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 Winters statistical forecasting method.

statistical forecasting method: what if scenario analysis forecasting beta multiplicative

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 dataset 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.

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 subsequent graphs represent forecasts using a Beta value of 0.05, 0.1, 0.2, 0.4 and 0.8.

Statistical Forecasting Method: Holt-Winters Multiplicative Beta Parameter Simulation Results

multiplicative forecast parameter simulation beta

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.

One can argue that when Beta is very high at 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 compared to October have as much to do with seasonality as they to do with the trend.

What-if Scenario Forecast Numbers

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 the next post, we will analyze how the seasonal parameter, Gamma, impacts the forecast.