Business Forecasting Topic 4

Question 1

Global models of time series

Answer 1

assume same trend or seasonal pattern applies to entire time series

Question 2

local models of time series

Answer 2

assume different trends or seasonal patterns can apply at different points in time

Question 3

exponential smoothing models

Answer 3

allow forecasts to take into account any changing patterns by updating estimates of patterns as new observation is available

• older/later data = less weight

Question 4

Simple (or single) exponential smoothing

Answer 4

• where series has flat trend
• subject to changes to new levels
• estimate current underlying level of time series (level when noise filtered out)
• estimate of current lvl = forecast for next period
• smooth out random fluctuations in series (not eliminate randomness)
• only works if not a trended series otherwise all same values

Question 5

SES forecasts formulae

Answer 5

ON SHEET!!
forecast = weighted average of latest observation and current forecast

• larger α = greater weight attached to most recent observation

more than 1 period ahead = one period ahead forecasts

Question 6

initial forecast for SES

Answer 6

required to start process
- average of past observations
- educated guess

Question 7

smoothing constant

Answer 7

α
0 = smooths thoroughly
1 = naive forecast

• value chosen to balance stability (not overact to freak figures) and sensitivity (respond to new conditions)
• α value with lowest MSE = produce future forecasts
• MSE over the fitting period, find optimal α to minimise MSE

Question 8

high α value

Answer 8

α = 1 = naive forecasts = shift 1 period
behave exactly like data
respond to sensitivity

Question 9

low α value

Answer 9

dont catch up data

Question 10

Exponentially weighted moving averages (EWMA)

Answer 10

each forecast = weighted average of all previous observations

most recent = highest weight
oldest = lower weight

Question 11

forecasting more than 1 period ahead

Answer 11

SES assume no upward or downward trend in time series = extrapolate flat line in future

• forecasts of more than 1 period ahead are identical to the one period ahead forecast

Question 12

advantages of SES

Answer 12

1. simple
2. easily automated
3. low data storage req
4. more accurate than many complicated methods

• large number forecast on regular basis

Question 13

tracking signals

Answer 13

• detect when forecasts = inaccurate
• α value needs to be adjusted

error high = tracking signal high = showing a widening gap between data and forecasts

Question 14

cumulative error

Answer 14

• if growing -> ideally values close to zero if unbiased forecasts
• alerts us when things are wrong

Question 15

issues with using cumulative error as method of alerting of issue

Answer 15

1. how large/small (small = -ve) does error have to be before alert
2. one large/unrepresentative error keeps it high/low -> even if subsequent forecasts are unbiased

Question 16

Smoothed error tracking signal formulae

Answer 16

• overcomes 2 problems of cumulative error

equation 1 = smoothes error by accounting for sign, expect close to 0 (errors of unbiased forecasts cancel each other)

tracking signal = close to zero = assume no problem

Question 17

Mt

Answer 17

estimate of mean absolute errors

forecast error large = mean absolute error = large = tolerant of smoothed mean error straying quite way from 0 before think there is problem

Question 18

adaptive response rate exponential smoothing (ARRSES)

Answer 18

tracking signal large = forecast failed to adapt, more sensitive = increase α
tracking signal small = coping well - small α will suffice

value of α varies denote value at period t

Question 19

formulae for ARRSES

Answer 19

Question 20

ARRSES strengths and limitations

Answer 20

• completely automated
• more attractive than SES if large numbers on regular basis
• unstable

Question 21

one period ahead forecast

Answer 21

main reason for = take into account the latest data

Question 22

data has continuous upward or continuous downward trend

Answer 22

SES forecasts will never be able to catch up with data

• forecasts cant catch as data is faster (increasing/decreasing)
• highest possible forecast, upward trend, α = 1 = naive forecast upward trend = forecast lagging behind data by 1 period