Business Forecasting Topic 2

Question 1

three bias and Accuracy Measures types:

Answer 1

1. Simple/Absolute Measures
2. Relative Measures
3. Measures using naive-1 forecast as a benchmark

Question 2

Simple/Absolute measures

Answer 2

1. Mean Error (ME)
2. Mean Absolute Error (MAE)
3. Mean Squared Error (MSE)

Question 3

Relative measures

Answer 3

1. Mean Absolute Percentage Error (MAPE)
2. Media Absolute Percentage Error (MdAPE)

Question 4

Measures using naive-1 forecast as a benchmark

Answer 4

1. Median Relative Absolute Error (MdRAE)
2. Mean Absolute Scaled Error (MASE)

Question 5

Error equation

Answer 5

Actual - Forecast
under = +Ve sign
over = -Ve sign

Question 6

Mean Error

Answer 6

Total Error divided by number of periods
- accounts for positives and negatives (cancel each other out)
- measures BIAS!, unsuitable accuracy measure

Question 7

Mean Absolute Error

Answer 7

• 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

Question 8

Squared Error

Answer 8

(Actual - forecast) squared

• penalises large erros more severely
• may reflect cost of error

Question 9

Mean Squared Error

Answer 9

• 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

Question 10

Relative measures

Answer 10

• takes into account seriousness of error

Question 11

Absolute Percentage Error

Answer 11

(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.

Question 12

Mean Absolute Percentage Error

Answer 12

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

Question 13

Median Absolute Percentage Error

Answer 13

• put APE values in order and find middle value
• removes influence of extreme values

Question 14

Naive 1 Forecasts

Answer 14

• 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

Question 15

Relative Absolute Error

Answer 15

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.

Question 16

Median Relative Absolute Error
interpreting the values

Answer 16

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

Question 17

Median Relative Absolute Error

Answer 17

• 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

Question 18

problems with MdRAE

Answer 18

• 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)

Question 19

Absolute Scaled Error

Answer 19

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

Question 20

Mean Absolute Scale Error

Answer 20

MASE interpreted in same way as MdRAE

Add up all ASE divided by number of values

Question 21

Prediction intervals

Answer 21

formulae based on assumptions :
- forecast errors = normally distributed with a mean of zero
- errors observed in past = typical of those in future

Question 22

transformations & adjustments

Answer 22

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