Mean absolute deviation (MAD)
MAD = SUM |Actual - Forecast| / n
Comparing methods when all misses cost roughly in proportion to their size. Expressed in the units of the series.
- n
- Number of periods for which a forecast existed
- |Actual - Forecast|
- Absolute error in one period
Mean squared error (MSE)
MSE = SUM (Actual - Forecast)^2 / n
When one large miss is much more damaging than several small ones. Units are squared, so use it for comparison, not description.
- (Actual - Forecast)^2
- Squared error in one period
- n
- Number of error terms
Mean absolute percentage error (MAPE)
MAPE = [ SUM ( |Actual - Forecast| / Actual ) / n ] x 100
Comparing forecast quality across products or series of different sizes. Each ratio is taken on the actual, never the forecast.
- Actual
- The denominator of each period's ratio
- n
- Number of error terms
Seasonal relative
Relative = average demand in that season / overall average demand
Deseasonalise: data point / relative
Seasonal forecast: trend estimate x relative
When a series repeats within the year. Deseasonalise before fitting a trend, then re-season the extrapolated forecast.
- season
- The repeating slot: a month, a quarter, a day of the week
- relative
- Above 1 for a peak season, below 1 for a trough; the set should average about 1
Linear trend equation
F(t) = a + b t
When a plot shows a trend. Unlike averaging methods it extrapolates, so it can forecast several periods ahead.
- a
- Value of F(t) at t = 0, the fitted intercept
- b
- Slope: change in the forecast per period
- t
- Number of periods from t = 0
Least-squares estimates
b = ( n x SUM(t y) - SUM(t) x SUM(y) ) / ( n x SUM(t^2) - (SUM(t))^2 )
a = ( SUM(y) - b x SUM(t) ) / n
Fitting the trend line. Set out columns t, y, ty and t squared, total them, compute b first.
- n
- Number of periods in the fit
- y
- Value of the time series in that period
- SUM(t^2)
- Sum of squared periods, not the square of the sum