Extreme Forecasting
1
Extreme Forecasting
Rob J Hyndman
Business & Economic Forecasting Unit
Extreme Forecasting
My perspective
2
Extreme Forecasting
My perspective
2
Extreme Forecasting
My perspective
2
Extreme Forecasting
My perspective
2
Extreme Forecasting
My perspective
2
Extreme Forecasting
My perspective
2
Extreme Forecasting
My perspective
2
Extreme Forecasting
My perspective
2
Extreme Forecasting
My perspective
By focusing on simplistic problems,
textbooks give the impression that
forecasting is easy, leading to badly
trained forecasters.
3
Extreme Forecasting
My perspective
By focusing on simplistic problems,
textbooks give the impression that
forecasting is easy, leading to badly
trained forecasters.
Real-world problems are often much more
difficult than existing forecasting methods
can handle.
3
Extreme Forecasting
My perspective
By focusing on simplistic problems,
textbooks give the impression that
forecasting is easy, leading to badly
trained forecasters.
Real-world problems are often much more
difficult than existing forecasting methods
can handle.
Many research papers tackle “small”
problems rather than the “big” problems
that arise in commercial forecasting.
3
Extreme Forecasting
My perspective
By focusing on simplistic problems,
textbooks give the impression that
forecasting is easy, leading to badly
trained forecasters.
Real-world problems are often much more
difficult than existing forecasting methods
can handle.
Many research papers tackle “small”
problems rather than the “big” problems
that arise in commercial forecasting.
Commercial forecasting problems can (and
should) motivate research.
3
Extreme Forecasting
Three case studies
1
Weekly airline passenger traffic: Ansett
Australia.
4
Extreme Forecasting
Three case studies
1
2
Weekly airline passenger traffic: Ansett
Australia.
Monthly government expenditure on
pharmaceutical benefits: Federal
Government of Australia.
4
Extreme Forecasting
Three case studies
1
2
3
Weekly airline passenger traffic: Ansett
Australia.
Monthly government expenditure on
pharmaceutical benefits: Federal
Government of Australia.
Half-hourly peak electricity demand:
Electricity planning council of South
Australia.
4
Extreme Forecasting
Three case studies
1
2
3
Weekly airline passenger traffic: Ansett
Australia.
Monthly government expenditure on
pharmaceutical benefits: Federal
Government of Australia.
Half-hourly peak electricity demand:
Electricity planning council of South
Australia.
4
Extreme Forecasting
Three case studies
1
2
3
Weekly airline passenger traffic: Ansett
Australia.
Monthly government expenditure on
pharmaceutical benefits: Federal
Government of Australia.
Half-hourly peak electricity demand:
Electricity planning council of South
Australia.
Highly complex data for which no standard models
were suitable.
4
Extreme Forecasting
Three case studies
1
2
3
Weekly airline passenger traffic: Ansett
Australia.
Monthly government expenditure on
pharmaceutical benefits: Federal
Government of Australia.
Half-hourly peak electricity demand:
Electricity planning council of South
Australia.
Highly complex data for which no standard models
were suitable.
Real-world complications that textbooks (and often
journals) don’t cover.
4
Extreme Forecasting
Three case studies
1
2
3
Weekly airline passenger traffic: Ansett
Australia.
Monthly government expenditure on
pharmaceutical benefits: Federal
Government of Australia.
Half-hourly peak electricity demand:
Electricity planning council of South
Australia.
Highly complex data for which no standard models
were suitable.
Real-world complications that textbooks (and often
journals) don’t cover.
Problems motivated some of my research papers.
4
Extreme Forecasting
Extremely messy data
Outline
1
Extremely messy data
2
Extremely expensive forecast errors
3
Extreme electricity demand
4
Extremely useful conclusions
5
Extreme Forecasting
Airline passenger traffic
Extremely messy data
6
Extreme Forecasting
Extremely messy data
Airline passenger traffic
0.0
1.0
2.0
First class passengers: Melbourne−Sydney
1988
1989
1990
1991
1992
1993
1992
1993
1992
1993
Year
0 2 4 6 8
Business class passengers: Melbourne−Sydney
1988
1989
1990
1991
Year
0
10
20
30
Economy class passengers: Melbourne−Sydney
1988
1989
1990
1991
Year
7
Extreme Forecasting
Extremely messy data
8
Airline passenger traffic
Weekly data with either 52 week or 53 week “years”.
Extreme Forecasting
Extremely messy data
8
Airline passenger traffic
Weekly data with either 52 week or 53 week “years”.
School holidays at different times in different cities.
Extreme Forecasting
Extremely messy data
8
Airline passenger traffic
Weekly data with either 52 week or 53 week “years”.
School holidays at different times in different cities.
Easter in different weeks each year.
Extreme Forecasting
Extremely messy data
8
Airline passenger traffic
Weekly data with either 52 week or 53 week “years”.
School holidays at different times in different cities.
Easter in different weeks each year.
Changing seasonality due to changes in travel
habits
Extreme Forecasting
Extremely messy data
8
Airline passenger traffic
Weekly data with either 52 week or 53 week “years”.
School holidays at different times in different cities.
Easter in different weeks each year.
Changing seasonality due to changes in travel
habits
Major industrial dispute led to almost no traffic for
several months in 1989.
Extreme Forecasting
Extremely messy data
8
Airline passenger traffic
Weekly data with either 52 week or 53 week “years”.
School holidays at different times in different cities.
Easter in different weeks each year.
Changing seasonality due to changes in travel
habits
Major industrial dispute led to almost no traffic for
several months in 1989.
Change of definition of “first class”, “business class”
and “economy class” for a few months in 1992.
Extreme Forecasting
Extremely messy data
8
Airline passenger traffic
Weekly data with either 52 week or 53 week “years”.
School holidays at different times in different cities.
Easter in different weeks each year.
Changing seasonality due to changes in travel
habits
Major industrial dispute led to almost no traffic for
several months in 1989.
Change of definition of “first class”, “business class”
and “economy class” for a few months in 1992.
New cut-price airline launched and failed during the
data period.
Extreme Forecasting
Extremely messy data
8
Airline passenger traffic
Weekly data with either 52 week or 53 week “years”.
School holidays at different times in different cities.
Easter in different weeks each year.
Changing seasonality due to changes in travel
habits
Major industrial dispute led to almost no traffic for
several months in 1989.
Change of definition of “first class”, “business class”
and “economy class” for a few months in 1992.
New cut-price airline launched and failed during the
data period.
Some missing data
Extreme Forecasting
Extremely messy data
8
Airline passenger traffic
Weekly data with either 52 week or 53 week “years”.
School holidays at different times in different cities.
Easter in different weeks each year.
Changing seasonality due to changes in travel
habits
Major industrial dispute led to almost no traffic for
several months in 1989.
Change of definition of “first class”, “business class”
and “economy class” for a few months in 1992.
New cut-price airline launched and failed during the
data period.
Some missing data
Forecasts required for several months ahead.
Extreme Forecasting
Extremely messy data
9
Airline passenger traffic
First class passengers: Melbourne−Sydney
2.0
1.0
1.6
−1.5
0.0
remainder
1.0
trend
2.2
−1.0
0.0
seasonal
0.0
data
STL decomposition
1988
1989
1990
time
1991
1992
1993
Extreme Forecasting
Extremely messy data
9
Airline passenger traffic
2.0
1.0
1.6
−1.5
0.0
remainder
1.0
trend
2.2
−1.0
0.0
seasonal
0.0
data
First class passengers: Melbourne−Sydney
1988
1989
1990
time
1991
1992
1993
Extreme Forecasting
Extremely messy data
9
Airline passenger traffic
4
0.0
−1.0
2.5
1.5
0
2
4
6
remainder
8
0.5
trend
seasonal
0
data
8
Business class passengers: Melbourne−Sydney
1988
1989
1990
time
1991
1992
1993
Extreme Forecasting
Extremely messy data
9
Airline passenger traffic
10 20 30
24
−20
−5
5
remainder
20
trend
−8
−4
0
seasonal
0
data
Economy class passengers: Melbourne−Sydney
1988
1989
1990
time
1991
1992
1993
Extreme Forecasting
Extremely messy data
Airline passenger traffic
Statistical models tend not to be able to
allow for the effects seen in these data.
10
Extreme Forecasting
Extremely messy data
Airline passenger traffic
Statistical models tend not to be able to
allow for the effects seen in these data.
A common approach is to use “cleaned”
data where the time series are
reconstructed to look like what might have
been if there were no strikes, no changes
of definition, etc.
10
Extreme Forecasting
Extremely messy data
Airline passenger traffic
Statistical models tend not to be able to
allow for the effects seen in these data.
A common approach is to use “cleaned”
data where the time series are
reconstructed to look like what might have
been if there were no strikes, no changes
of definition, etc.
Probably has small effect on point
forecasts, but may have large effect on
prediction intervals.
10
Extreme Forecasting
Extremely messy data
Airline passenger traffic
25
20
15
10
5
0
Passengers (thousands)
30
35
Economy Class Passengers: Melbourne−Sydney
1988
1989
1990
1991
1992
1993
11
Extreme Forecasting
Extremely messy data
Airline passenger traffic
25
20
15
10
5
0
Passengers (thousands)
30
35
Economy Class Passengers: Melbourne−Sydney
1988
1989
1990
1991
1992
1993
11
Extreme Forecasting
Extremely messy data
Airline passenger traffic
25
20
15
10
5
0
Passengers (thousands)
30
35
Economy Class Passengers: Melbourne−Sydney
1988
1989
1990
1991
1992
1993
11
Extreme Forecasting
Extremely messy data
Possible model
Yt = Yt∗ + Zt
Yt∗ = β0 +
X
βj xt,j + Nt
j
Yt = observed data for one passenger class.
Yt∗ = reconstructed data.
Zt = latent process (usually equal to zero).
xt,j are covariates and dummy variables.
Nt = seasonal ARIMA process of period 52.
12
Extreme Forecasting
Extremely messy data
Possible model
Yt = Yt∗ + Zt
Yt∗ = β0 +
X
βj xt,j + Nt
j
Yt = observed data for one passenger class.
Yt∗ = reconstructed data.
Zt = latent process (usually equal to zero).
xt,j are covariates and dummy variables.
Nt = seasonal ARIMA process of period 52.
Research issues
How to model Zt in the presence of industrial
action and changing definitions?
12
Extreme Forecasting
Extremely messy data
Possible model
Yt = Yt∗ + Zt
Yt∗ = β0 +
X
βj xt,j + Nt
j
Yt = observed data for one passenger class.
Yt∗ = reconstructed data.
Zt = latent process (usually equal to zero).
xt,j are covariates and dummy variables.
Nt = seasonal ARIMA process of period 52.
Research issues
What to do with the non-integer seasonality?
(average 52.19)?
12
Extreme Forecasting
Extremely messy data
Possible model
Yt = Yt∗ + Zt
Yt∗ = β0 +
X
βj xt,j + Nt
j
Yt = observed data for one passenger class.
Yt∗ = reconstructed data.
Zt = latent process (usually equal to zero).
xt,j are covariates and dummy variables.
Nt = seasonal ARIMA process of period 52.
Research issues
How to deal with the correlations between
classes and between routes?
12
Extreme Forecasting
Extremely expensive forecast errors
Outline
1
Extremely messy data
2
Extremely expensive forecast errors
3
Extreme electricity demand
4
Extremely useful conclusions
13
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
14
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
The Pharmaceutical Benefits Scheme (PBS)
is the Australian government drugs subsidy
scheme.
15
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
The Pharmaceutical Benefits Scheme (PBS)
is the Australian government drugs subsidy
scheme.
Many drugs bought from pharmacies
(“drug stores” in the US) are subsidised to
allow more equitable access to modern drugs.
15
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
The Pharmaceutical Benefits Scheme (PBS)
is the Australian government drugs subsidy
scheme.
Many drugs bought from pharmacies
(“drug stores” in the US) are subsidised to
allow more equitable access to modern drugs.
The cost to government is determined by
the number and types of drugs purchased.
Currently nearly 1% of GDP.
15
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
The Pharmaceutical Benefits Scheme (PBS)
is the Australian government drugs subsidy
scheme.
Many drugs bought from pharmacies
(“drug stores” in the US) are subsidised to
allow more equitable access to modern drugs.
The cost to government is determined by
the number and types of drugs purchased.
Currently nearly 1% of GDP.
The total cost is budgeted based on
forecasts of drug usage.
15
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
16
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
In 2001: $4.5 billion budget,
under-forecasted by $800 million.
17
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
In 2001: $4.5 billion budget,
under-forecasted by $800 million.
Thousands of products. Seasonal demand.
17
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
In 2001: $4.5 billion budget,
under-forecasted by $800 million.
Thousands of products. Seasonal demand.
Subject to covert marketing, volatile
products, uncontrollable expenditure.
17
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
In 2001: $4.5 billion budget,
under-forecasted by $800 million.
Thousands of products. Seasonal demand.
Subject to covert marketing, volatile
products, uncontrollable expenditure.
Although monthly data available for 10
years, data are aggregated to annual
values, and only the first three years are
used in estimating the forecasts.
17
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
In 2001: $4.5 billion budget,
under-forecasted by $800 million.
Thousands of products. Seasonal demand.
Subject to covert marketing, volatile
products, uncontrollable expenditure.
Although monthly data available for 10
years, data are aggregated to annual
values, and only the first three years are
used in estimating the forecasts.
All forecasts being done with the FORECAST
function in MS-Excel!
17
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
New drugs forecasts and new policy
impacts estimated using judgemental
methods.
18
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
New drugs forecasts and new policy
impacts estimated using judgemental
methods.
Monthly data on thousands of drug groups
and 4 concession types available from 1991.
18
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
New drugs forecasts and new policy
impacts estimated using judgemental
methods.
Monthly data on thousands of drug groups
and 4 concession types available from 1991.
Method needs to be automated and
implemented within Excel.
18
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
New drugs forecasts and new policy
impacts estimated using judgemental
methods.
Monthly data on thousands of drug groups
and 4 concession types available from 1991.
Method needs to be automated and
implemented within Excel.
Exponential smoothing seems appropriate
(monthly data with changing trends and
seasonal patterns), but in 2001,
automated exponential smoothing was not
well-developed.
18
Extreme Forecasting
Extremely expensive forecast errors
ATC drug classification
A
B
C
D
G
H
J
L
M
N
P
R
S
V
Alimentary tract and metabolism
Blood and blood forming organs
Cardiovascular system
Dermatologicals
Genito-urinary system and sex hormones
Systemic hormonal preparations, excluding sex hormones and insulins
Anti-infectives for systemic use
Antineoplastic and immunomodulating agents
Musculo-skeletal system
Nervous system
Antiparasitic products, insecticides and repellents
Respiratory system
Sensory organs
Various
19
Extreme Forecasting
Extremely expensive forecast errors
20
ATC drug classification
14 classes
A
84 classes
A10
A10B
Alimentary tract and metabolism
Drugs used in diabetes
Blood glucose lowering drugs
A10BA
Biguanides
A10BA02
Metformin
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
Research issues
1
How to automate exponential smoothing
to give robust and reliable forecasts for a
wide range of time series?
21
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
Research issues
1
2
How to automate exponential smoothing
to give robust and reliable forecasts for a
wide range of time series?
How to generate prediction intervals for all
varieties of exponential smoothing
forecasts?
21
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
Research issues
1
2
3
How to automate exponential smoothing
to give robust and reliable forecasts for a
wide range of time series?
How to generate prediction intervals for all
varieties of exponential smoothing
forecasts?
Data can be disaggregated at five levels of
a drug hierarchy. At what level of
disaggregation should we forecast?
21
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
Research issues
1
2
3
4
How to automate exponential smoothing
to give robust and reliable forecasts for a
wide range of time series?
How to generate prediction intervals for all
varieties of exponential smoothing
forecasts?
Data can be disaggregated at five levels of
a drug hierarchy. At what level of
disaggregation should we forecast?
How can correlations and substitutions
between drugs be handled across a very
large hierarchy of time series?
21
Extreme Forecasting
Extremely expensive forecast errors
Total cost: A03 concession safety net group
600
400
200
0
$ thousands
800
1000
1200
PBS data
1995
2000
Time
2005
22
Extreme Forecasting
Extremely expensive forecast errors
PBS data
100
50
0
$ thousands
150
200
Total cost: A05 general copayments group
1995
2000
Time
2005
22
Extreme Forecasting
Extremely expensive forecast errors
Total cost: D01 general copayments group
400
300
200
100
0
$ thousands
500
600
700
PBS data
1995
2000
Time
2005
22
Extreme Forecasting
Extremely expensive forecast errors
PBS data
1000
500
0
$ thousands
1500
Total cost: S01 general copayments group
1995
2000
Time
2005
22
Extreme Forecasting
Extremely expensive forecast errors
PBS data
4000
3000
2000
1000
$ thousands
5000
Total cost: R03 general copayments group
1995
2000
Time
2005
22
Extreme Forecasting
Extremely expensive forecast errors
Exponential smoothing
Exponential smoothing is extremely
popular, simple to implement, and
performs well in forecasting competitions.
23
Extreme Forecasting
Extremely expensive forecast errors
Exponential smoothing
Exponential smoothing is extremely
popular, simple to implement, and
performs well in forecasting competitions.
“Unfortunately, exponential
smoothing methods do not
allow easy calculation of prediction intervals.”
Makridakis, Wheelwright
and Hyndman, p.177.
(Wiley, 3rd ed., 1998)
23
Extreme Forecasting
Extremely expensive forecast errors
Exponential smoothing
JASA, 1997
24
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
As part of this project, we developed an
automatic forecasting algorithm for
exponential smoothing state space models
based on the AIC.
25
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
As part of this project, we developed an
automatic forecasting algorithm for
exponential smoothing state space models
based on the AIC.
Exponential smoothing models allowed for
time-changing trend and seasonal
patterns.
25
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
As part of this project, we developed an
automatic forecasting algorithm for
exponential smoothing state space models
based on the AIC.
Exponential smoothing models allowed for
time-changing trend and seasonal
patterns.
State space models provide prediction
intervals which give a sense of uncertainty.
25
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
As part of this project, we developed an
automatic forecasting algorithm for
exponential smoothing state space models
based on the AIC.
Exponential smoothing models allowed for
time-changing trend and seasonal
patterns.
State space models provide prediction
intervals which give a sense of uncertainty.
Forecast MAPE reduced from 15–20% to
about 0.6%.
25
Extreme Forecasting
Extremely expensive forecast errors
Total cost: A03 concession safety net group
600
400
200
0
$ thousands
800
1000
1200
Forecasting the PBS
1995
2000
2005
2010
26
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
150
100
50
0
$ thousands
200
250
Total cost: A05 general copayments group
1995
2000
2005
2010
26
Extreme Forecasting
Extremely expensive forecast errors
Total cost: D01 general copayments group
400
300
200
100
0
$ thousands
500
600
700
Forecasting the PBS
1995
2000
2005
2010
26
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
4000
3000
2000
1000
0
$ thousands
5000
6000
Total cost: S01 general copayments group
1995
2000
2005
2010
26
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
1000 2000 3000 4000 5000 6000 7000
$ thousands
Total cost: R03 general copayments group
1995
2000
2005
2010
26
Extreme Forecasting
Extremely expensive forecast errors
Exponential smoothing
Since 2002. . .
a general class of state space models
proposed underlying all the common
exponential smoothing methods.
27
Extreme Forecasting
Extremely expensive forecast errors
Exponential smoothing
Since 2002. . .
a general class of state space models
proposed underlying all the common
exponential smoothing methods.
analytical results for prediction intervals.
27
Extreme Forecasting
Extremely expensive forecast errors
Exponential smoothing
Since 2002. . .
a general class of state space models
proposed underlying all the common
exponential smoothing methods.
analytical results for prediction intervals.
likelihood calculation for estimation.
27
Extreme Forecasting
Extremely expensive forecast errors
Exponential smoothing
Since 2002. . .
a general class of state space models
proposed underlying all the common
exponential smoothing methods.
analytical results for prediction intervals.
likelihood calculation for estimation.
AIC for model selection.
27
Extreme Forecasting
Extremely expensive forecast errors
Exponential smoothing
Since 2002. . .
a general class of state space models
proposed underlying all the common
exponential smoothing methods.
analytical results for prediction intervals.
likelihood calculation for estimation.
AIC for model selection.
an algorithm for automatic forecasting
using the new class of models.
27
Extreme Forecasting
Extremely expensive forecast errors
Exponential smoothing
Since 2002. . .
a general class of state space models
proposed underlying all the common
exponential smoothing methods.
analytical results for prediction intervals.
likelihood calculation for estimation.
AIC for model selection.
an algorithm for automatic forecasting
using the new class of models.
new results on admissible parameter space.
27
Extreme Forecasting
Extremely expensive forecast errors
Exponential smoothing
Since 2002. . .
a general class of state space models
proposed underlying all the common
exponential smoothing methods.
analytical results for prediction intervals.
likelihood calculation for estimation.
AIC for model selection.
an algorithm for automatic forecasting
using the new class of models.
new results on admissible parameter space.
algorithm now part of forecast package in R.
27
Extreme Forecasting
Extremely expensive forecast errors
28
Recent book
Springer Series in Statistics
Rob J. Hyndman · Anne B. Koehler
J. Keith Ord · Ralph D. Snyder
Forecasting
with Exponential
Smoothing
The State Space Approach
13
State space modeling
framework
Prediction intervals
Model selection
Maximum likelihood
estimation
All the important research
results in one place with
consistent notation
Many new results
375 pages but only
US$54.95 / £33.99 / e38.88
Extreme Forecasting
Extremely expensive forecast errors
28
Recent book
State space modeling
framework
Prediction intervals
Rob J. Hyndman · Anne B. Koehler
Model selection
J. Keith Ord · Ralph D. Snyder
Maximum likelihood
Forecasting
estimation
with Exponential
All the important research
Smoothing
results in one place with
consistent notation
The State Space Approach
Many new results
375 pages but only
13
US$54.95 / £33.99 / e38.88
www.exponentialsmoothing.net
Springer Series in Statistics
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
Research issues
1
2
3
4
How to automate exponential smoothing
to give robust and reliable forecasts for a
wide range of time series?
How to generate prediction intervals for all
varieties of exponential smoothing
forecasts?
Data can be disaggregated at five levels of
a drug hierarchy. At what level of
disaggregation should we forecast?
How can correlations and substitutions
between drugs be handled across a very
large hierarchy of time series?
29
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
"
Research issues
1
2
3
4
How to automate exponential smoothing
to give robust and reliable forecasts for a
wide range of time series?
How to generate prediction intervals for all
varieties of exponential smoothing
forecasts?
Data can be disaggregated at five levels of
a drug hierarchy. At what level of
disaggregation should we forecast?
How can correlations and substitutions
between drugs be handled across a very
large hierarchy of time series?
29
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
"
"
Research issues
1
2
3
4
How to automate exponential smoothing
to give robust and reliable forecasts for a
wide range of time series?
How to generate prediction intervals for all
varieties of exponential smoothing
forecasts?
Data can be disaggregated at five levels of
a drug hierarchy. At what level of
disaggregation should we forecast?
How can correlations and substitutions
between drugs be handled across a very
large hierarchy of time series?
29
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
"
"
Research issues
1
2
3
?
4
How to automate exponential smoothing
to give robust and reliable forecasts for a
wide range of time series?
How to generate prediction intervals for all
varieties of exponential smoothing
forecasts?
Data can be disaggregated at five levels of
a drug hierarchy. At what level of
disaggregation should we forecast?
How can correlations and substitutions
between drugs be handled across a very
large hierarchy of time series?
29
Extreme Forecasting
Extremely expensive forecast errors
Forecasting the PBS
"
"
Research issues
1
2
3
?
4
?
How to automate exponential smoothing
to give robust and reliable forecasts for a
wide range of time series?
How to generate prediction intervals for all
varieties of exponential smoothing
forecasts?
Data can be disaggregated at five levels of
a drug hierarchy. At what level of
disaggregation should we forecast?
How can correlations and substitutions
between drugs be handled across a very
large hierarchy of time series?
29
Extreme Forecasting
Extreme electricity demand
Outline
1
Extremely messy data
2
Extremely expensive forecast errors
3
Extreme electricity demand
4
Extremely useful conclusions
30
Extreme Forecasting
Extreme electricity demand
Extreme electricity demand
Joint work with
Dr Shu Fan
31
Extreme Forecasting
Extreme electricity demand
The problem
We want to forecast the peak electricity
demand in a half-hour period in ten years
time.
32
Extreme Forecasting
Extreme electricity demand
The problem
We want to forecast the peak electricity
demand in a half-hour period in ten years
time.
We have twelve years of half-hourly
electricity data, temperature data and
some economic and demographic data.
32
Extreme Forecasting
Extreme electricity demand
The problem
We want to forecast the peak electricity
demand in a half-hour period in ten years
time.
We have twelve years of half-hourly
electricity data, temperature data and
some economic and demographic data.
The location is South Australia: home to
the most volatile electricity demand in the
world.
32
Extreme Forecasting
Extreme electricity demand
The problem
We want to forecast the peak electricity
demand in a half-hour period in ten years
time.
We have twelve years of half-hourly
electricity data, temperature data and
some economic and demographic data.
The location is South Australia: home to
the most volatile electricity demand in the
world.
32
Extreme Forecasting
Extreme electricity demand
The problem
We want to forecast the peak electricity
demand in a half-hour period in ten years
time.
We have twelve years of half-hourly
electricity data, temperature data and
some economic and demographic data.
The location is South Australia: home to
the most volatile electricity demand in the
world.
Sounds impossible?
32
Extreme Forecasting
Extreme electricity demand
Demand data
2.5
2.0
1.5
1.0
Demand (GW)
3.0
3.5
SA state wide demand (summers only)
97/98
99/00
01/02
03/04
05/06
07/08
33
Extreme Forecasting
Extreme electricity demand
Demand data
3.0
2.5
2.0
1.5
1.0
SA state wide demand (GW)
3.5
SA state wide demand (summer 08/09)
Oct 08
Nov 08
Dec 08
Jan 09
Feb 09
Mar 09
34
Extreme Forecasting
Extreme electricity demand
Demand data
2.5
2.0
1.5
1.0
SA demand (GW)
3.0
3.5
SA state wide demand (January 2009)
1
3
5
7
9
11
13
15
17
19
Date in January
21
23
25
27
29
31
35
Extreme Forecasting
Extreme electricity demand
Demand boxplots
2.5
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1.5
2.0
●
1.0
Demand (GW)
3.0
3.5
Time: 12 midnight
●
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Mon
Day of week
36
Extreme Forecasting
Extreme electricity demand
Temperature data
2.5
● ●
1.5
2.0
●
1.0
Demand (GW)
3.0
3.5
Time: 12 midnight
Working day
Non working day
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10
20
Average temperature
30
40
37
Extreme Forecasting
Demand drivers
calendar effects
Extreme electricity demand
38
Extreme Forecasting
Extreme electricity demand
Demand drivers
calendar effects
prevailing and recent weather conditions
38
Extreme Forecasting
Extreme electricity demand
Demand drivers
calendar effects
prevailing and recent weather conditions
climate changes
38
Extreme Forecasting
Extreme electricity demand
Demand drivers
calendar effects
prevailing and recent weather conditions
climate changes
economic and demographic changes
38
Extreme Forecasting
Extreme electricity demand
Demand drivers
calendar effects
prevailing and recent weather conditions
climate changes
economic and demographic changes
changing technology
38
Extreme Forecasting
Extreme electricity demand
Demand drivers
calendar effects
prevailing and recent weather conditions
climate changes
economic and demographic changes
changing technology
38
Extreme Forecasting
Extreme electricity demand
Demand drivers
calendar effects
prevailing and recent weather conditions
climate changes
economic and demographic changes
changing technology
Modelling framework
Semi-parametric additive models with
correlated errors.
38
Extreme Forecasting
Extreme electricity demand
Demand drivers
calendar effects
prevailing and recent weather conditions
climate changes
economic and demographic changes
changing technology
Modelling framework
Semi-parametric additive models with
correlated errors.
Each half-hour period modelled separately.
38
Extreme Forecasting
Extreme electricity demand
Demand drivers
calendar effects
prevailing and recent weather conditions
climate changes
economic and demographic changes
changing technology
Modelling framework
Semi-parametric additive models with
correlated errors.
Each half-hour period modelled separately.
Variables selected to provide best
out-of-sample predictions using
cross-validation on each summer.
38
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
yt,p denotes per capita demand at time t (measured
in half-hourly intervals) during period p,
p = 1, . . . , 48;
39
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
yt,p denotes per capita demand at time t (measured
in half-hourly intervals) during period p,
p = 1, . . . , 48;
hp (t ) models all calendar effects;
39
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
yt,p denotes per capita demand at time t (measured
in half-hourly intervals) during period p,
p = 1, . . . , 48;
hp (t ) models all calendar effects;
fp (w1,t , w2,t ) models all temperature effects where
w1,t is a vector of recent temperatures at location 1
and w2,t is a vector of recent temperatures at
location 2;
39
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
yt,p denotes per capita demand at time t (measured
in half-hourly intervals) during period p,
p = 1, . . . , 48;
hp (t ) models all calendar effects;
fp (w1,t , w2,t ) models all temperature effects where
w1,t is a vector of recent temperatures at location 1
and w2,t is a vector of recent temperatures at
location 2;
zj,t is a demographic or economic variable at time t
39
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
yt,p denotes per capita demand at time t (measured
in half-hourly intervals) during period p,
p = 1, . . . , 48;
hp (t ) models all calendar effects;
fp (w1,t , w2,t ) models all temperature effects where
w1,t is a vector of recent temperatures at location 1
and w2,t is a vector of recent temperatures at
location 2;
zj,t is a demographic or economic variable at time t
nt denotes the model error at time t.
39
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
hp (t ) includes handle annual, weekly and daily seasonal
patterns as well as public holidays:
hp (t ) = `p (t ) + αt,p + βt,p
`p (t) is “time of summer” effect (a regression spline);
40
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
hp (t ) includes handle annual, weekly and daily seasonal
patterns as well as public holidays:
hp (t ) = `p (t ) + αt,p + βt,p
`p (t) is “time of summer” effect (a regression spline);
αt,p is day of week effect;
40
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
hp (t ) includes handle annual, weekly and daily seasonal
patterns as well as public holidays:
hp (t ) = `p (t ) + αt,p + βt,p
`p (t) is “time of summer” effect (a regression spline);
αt,p is day of week effect;
βt,p is “holiday” effect;
40
Extreme Forecasting
Extreme electricity demand
Fitted results (3pm)
0.4
0.2
−0.4
0
50
100
150
0.2
0.0
−0.4
Normal
Day before
Holiday
Holiday
Mon
Tue
Wed
Thu
Fri
Day of week
0.4
Day of summer
Effect on demand
0.0
Effect on demand
0.2
0.0
−0.4
Effect on demand
0.4
Time: 3:00 pm
Day after
Sat
Sun
41
Extreme Forecasting
Extreme electricity demand
42
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
Extreme Forecasting
Extreme electricity demand
42
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
Extreme Forecasting
Extreme electricity demand
42
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
xt+ is max of xt values in past 24 hours;
Extreme Forecasting
Extreme electricity demand
42
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
xt+ is max of xt values in past 24 hours;
xt− is min of xt values in past 24 hours;
Extreme Forecasting
Extreme electricity demand
42
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
xt+ is max of xt values in past 24 hours;
xt− is min of xt values in past 24 hours;
x̄t is ave temp in past seven days.
Extreme Forecasting
Extreme electricity demand
42
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
xt+ is max of xt values in past 24 hours;
xt− is min of xt values in past 24 hours;
x̄t is ave temp in past seven days.
Extreme Forecasting
Extreme electricity demand
42
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
xt+ is max of xt values in past 24 hours;
xt− is min of xt values in past 24 hours;
x̄t is ave temp in past seven days.
Each function is smooth and estimated using regression splines.
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Other variables described by linear
relationships with coefficients c1 , . . . , cJ .
43
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Other variables described by linear
relationships with coefficients c1 , . . . , cJ .
Estimation based on annual data.
43
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Other variables described by linear
relationships with coefficients c1 , . . . , cJ .
Estimation based on annual data.
43
Extreme Forecasting
Extreme electricity demand
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Other variables described by linear
relationships with coefficients c1 , . . . , cJ .
Estimation based on annual data.
Variable
Per-capita GSP
Lag Price
Cooling Degree Days (×1000)
Coefficient
18.56
−0.0179
0.1002
Std. Error
1.174
0.00491
0.00456
P value
0.000
0.002
0.043
43
Extreme Forecasting
Extreme electricity demand
44
Predictions
80
75
70
65
R−squared (%)
85
90
95
R−squared
12 midnight 3:00 am
6:00 am
9:00 am
12 noon
Time of day
3:00 pm
6:00 pm
9:00 pm 12 midnight
Extreme Forecasting
Predictions
Extreme electricity demand
44
Extreme Forecasting
Extreme electricity demand
Predictions
4.0
SA state wide demand (January 2009)
3.0
2.5
2.0
1.5
1.0
SA demand (GW)
3.5
Actual
Predicted
1
3
5
7
9
11
13
15
17
19
Date in January
21
23
25
27
29
31
44
Extreme Forecasting
Extreme electricity demand
45
110
Average temperature (January−February 2009)
70
60
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Date in January/February 2009
Degrees Fahrenheit
90
80
30
25
20
15
Degrees Celsius
35
100
40
45
The heatwave
Extreme Forecasting
Extreme electricity demand
45
110
Average temperature (January−February 2009)
70
60
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Date in January/February 2009
Degrees Fahrenheit
90
80
30
25
20
15
Degrees Celsius
35
100
40
45
The heatwave
Extreme Forecasting
Extreme electricity demand
46
110
Average temperature (January−February 2009)
70
60
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Date in January/February 2009
Degrees Fahrenheit
90
80
30
25
20
15
Degrees Celsius
35
100
40
45
The heatwave
Extreme Forecasting
The heatwave
Extreme electricity demand
47
Extreme Forecasting
The heatwave
Extreme electricity demand
47
Extreme Forecasting
The heatwave
Extreme electricity demand
47
Extreme Forecasting
Extreme electricity demand
Modified predictions
Original model
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
j =1
cj zj,t + nt
48
Extreme Forecasting
Extreme electricity demand
Modified predictions
Original model
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Model allowing saturated usage
qt,p = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
log(yt,p ) =
if qt,p ≤ τ ;
τ + k(qt,p − τ ) if qt,p > τ .
qt,p
48
Extreme Forecasting
Extreme electricity demand
Peak demand forecasting
qt,p = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j=1
log(yt,p ) =
if qt,p ≤ τ ;
τ + k(qt,p − τ ) if qt,p > τ .
qt,p
Multiple alternative futures created:
resample residuals using seasonal bootstrap;
49
Extreme Forecasting
Extreme electricity demand
Peak demand forecasting
qt,p = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j=1
log(yt,p ) =
if qt,p ≤ τ ;
τ + k(qt,p − τ ) if qt,p > τ .
qt,p
Multiple alternative futures created:
resample residuals using seasonal bootstrap;
simulate future temperatures using
seasonal bootstrap (with adjustment for
climate change);
49
Extreme Forecasting
Extreme electricity demand
Peak demand forecasting
qt,p = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j=1
log(yt,p ) =
if qt,p ≤ τ ;
τ + k(qt,p − τ ) if qt,p > τ .
qt,p
Multiple alternative futures created:
resample residuals using seasonal bootstrap;
simulate future temperatures using
seasonal bootstrap (with adjustment for
climate change);
use assumed values for GSP and Price.
49
Extreme Forecasting
Extreme electricity demand
Peak demand distribution
4.0
PoE (annual interpretation)
●
3.0
●
●
●
●
●
●
●
2.5
●
●
●
●
2.0
PoE Demand
3.5
1%
5%
10 %
50 %
90 %
97/98 98/99 99/00 00/01 01/02 02/03 03/04 04/05 05/06 06/07 07/08 08/09
Year
50
Extreme Forecasting
Extreme electricity demand
Peak demand distribution
5
6
Annual POE levels
4
●
3
●
●
●
●
●
●
●
●
●
●
●
2
PoE Demand
●
1 % POE
5 % POE
10 % POE
50 % POE
90 % POE
Actual annual maximum
97/98 99/00 01/02 03/04 05/06 07/08 09/10 11/12 13/14 15/16 17/18
Year
51
Extreme Forecasting
Extreme electricity demand
Results
We have successfully forecast the extreme upper
tail in ten years time using only twelve years of data!
52
Extreme Forecasting
Extreme electricity demand
Results
We have successfully forecast the extreme upper
tail in ten years time using only twelve years of data!
This method has now been adopted for the official
South Australian and Victorian long-term peak
electricity demand forecasts.
52
Extreme Forecasting
Extreme electricity demand
Results
We have successfully forecast the extreme upper
tail in ten years time using only twelve years of data!
This method has now been adopted for the official
South Australian and Victorian long-term peak
electricity demand forecasts.
52
Extreme Forecasting
Extreme electricity demand
Results
We have successfully forecast the extreme upper
tail in ten years time using only twelve years of data!
This method has now been adopted for the official
South Australian and Victorian long-term peak
electricity demand forecasts.
Research issues
Extend method for short-term demand
forecasting.
52
Extreme Forecasting
Extreme electricity demand
Results
We have successfully forecast the extreme upper
tail in ten years time using only twelve years of data!
This method has now been adopted for the official
South Australian and Victorian long-term peak
electricity demand forecasts.
Research issues
Extend method for short-term demand
forecasting.
Generalize model to allow coincident
peaks across different interconnected
markets.
52
Extreme Forecasting
Extreme electricity demand
Results
We have successfully forecast the extreme upper
tail in ten years time using only twelve years of data!
This method has now been adopted for the official
South Australian and Victorian long-term peak
electricity demand forecasts.
Research issues
Extend method for short-term demand
forecasting.
Generalize model to allow coincident
peaks across different interconnected
markets.
How to measure forecast accuracy for a
1-in-10 year event?
52
Extreme Forecasting
Extremely useful conclusions
Outline
1
Extremely messy data
2
Extremely expensive forecast errors
3
Extreme electricity demand
4
Extremely useful conclusions
53
Extreme Forecasting
Extremely useful conclusions
Research and reality
A lot of published research deals
with minor variations on existing
problems.
54
Extreme Forecasting
Extremely useful conclusions
Research and reality
A lot of published research deals
with minor variations on existing
problems.
There are lots of tough research
problems that few people are
addressing.
54
Extreme Forecasting
Extremely useful conclusions
Research and reality
A lot of published research deals
with minor variations on existing
problems.
There are lots of tough research
problems that few people are
addressing.
If only academics and practitioners
talked more . . .
54
Extreme Forecasting
Extremely useful conclusions
Complexity
Real data is complex, and we need
methods to handle this.
55
Extreme Forecasting
Extremely useful conclusions
Complexity
Real data is complex, and we need
methods to handle this.
Textbook approaches are building blocks,
not the final word.
55
Extreme Forecasting
Extremely useful conclusions
Complexity
Real data is complex, and we need
methods to handle this.
Textbook approaches are building blocks,
not the final word.
Understand what is driving your data, and
try to build it into a model.
55
Extreme Forecasting
Extremely useful conclusions
Complexity
Real data is complex, and we need
methods to handle this.
Textbook approaches are building blocks,
not the final word.
Understand what is driving your data, and
try to build it into a model.
Complex methods work well when there is
a lot of information the data.
55
Extreme Forecasting
Extremely useful conclusions
Complexity
Real data is complex, and we need
methods to handle this.
Textbook approaches are building blocks,
not the final word.
Understand what is driving your data, and
try to build it into a model.
Complex methods work well when there is
a lot of information the data.
Simple methods work better when there is
mostly noise in the data.
55
Extreme Forecasting
Extremely useful conclusions
Complexity
Real data is complex, and we need
methods to handle this.
Textbook approaches are building blocks,
not the final word.
Understand what is driving your data, and
try to build it into a model.
Complex methods work well when there is
a lot of information the data.
Simple methods work better when there is
mostly noise in the data.
Choose methods to model all the
information available, but no more.
55
Extreme Forecasting
Extremely useful conclusions
Stationarity and structural
change
Herakleitos (c.500BC)
All is flux, nothing is stationary.
56
Extreme Forecasting
Extremely useful conclusions
Stationarity and structural
change
Herakleitos (c.500BC)
All is flux, nothing is stationary.
Change happens, but the rate at which
things change is often constant.
56
Extreme Forecasting
Extremely useful conclusions
Stationarity and structural
change
Herakleitos (c.500BC)
All is flux, nothing is stationary.
Change happens, but the rate at which
things change is often constant.
Don’t throw away data just because things
have changed.
56
Extreme Forecasting
Extremely useful conclusions
Stationarity and structural
change
Herakleitos (c.500BC)
All is flux, nothing is stationary.
Change happens, but the rate at which
things change is often constant.
Don’t throw away data just because things
have changed.
Methods need to be adaptive but history is
important for measuring the rate of change.
56
Extreme Forecasting
Extremely useful conclusions
Stationarity and structural
change
Herakleitos (c.500BC)
All is flux, nothing is stationary.
Change happens, but the rate at which
things change is often constant.
Don’t throw away data just because things
have changed.
Methods need to be adaptive but history is
important for measuring the rate of change.
Uncertainty is not always easy to measure,
is not always easy to compute, but is often
the thing of most interest.
56
Extreme Forecasting
Extremely useful conclusions
Go forth and forecast
A good forecaster is not smarter than
everyone else, he merely has his
ignorance better organised.
(Anonymous)
57
Extreme Forecasting
Extremely useful conclusions
Go forth and forecast
A good forecaster is not smarter than
everyone else, he merely has his
ignorance better organised.
(Anonymous)
Slides available from
www.robjhyndman.com
57