Fotios Petropoulos and I have recently written a paper about a statistical model, underlying Simple Moving Average. Although we are usually taught in Forecasting courses, that there is no such thing, we found one. We have submitted this paper to International Journal of Production Research, and it has been recently accepted (took us ~4 months). Frankly speaking, this is not a “break through” paper, but it should be interesting for a broad audience of academics and practitioners. The model discussed in this paper is already implemented in sma() function in smooth package for R.
Simple moving average (SMA) is a well-known forecasting method. It is easy to understand and interpret and easy to use, but it does not have an appropriate length selection mechanism and does not have an underlying statistical model. In this paper we show two statistical models underlying SMA and demonstrate that the automatic selection of the optimal length of the model can easily be done using this finding. We then evaluate the proposed model on a real dataset and compare its performance with other popular simple forecasting methods. We find that SMA performs better both in terms of point forecasts and prediction intervals in cases of normal and cumulative values.