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Sem 5 Prep
← OperationsForecast accuracy and trend

Formulas for this chapter

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
Step 2 of 24
The real wordsTheory

Error, and why it is monitored

Error = Actual - Forecast

Allowances should be made for forecast errors, and it is important to indicate the extent to which the forecast might deviate from the value that actually occurs.

Forecast errors should be monitored. If errors fall beyond acceptable bounds, corrective action may be necessary.

Keep the sign in the error column. A run of same-sign errors is bias, and bias is a different disease from noise.

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