,328 43,535 47,084 Oct-15 45,607 Oct-18 42,581 42,941 43,589 44,633 46,212 Nov-15 45,457 Nov-18 40,144 40,031 39,912 39,980 40,456 Dec-15 47,582 Jan-16 46,313 Feb-16 39,110 Mar-16 56,107 Apr-16 48,553 May-16 39,483 Jun-16 43,245 Jul-16 41,954 Aug-16 48,323 Sep-16 52,052 Oct-16 49,837 Nov-16 41,619

So, in businesses where there have been quite some changes within the last one year that impacts seasonality – for example: acquired new customer or added another product line – which would continue in the subsequent years, then we might want to use higher values of Gamma so that the seasonality from the recent year is captured in the forecast moving forward.