Add mean absolute deviations (MAD)

[mitchelloharawild]

Deviations using the forecast median rather than the forecast mean.
Requires distribution inputs (i.e. out-of-sample) until #137.

[robjhyndman]

Further to our discussion, MAD is usually median absolute deviation, where deviation refers to median-centred observations. e.g., stats::mad.

[mitchelloharawild]

Further to this median / mean distinction @robjhyndman, I am also contemplating the design of obtaining 'scaled errors' (not just scale in the MASE sense, but as scores, e.g. the ASE without the summary mean operation of MASE) for accuracy evaluation.

I find myself more interested in the density of scores rather than a 1-value summary for comparison. This also more naturally extends to computing summaries over other slices of the data (e.g. accuracy by horizon, by origin, by series, by model, etc.)

Do you have thoughts on using pre-summarised accuracy scores for evaluation?

[robjhyndman]

Sure, that makes sense. I guess the only issue is breaking changes