Chapter 10 ADAM ARIMA
There are different ways to formulate and implement ARIMA. The one discussed in the previous section is the conventional way, and the model in that case can be estimate directly, assuming that its initialisation happens some time before the Big Bang: the conventional ARIMA assumes that there is no starting point of the model, we just observe a specific piece of data from a population without any beginning or end. Obviously this assumption is idealistic and does not necessarily agree with reality (imagine the series of infinitely lasting sales of Siemens S45 mobile phones. Do you even remember such thing?).
But besides the conventional formulation, there is also a state space form of ARIMA, implemented in SSOE (Rob J. Hyndman et al. 2008). I. Svetunkov and Boylan (2020b) adapted this state space model for supply chain forecasting, developing an order selection mechanism, sidesteping the hypothesis testing and focusing on information criteria. However, the main issue with this approach is that the resulting ARIMA model works very slow on the data with large frequencies (because the transition matrix becomes huge). Luckily, there is an alternative SSOE state space formulation, using the same idea of lags as ADAM ETS. This model is already implemented in
msarima() function of
smooth package and was also used as the basis for the ADAM ARIMA.
Hyndman, Rob J., Anne B. Koehler, J. Keith Ord, and Ralph D. Snyder. 2008. Forecasting with Exponential Smoothing. Springer Berlin Heidelberg.
Svetunkov, Ivan, and John E. 2020b. “State-space ARIMA for supply-chain forecasting.” International Journal of Production Research 58 (3): 818–27. https://doi.org/10.1080/00207543.2019.1600764.