The last blog post focused on probably the most popular and well-know family of forecasting models; exponential smoothing models. In this post, we’ll look at the next most well-known family of forecasting models; the ARIMA models.
ARIMA is an acronym for for “AutoRegressive Integrated Moving Average” that was developed in the 1960′s by the statisticians George Box and Gwilym Jenkins. It uses a different set of mathematical techniques than exponential smoothing that also aim at capturing trend, seasonal, cyclical, and error information in a time series (such as demand history) for the purpose of forecasting. It often gives more accurate forecasts than simpler exponential smoothing models with the trade-off of requiring more data up front.
Let’s illustrate forecasting with an ARIMA verses exponential smoothing forecasting with the data set from our previous post and the “auto.arima” and “ets” function from the R forecast package. We are using 5 years of data (1988-1992) and the following forecasts for 1993 get generated:
The accuracy of this model is a MASE value of 0.53 (and a MAPE of 5.21%). Our ETS model applied to the same series produces a slightly less accurate model at MASE=0.53 (and MAPE of 5.65%):
In the forecasting process being developed for Business Data Insights, we are examining both model families when the accuracy of both have MASE<1 and selecting the model with the lower number.
Next, we’ll be looking at cases where no model with a MASE<1 can be fit, so the most appropriate demand model becomes a bootstrapped distribution of demand during replenishment leadtime.
