What if scenario forecast simulation: what is the effect of changing the beta parameter in Holt-Winters method?

In the previous blog, we experimented with Alpha – the intercept parameter of Holt-Winters 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 Beta, the trend parameter. We will use the same historical data set for our analysis. As we discussed in the last post about Alpha, Beta can also take values ranging from 0 to 1; and the larger the value of Beta the more weightage is on the recent historical trend.

[Read Previous: What-if Wednesday: Forecast Simulation – What Happens if You Change The Alpha Parameter in a Forecasting Method?]

## What if scenario forecast simulation Analysis Using The Beta Parameter

For our analysis, we will keep the alpha value at 0.05 and will vary the Beta value from 0.05 to 0.8 and 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 following graphs represent forecasts using a Beta value of 0.05, 0.1, 0.2, 0.4 and 0.8.

We observe that as the Beta value changes from 0.05 to 0.1 to 0.2, there is minimal impact on the forecast. The trend continues to follow a general downward trend that exists from the last 3 years. But as we make the parameter large and put more weightage on the recent trend – 40 and 80 percent – we see the forecast picking up based on the trend from the last 5-6 months.

[Related: Using What-if Scenarios To Create A Dynamic S&OP Paradigm ]

One can argue that when Beta is very high, 80%, the forecast should show a downward trend since the last months’ (Nov’16) actuals are less as compared to the previous month (Oct’16). But from the above charts, we see that it takes more than just 2 months to impact the trend, even when the parameter is set to be as high as 80%. Moreover, low values for November as compared to October have as much to do with seasonality as they have to do with the trend.

 Month History Month ForecastB.05 ForecastB.1 ForecastB.2 ForecastB.4 ForecastB.8 Dec-13 62,719 Dec-16 41,264 40,857 40,362 41,840 49,359 Jan-14 60,312 Jan-17 42,447 42,060 41,681 43,643 51,561 Feb-14 38,119 Feb-17 30,517 30,147 29,868 32,239 40,489 Mar-14 51,926 Mar-17 43,688 43,332 43,138 45,854 54,375 Apr-14 64,856 Apr-17 44,740 44,397 44,274 47,281 56,022 May-14 67,589 May-17 45,212 44,880 44,817 48,069 56,990 Jun-14 57,151 Jun-17 39,641 39,318 39,308 42,766 51,834 Jul-14 53,502 Jul-17 42,116 41,802 41,835 45,465 54,654 Aug-14 47,696 Aug-17 39,933 39,625 39,695 43,469 52,757 Sep-14 49,189 Sep-17 41,787 41,485 41,586 45,478 54,848 Oct-14 62,103 Oct-17 46,167 45,870 45,996 49,984 59,422 Nov-14 45,289 Nov-17 38,071 37,778 37,925 41,992 51,490 Dec-14 38,105 Dec-17 39,674 39,366 39,505 43,707 53,616 Jan-15 45,149 Jan-18 41,095 40,791 40,953 45,229 55,180 Feb-15 38,361 Feb-18 29,368 29,069 29,249 33,588 43,565 Mar-15 46,655 Mar-18 42,711 42,416 42,611 47,001 56,990 Apr-15 44,090 Apr-18 43,910 43,618 43,827 48,256 58,244 May-15 51,350 May-18 44,506 44,218 44,437 48,898 58,879 Jun-15 40,574 Jun-18 39,041 38,755 38,984 43,470 53,440 Jul-15 52,236 Jul-18 41,606 41,323 41,560 46,064 56,019 Aug-15 44,306 Aug-18 39,499 39,219 39,462 43,978 53,917 Sep-15 43,866 Sep-18 41,419 41,140 41,388 45,910 55,834 Oct-15 45,607 Oct-18 45,854 45,576 45,827 50,352 60,260 Nov-15 45,457 Nov-18 37,805 37,529 37,781 42,305 52,203 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, if there is a business case where a company has introduced a couple of new products and is seeing a growth in sales in the last 6 months, they can consider increasing the trend parameter so that the forecast follows the increasing trend.

In our next What-if Wednesday post, we will analyze how the seasonal parameter, Gamma, impacts the forecast.