Business Forecasting Topic 3 Flashcards

1
Q

purpose of decomposition

A
  • explore/identify characteristics of time series as a prelude to forecasting
  • pre processing
  • split data -> forecast
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2
Q

4 components of time series

A
  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
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3
Q

Trend cycle

A

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

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4
Q

Moving Averages

A
  • used to identify the trend (group not homogenous)
  • “average out” seasonal effects and smooth out random variation = isolate trend
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5
Q

Order of moving average

A

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)

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6
Q

Centred average

A

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

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7
Q

Seasonal variation models:

A
  1. Additive Model
  2. Multiplicative model
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8
Q

Additive model formulae

A

Y = T + S + E

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9
Q

Multiplicative model formulae

A

Y = T x S x E

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10
Q

Additive model

A

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

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11
Q

individual seasonal deviation

A

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
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12
Q

Average of individual seasonal deviations

A

means!
should sum to zero

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13
Q

adjust the seasonal deviations

A

to make sure they sum to zero

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14
Q

Deseasonalising data using additive model

A

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
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15
Q

crude forecasting using additive model

A
  1. extrapolate trend (possible judgment)
  2. add appropriate average seasonal deviation
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16
Q

Estimating the fit of the additive model for the data

A

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
17
Q

comparison

A

compare signal values to actual values

calculate errors then MSE

tells us how closely additive model fits time series

18
Q

multiplicative model

A

INDEX
- individual seasonal index

trend not linear = curved
Em

19
Q

individual seasonal index

A

actual sales divided by centred average

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

  • average out individual indices to remove random component
20
Q

adjusting individual seasonal index

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

4 divided by sum of average indices

21
Q

Deaseasonalising data using multiplicative model

A

deseasonalised observation = original observation / appropriate average seasonal index

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

22
Q

crude forecasting using multiplicative model

A
  1. extrapolate trend (judgment maybe)
  2. multiply the trend forecast by the appropriate average seasonal index
23
Q

fit of multiplicative model

A

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
24
Q

MSE comparisons for additive and multiplicative

A

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

25
Q

process of the seasonal variation models

A
  1. 4QMA
  2. centred average
  3. seasonal deviation/index
  4. adjusted values
  5. deseasonalise
26
Q

adjustment to seasonal deviation

A

required because of difference in seasonal patterns between cycles