Business Forecasting Topic 3 Flashcards
purpose of decomposition
- explore/identify characteristics of time series as a prelude to forecasting
- pre processing
- split data -> forecast
4 components of time series
- Trend (T) -> LT underlying movement
- Cyclical (C) -> movement from boom to slump (economic cycle)
- Seasonal (S)
- Irregular/Random (E) -> doesnt have pattern but calculated using T and S -> movements in time series not explained by other components
Trend cycle
trend and cycle grouped together
difficult to distinguish -> referred to as trend
Moving Averages
- used to identify the trend (group not homogenous)
- “average out” seasonal effects and smooth out random variation = isolate trend
Order of moving average
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)
Centred average
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
Seasonal variation models:
- Additive Model
- Multiplicative model
Additive model formulae
Y = T + S + E
Multiplicative model formulae
Y = T x S x E
Additive model
DEVIATION -> individual each observation
- represent seasonal pattern
- constant amplitude
- no change in width or height of seasonal period
Ea
individual seasonal deviation
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
Average of individual seasonal deviations
means!
should sum to zero
adjust the seasonal deviations
to make sure they sum to zero
Deseasonalising data using additive model
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
crude forecasting using additive model
- extrapolate trend (possible judgment)
- add appropriate average seasonal deviation