Bias

The Bias is simply the arithmetic mean of the errors. We would, of course, like it to be zero. A
positive bias means that the model, on the average, forecasts low. Negative means the reverse.

Bias = ∑  (Actual-Forecast)

n

Mean Absolute Deviation

MAD penalizes all errors equally, in direct proportion to their magnitude.
You can interpret the MAD as meaning the amount by which the forecast model missed on the
average.

MAD = ∑  ABS(Actual-Forecast)

n

Mean Absolute Proportional Error (or Mean Absolute Percent Error).

This is like MAD, but
penalizes error on the basis of what proportion of the actual value it is rather than its raw numeric
amount.


MAPE = ∑  ABS(Actual-Forecast)
                   Actual                

n

Mean Square Error

MSE, as we usually call it, is very much like the simple variance you learned in
statistics. It penalizes larger errors much more heavily than smaller ones.

MSE =∑(Actual-Forecast)²

  n

Simple Exponential Smoothing

The Simple Exponential Smoothing model is of the form

F_t = ∂ª ´Yt-1 + (1-a)´Ft-1