Business Forecasting Topic 3

Question 1

purpose of decomposition

Answer 1

• explore/identify characteristics of time series as a prelude to forecasting
• pre processing
• split data -> forecast

Question 2

4 components of time series

Answer 2

1. Trend (T) -> LT underlying movement
2. Cyclical (C) -> movement from boom to slump (economic cycle)
3. Seasonal (S)
4. Irregular/Random (E) -> doesnt have pattern but calculated using T and S -> movements in time series not explained by other components

Question 3

Trend cycle

Answer 3

trend and cycle grouped together
difficult to distinguish -> referred to as trend

Question 4

Moving Averages

Answer 4

• used to identify the trend (group not homogenous)
• “average out” seasonal effects and smooth out random variation = isolate trend

Question 5

Order of moving average

Answer 5

even = centred moving average
high order = decrease accuracy = more numbers
higher order = less the loss of info about data
higher order = smoother trend cycle line (some essential data could be lost)

Question 6

Centred average

Answer 6

means of adjacent pairs of moving averages

needed to work out seasonal component easily by aligning centred average with data points

2 x 4QMA centred average = trend cycle component

Question 7

Seasonal variation models:

Answer 7

1. Additive Model
2. Multiplicative model

Question 8

Additive model formulae

Answer 8

Y = T + S + E

Question 9

Multiplicative model formulae

Answer 9

Y = T x S x E

Question 10

Additive model

Answer 10

DEVIATION -> individual each observation
- represent seasonal pattern
- constant amplitude
- no change in width or height of seasonal period
Ea

Question 11

individual seasonal deviation

Answer 11

actual sales - centred average

• tells us extent to which sales observation falls above or below trend (distance of sales from trend line)
  -contain element of randomness
• cant do for 1st and last 1 observations as dont have adjacent centred averages for these values

Question 12

Average of individual seasonal deviations

Answer 12

means!
should sum to zero

Question 13

adjust the seasonal deviations

Answer 13

to make sure they sum to zero

Question 14

Deseasonalising data using additive model

Answer 14

Deseasonalised observation = original observation - appropriate average seasonal deviation

• the sum of centred average and irregular component
• consists of the effects of trend (and cycle) and irregular factors (error)
• values represent both trend and error

Question 15

crude forecasting using additive model

Answer 15

1. extrapolate trend (possible judgment)
2. add appropriate average seasonal deviation

Question 16

Estimating the fit of the additive model for the data

Answer 16

since Y = T + S + E

-determine estimated values of signal (observations with noise removed) using…

estimated signal = centred average +average seasonal deviation for that time of year

• values only calculated for observations associated with centred average

Question 17

comparison

Answer 17

compare signal values to actual values

calculate errors then MSE

tells us how closely additive model fits time series

Question 18

multiplicative model

Answer 18

INDEX
- individual seasonal index

trend not linear = curved
Em

Question 19

individual seasonal index

Answer 19

actual sales divided by centred average

index > 1 = sales are above trend
< 1 sales below trend

• average out individual indices to remove random component

Question 20

adjusting individual seasonal index

Answer 20

• should have average value of 1 therefore if 4 quarters should sum to 4

4 divided by sum of average indices

Question 21

Deaseasonalising data using multiplicative model

Answer 21

deseasonalised observation = original observation / appropriate average seasonal index

deseasonalised observation consists of effects of trend ( & cycle) and irregular factors

Question 22

crude forecasting using multiplicative model

Answer 22

1. extrapolate trend (judgment maybe)
2. multiply the trend forecast by the appropriate average seasonal index

Question 23

fit of multiplicative model

Answer 23

Y = T x S x E

Estimating signal = centred average x average seasonal index

• only calculated for observations associated with centred average
• compare signal values with actual and calculate the MSE = tells us how closely the multiplicative model fits the time series

Question 24

MSE comparisons for additive and multiplicative

Answer 24

multiplicative MSE is smaller than additive - > suggests seasonal pattern is multiplicative

Question 25

process of the seasonal variation models

Answer 25

1. 4QMA
2. centred average
3. seasonal deviation/index
4. adjusted values
5. deseasonalise

Question 26

adjustment to seasonal deviation

Answer 26

required because of difference in seasonal patterns between cycles