Business Forecasting Topic 2 Flashcards
three bias and Accuracy Measures types:
- Simple/Absolute Measures
- Relative Measures
- Measures using naive-1 forecast as a benchmark
Simple/Absolute measures
- Mean Error (ME)
- Mean Absolute Error (MAE)
- Mean Squared Error (MSE)
Relative measures
- Mean Absolute Percentage Error (MAPE)
- Media Absolute Percentage Error (MdAPE)
Measures using naive-1 forecast as a benchmark
- Median Relative Absolute Error (MdRAE)
- Mean Absolute Scaled Error (MASE)
Error equation
Actual - Forecast
under = +Ve sign
over = -Ve sign
Mean Error
Total Error divided by number of periods
- accounts for positives and negatives (cancel each other out)
- measures BIAS!, unsuitable accuracy measure
Mean Absolute Error
- remove negative signs
- divided by no. of points that is relevant to the data you have
- issue = dont know if over or under estimated
LOW MAE = few bigger errors - low = RSME is high (few large errors and others are small)
RMSE penalises the larger errors more than the MAE does
Squared Error
(Actual - forecast) squared
- penalises large erros more severely
- may reflect cost of error
Mean Squared Error
- square the errors then add then divide by number of points
- rid of +ve and -ve = cant see if over or under
- large values amplified
HIGH MSE = errors are smaller - easy to handle mathematically - MSE decomposed to smaller components = show cause of forecast error
- more difficult to interpret than MAE
- squaring = penalise larger severely vs MAE
RMSE penalises the larger errors more than the MAE does
Relative measures
- takes into account seriousness of error
Absolute Percentage Error
(Absolute error divided by actual ) x 100
- unaffected by unit of measurement
- one observation small (occasional low actual value) = APE very high
- actual is zero = APE is infinity (cant be calculated)
- very small value for one of the observations APE is very likely going to be higher than all other measures
APE is a relative measure with regards to the data value.
Mean Absolute Percentage Error
add up all APE divide by number of points
- affected by extreme values
- cant be calculated if any actual values are zero
- removes effect of the scale on which the forecast variable is measured
low value of MAPE = one of the best indicators of a good forecast
Median Absolute Percentage Error
- put APE values in order and find middle value
- removes influence of extreme values
Naive 1 Forecasts
- last observation -> forecast for next period
- forecasts from a random walk model
- compare accuracy of forecast with naive 1 = assess whether worth going to trouble of complex methods
Relative Absolute Error
comparing forecasting to naive 1 forecast
greater than 1 is bad forecast
ABSOLUTE VALUES
absolute forecast error / naive forecast error
RAE is related to comparing with Naive forecast where as the APE is a relative measure with regards to the data value.
Median Relative Absolute Error
interpreting the values
median of RAEs
MdRAE = 1 naive 1 method good as forecast method being evaluated
MdRAE < 1 method evaluated better than naive 1
MdRAE > 1 naive 1 more accurate than one being evaluated no point using
Median Relative Absolute Error
- easy interpret
- no squaring - large errors NOT penalised more heavily
- stops large occasional RAE = undue influence
- removes effect of scale on which forecast variable measured
- decide if worth using more complex forecasting method
- volatile/difficult to forecast = naive 1 = large errors -> MdRAE measures accuracy after allowing for difficulty
problems with MdRAE
- RAE cant have finite value when naive forecast = perfect accurate
- forecast error and naive error are zero -> RAE indeterminate = cant calculate MdRAE (MASE overcomes this)
Absolute Scaled Error
Absolute error / MAE of naive method
ASE measure addresses a problem/ problems the RAE measure has.
- Naive method gives a perfectly accurate forecast
- When the Naive method has very small errors
Mean Absolute Scale Error
MASE interpreted in same way as MdRAE
Add up all ASE divided by number of values
Prediction intervals
formulae based on assumptions :
- forecast errors = normally distributed with a mean of zero
- errors observed in past = typical of those in future
transformations & adjustments
make forecasting easier (% growth is easier to extrapolate)
e.g. log transform - useful series = subject to % growth (linear = use logarithm)
opposite of exponential is logarithm
