Business Forecasting Topic 5 Flashcards
extending simple exponential smoothing formulae
latest estimate = weighted average of 2 estimates of level
1. latest observation
2. previous estimate of level
larger α = more weight on more recent = more responsiveness to new situations
inaccuracy for SES
not accurate forecasting method when upward or downward trend or seasonal pattern
- forecasts tended to lag behind pattern
Holt’s method
- extension of SES
- produce forecasts where linear trend which is subject to changes
Holt method updates estimates of 2 values
after new observation
- underlying level of series at that point in time (changes period by period)
- the trend
trend
at a point in time
difference between levels in consecutive periods
Holt’s method of updating estimate of underlying level
- identical to SES but there is a trend in series - previous level not good guide for current level
- trend = expect level to change dont want previous level estimate on our weighted average -> overcome this by add our latest trend estimate to last period’s estimate of level
Holt’s method of updating the estimate of the trend
FORMULAE SHEET!
Holt’s method smoothing constant
different smoothing constant for the trend
β
between 0 and 1
- allows to have different degrees of responsiveness to changing levels and changing trends - if time series suggest this is appropriate
making a forecast for Holt’s method
FORMULAE SHEET!
- - add our latest trend estimate to latest level estimate
assume trend is linear = make forecasts for longer periods ahead
Holt’s method formulae summary
FORMULAE SHEET!
Holt’s method starting values
need initial for level and trend
LEVEL - set level equal to first observation
L1 - Y1
TREND - let initial trend estimate = difference between first 2 observations
b1= Y2-Y1
optimal α and β values
chosen to minimise MSE or some other measure
Excel solver used here
Holt’s method
- assume linear trend (increase at current rate)
- form of Holts = Damped Holts = assume future increase rate will gradually decline = damped trend projected
- method not used for seasonal data (unless deseasonalised)
- if α = β -> Brown’s double exponential smoothing (holt = more flexible than brown as different levels of responsiveness to changes on level and trend
- can handle horizontal pattern
- assign initial trend as zero and beta is 0 this becomes the SES method
underlying level = forecast if beta is zero
Holt-Winters method
- series have both trend and seasonal pattern both subject to change over time
- only handling multiplicative seasonality
Holt Winters updates estimates
new observations available:
- underlying level of sales
- underlying trend
- seasonal pattern
underpinning
- seasonal index -> ration of actual observation to height of underlying trend line - height represented by underlying level of series
= actual at time t divided by level at time t - deseasonalised value = actual value divided by appropriate average seasonal index
Holt winters method of updating the estimate of the level
- use deseasonalised latest observation
Holt Winters updating the estimate of the trend
same as Holt method
Holt Winters updating the estimate of the seasonal index for current season
- third smoothing constant ɣ
seasonal index smoothing constant for Holt Winters
ɣ gamma
between 0-1
closer to 1 indicates differing seasonal deviations across the cycles in the data
making a forecast for Holt Winters method
FORMUALE SHEET
Holt winters formulae
FORMULAE SHEET!
Holt Winters starting level value
LEVEL - average of monthly or quarterly observations for first year
Holt winters starting trend value
crude method -
monthly data = actual in yr 2 - actual in yr 1 divided by 12
quarterly data = actual in Q1 year 2 - actual in Q1 of year 1 divided by 4
Holt Winters starting seasonal index
actual for January or Q1 divided by starting level
holt winters optimal values α β ɣ
chosen to minimise MSE or other measure
Excel Solver
Holt’s Winters method
- assume trend is linear - assume increasing at current rate
- where think trend is changing but seasonal pattern is stable -> prefer to use Holt method on deseasonalised data then re-seasonalise to obtain forecast
impact of initial values
substantial impact deepens on values of alpha beta gamma and the length of the data series
linear trend
inherent randomness
stable seasonal pattern
holt method using deseasonalised data
