# Median for forecasting in time series

I have a time series about demand of a product with many zeros.

I was reading the forecasting book by Hyndman and Athanasopoulos  (section 2.3), which mentioned the average method for forecasting time series.

I was wondering if is it possible to use a median method for forecasting time series?

 Hyndman, R.J. and Athanasopoulos, G. (2013)
Forecasting: principles and practice.
OTexts: Melbourne, Australia. Section 2/3. https://www.otexts.org/fpp/2/3 Accessed on August 18 2016.

Yes. It's quite possible to use a median as a forecast.

In situations where the location (level) and variability is not really changing over time, and the serial dependence between consecutive observations is weak, means or medians (or various other possible estimates of location) may be quite reasonable as forecasts.

Medians would tend to be more suitable than means when the distribution is peaky/heavy tailed, for example.

If you have a lot of zeros you may end up forecasting 0. That may be good or not so good depending on what kind of properties you seek.

The current trend in forecasting is to forecast the distribution of outcomes, e.g. take a look at fan charts popularized by Bank of England.

The expectation (mean) is a popular choice for a point forecast. However, there are many other kinds of point forecasts. For instance, the naive forecast: your forecast equals the last observed value. Hence, yes, you can use a median.

The reason why mean is used so much is because it happens to be an optimal point forecast, i.e. it minimizes the expected forecast error. However, depending on your lost function and the forecast error distribution the mean may be suboptimal, and some other point forecast would be better. In some cases that could be the median which is optimal.