Rob J Hyndman
Functional time series
with applications in demography
8. Stochastic population forecasting
Annual age-specific population
Functional time series with applications in demography
8. Stochastic population forecasting
2
Annual age-specific population
100000
0
50000
Population
150000
Australia: male population (1950−2009)
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
3
Annual age-specific population
100000
0
50000
Population
150000
Australia: female population (1950−2009)
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
3
Stochastic population forecasts
Key ideas
Population is a function of mortality, fertility
and net migration.
Build an age-sex-specific stochastic model
for each of mortality, fertility & net migration.
Use the models to simulate future sample
paths of all components.
Compute future births, deaths, net migrants
and populations from simulated rates.
Combine the results to get age-specific
stochastic population forecasts.
Functional time series with applications in demography
8. Stochastic population forecasting
4
Stochastic population forecasts
Key ideas
Population is a function of mortality, fertility
and net migration.
Build an age-sex-specific stochastic model
for each of mortality, fertility & net migration.
Use the models to simulate future sample
paths of all components.
Compute future births, deaths, net migrants
and populations from simulated rates.
Combine the results to get age-specific
stochastic population forecasts.
Functional time series with applications in demography
8. Stochastic population forecasting
4
Stochastic population forecasts
Key ideas
Population is a function of mortality, fertility
and net migration.
Build an age-sex-specific stochastic model
for each of mortality, fertility & net migration.
Use the models to simulate future sample
paths of all components.
Compute future births, deaths, net migrants
and populations from simulated rates.
Combine the results to get age-specific
stochastic population forecasts.
Functional time series with applications in demography
8. Stochastic population forecasting
4
Stochastic population forecasts
Key ideas
Population is a function of mortality, fertility
and net migration.
Build an age-sex-specific stochastic model
for each of mortality, fertility & net migration.
Use the models to simulate future sample
paths of all components.
Compute future births, deaths, net migrants
and populations from simulated rates.
Combine the results to get age-specific
stochastic population forecasts.
Functional time series with applications in demography
8. Stochastic population forecasting
4
Stochastic population forecasts
Key ideas
Population is a function of mortality, fertility
and net migration.
Build an age-sex-specific stochastic model
for each of mortality, fertility & net migration.
Use the models to simulate future sample
paths of all components.
Compute future births, deaths, net migrants
and populations from simulated rates.
Combine the results to get age-specific
stochastic population forecasts.
Functional time series with applications in demography
8. Stochastic population forecasting
4
Demographic growth-balance equation
Demographic growth-balance equation
Pt+1 (x + 1) = Pt (x) − Dt (x, x + 1) + Gt (x, x + 1)
Pt+1 (0) = Bt
x = 0, 1, 2, . . . .
Pt (x) =
Bt =
Dt (x, x + 1) =
Dt (B, 0) =
Gt (x, x + 1) =
Gt (B, 0) =
− Dt (B, 0)
+ Gt (B, 0)
population of age x at 1 January, year t
births in calendar year t
deaths in calendar year t of persons aged x at
the beginning of year t
infant deaths in calendar year t
net migrants in calendar year t of persons
aged x at the beginning of year t
net migrants of infants born in calendar year t
Functional time series with applications in demography
8. Stochastic population forecasting
5
Demographic growth-balance equation
Demographic growth-balance equation
Pt+1 (x + 1) = Pt (x) − Dt (x, x + 1) + Gt (x, x + 1)
Pt+1 (0) = Bt
x = 0, 1, 2, . . . .
Pt (x) =
Bt =
Dt (x, x + 1) =
Dt (B, 0) =
Gt (x, x + 1) =
Gt (B, 0) =
− Dt (B, 0)
+ Gt (B, 0)
population of age x at 1 January, year t
births in calendar year t
deaths in calendar year t of persons aged x at
the beginning of year t
infant deaths in calendar year t
net migrants in calendar year t of persons
aged x at the beginning of year t
net migrants of infants born in calendar year t
Functional time series with applications in demography
8. Stochastic population forecasting
5
The available data
The following data are available:
Pt (x) = population of age x at 1 January, year t
Et (x) = population of age x at 30 June, year t
Bt (x) = births in year t to females of age x
Dt (x) = deaths in year t of persons of age x
From these, we can estimate:
mt (x) = Dt (x)/Et (x) = central death rate in
calendar year t;
ft (x) = Bt (x)/EFt (x) = fertility rate for females of
age x in calendar year t.
Dt (x, x + 1) and Dt (B, 0).
Functional time series with applications in demography
8. Stochastic population forecasting
6
The available data
The following data are available:
Pt (x) = population of age x at 1 January, year t
Et (x) = population of age x at 30 June, year t
Bt (x) = births in year t to females of age x
Dt (x) = deaths in year t of persons of age x
From these, we can estimate:
mt (x) = Dt (x)/Et (x) = central death rate in
calendar year t;
ft (x) = Bt (x)/EFt (x) = fertility rate for females of
age x in calendar year t.
Dt (x, x + 1) and Dt (B, 0).
Functional time series with applications in demography
8. Stochastic population forecasting
6
The available data
The following data are available:
Pt (x) = population of age x at 1 January, year t
Et (x) = population of age x at 30 June, year t
Bt (x) = births in year t to females of age x
Dt (x) = deaths in year t of persons of age x
From these, we can estimate:
mt (x) = Dt (x)/Et (x) = central death rate in
calendar year t;
ft (x) = Bt (x)/EFt (x) = fertility rate for females of
age x in calendar year t.
Dt (x, x + 1) and Dt (B, 0).
Functional time series with applications in demography
8. Stochastic population forecasting
6
The available data
The following data are available:
Pt (x) = population of age x at 1 January, year t
Et (x) = population of age x at 30 June, year t
Bt (x) = births in year t to females of age x
Dt (x) = deaths in year t of persons of age x
From these, we can estimate:
mt (x) = Dt (x)/Et (x) = central death rate in
calendar year t;
ft (x) = Bt (x)/EFt (x) = fertility rate for females of
age x in calendar year t.
Dt (x, x + 1) and Dt (B, 0).
Functional time series with applications in demography
8. Stochastic population forecasting
6
Mortality rates
−4
−6
−10
−8
Log death rate
−2
Australia: male death rates (1950−2009)
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
7
Mortality rates
−4
−6
−10
−8
Log death rate
−2
Australia: female death rates (1950−2009)
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
7
Fertility rates
150
100
0
50
Fertility rate
200
250
Australia fertility rates (1950−2009)
15
20
25
30
35
40
45
50
Age
Functional time series with applications in demography
8. Stochastic population forecasting
8
Net migration
We need to estimate migration data based on
difference in population numbers after adjusting for
births and deaths.
Note: “net migration” numbers also include errors
associated with all estimates. i.e., a “residual”.
Functional time series with applications in demography
8. Stochastic population forecasting
9
Net migration
We need to estimate migration data based on
difference in population numbers after adjusting for
births and deaths.
Demographic growth-balance equation
Pt+1 (x + 1) = Pt (x) − Dt (x, x + 1) + Gt (x, x + 1)
Pt+1 (0) = Bt
x = 0, 1, 2, . . . .
− Dt (B, 0)
+ Gt (B, 0)
Note: “net migration” numbers also include errors
associated with all estimates. i.e., a “residual”.
Functional time series with applications in demography
8. Stochastic population forecasting
9
Net migration
We need to estimate migration data based on
difference in population numbers after adjusting for
births and deaths.
Demographic growth-balance equation
Gt (x, x + 1) = Pt+1 (x + 1) − Pt (x) + Dt (x, x + 1)
Gt (B, 0) = Pt+1 (0)
x = 0, 1, 2, . . . .
− Bt
+ Dt (B, 0)
Note: “net migration” numbers also include errors
associated with all estimates. i.e., a “residual”.
Functional time series with applications in demography
8. Stochastic population forecasting
9
Net migration
We need to estimate migration data based on
difference in population numbers after adjusting for
births and deaths.
Demographic growth-balance equation
Gt (x, x + 1) = Pt+1 (x + 1) − Pt (x) + Dt (x, x + 1)
Gt (B, 0) = Pt+1 (0)
x = 0, 1, 2, . . . .
− Bt
+ Dt (B, 0)
Note: “net migration” numbers also include errors
associated with all estimates. i.e., a “residual”.
Functional time series with applications in demography
8. Stochastic population forecasting
9
Net migration
4000
2000
−4000
0
Net migration
6000
8000
Australia: male net migration (1950−2008)
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
10
Net migration
4000
2000
−4000
0
Net migration
6000
8000
Australia: female net migration (1950−2008)
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
10
Functional time series model
40
60
80
100
20
40
60
80
0.1
100
0
20
40
60
80
Age
Coefficient 2
−5
−10
Coefficient 1
0
0
5
Age
−3
−15
Mortality
product model
with forecasts
0.0
Basis function 2
−0.2
0
Age
−1
20
−2
0
1.3%
−0.1
0.15
0.10
Basis function 1
0.05
−4
Mean
96.6%
−8
−6
0.2
Interaction
−2
Main effects
1960
2000
Year
Functional time series with applications in demography
2040
1960
2000
2040
Year
8. Stochastic population forecasting
11
100
Mortality forecasts
−4
−6
−10
−8
Mortality rate
−2
0
Mortality forecasts product: 2010:2059
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
12
Mortality forecasts
−4
−6
−10
−8
Mortality rate
−2
0
Mortality forecasts product: 2010
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
12
Mortality forecasts
−4
−6
−10
−8
Mortality rate
−2
0
Mortality forecasts product: 2029
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
12
Mortality forecasts
−4
−6
−10
−8
Mortality rate
−2
0
Mortality forecasts product: 2059
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
12
Functional time series model
−0.05
−0.10
40
60
80
100
0
20
60
80
100
0
20
40
Age
Coefficient 2
0.5
0.0
80
−0.6
Coefficient 1
60
Age
−0.5
Mortality ratio
model (M/F)
with forecasts
40
0.4
Age
0.2
20
−0.2 0.0
0
18.9%
0.15
0.10
Basis function 2
0.20
49.3%
0.00
Basis function 1
0.5
0.4
0.1
Mean
0.3
0.2
0.25
Interaction
0.05
Main effects
1960
2000
Year
Functional time series with applications in demography
2040
1960
2000
2040
Year
8. Stochastic population forecasting
13
100
Mortality forecasts
0.4
0.2
0.0
Mortality rate
0.6
Mortality forecasts ratio (M/F): 2010:2059
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
14
Mortality forecasts
0.4
0.2
0.0
Mortality rate
0.6
Mortality forecasts ratio: 2010
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
14
Mortality forecasts
0.4
0.2
0.0
Mortality rate
0.6
Mortality forecasts ratio: 2029
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
14
Mortality forecasts
0.4
0.2
0.0
Mortality rate
0.6
Mortality forecasts ratio: 2059
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
14
Functional time series model
−0.1
0.0
25
30
35
40
45
50
15
20
25
35
40
45
50
15
20
Age
25
30
35
40
45
Age
10
Coefficient 2
0
−10
−40
0
−20
Coefficient 1
Fertility model
with forecasts
30
30
Age
20
20
10
15
19.7%
0.1
Basis function 2
0.2
0.1
0
5
mu(x)
10
Basis function 1
0.3
15
78.3%
0.2
0.3
Interaction
0.0
Main effects
1960
2000
Year
Functional time series with applications in demography
2040
1960
2000
2040
Year
8. Stochastic population forecasting
15
50
Fertility forecasts
150
100
0
50
Fertility rate
200
250
Fertility forecasts: 2010−2059
15
20
25
30
35
40
45
50
Age
Functional time series with applications in demography
8. Stochastic population forecasting
16
Fertility forecasts
150
100
0
50
Fertility rate
200
250
Fertility forecasts: 2010
15
20
25
30
35
40
45
50
Age
Functional time series with applications in demography
8. Stochastic population forecasting
16
Fertility forecasts
150
100
0
50
Fertility rate
200
250
Fertility forecasts: 2029
15
20
25
30
35
40
45
50
Age
Functional time series with applications in demography
8. Stochastic population forecasting
16
Fertility forecasts
150
100
0
50
Fertility rate
200
250
Fertility forecasts: 2059
15
20
25
30
35
40
45
50
Age
Functional time series with applications in demography
8. Stochastic population forecasting
16
Functional time series model
40
60
80
Basis function 2
0.20
0.10
100
0
20
60
80
100
0
20
40
Age
Coefficient 2
15000
5000
0
Coefficient 1
60
80
Age
−5000
Migration
mean model
with forecasts
40
4000
Age
1960
2000
Year
Functional time series with applications in demography
2040
2000
20
0
0
9.4%
−0.2
0
0.00
500
Mean
1000
Basis function 1
80.3%
0.0 0.1 0.2 0.3 0.4
Interaction
−4000 −2000
1500
Main effects
1960
2000
2040
Year
8. Stochastic population forecasting
17
100
Migration forecasts
4000
2000
0
Net migration
6000
Migration forecasts product: 2010−2059
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
18
Migration forecasts
4000
2000
0
Net migration
6000
Migration forecasts product: 2010
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
18
Migration forecasts
4000
2000
0
Net migration
6000
Migration forecasts product: 2029
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
18
Migration forecasts
4000
2000
0
Net migration
6000
Migration forecasts product: 2059
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
18
Functional time series model
60
80
100
0
20
60
80
100
0
20
40
Age
2000
Coefficient 2
1000
80
−500
0
Coefficient 1
60
Age
−1000
Migration
difference
model (M-F)
with forecasts
40
1000
Age
500
40
0
20
0.2
−0.2
0.0
0
14.3%
0.1
0.2
Basis function 2
0.3
67.2%
0.1
Basis function 1
100
−50
Mean
50
0
0.3
Interaction
0.0
Main effects
1960
2000
Year
Functional time series with applications in demography
2040
1960
2000
2040
Year
8. Stochastic population forecasting
19
100
Migration forecasts
200
0
−400
−200
Net migration
400
600
Migration forecasts ratio (M/F): 2010−2059
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
20
Migration forecasts
200
0
−400
−200
Net migration
400
600
Migration forecasts ratio: 2010
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
20
Migration forecasts
200
0
−400
−200
Net migration
400
600
Migration forecasts ratio: 2029
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
20
Migration forecasts
200
0
−400
−200
Net migration
400
600
Migration forecasts ratio: 2059
0
20
40
60
80
100
Age
Functional time series with applications in demography
8. Stochastic population forecasting
20
Stochastic population forecasts
Component models
Data: age/sex-specific mortality rates, fertility
rates and net migration.
Models: Functional time series models for
mortality (M/F), fertility and net migration (M/F)
assuming independence between components
and coherence between sexes.
Generate random sample paths of each
component conditional on observed data.
Use simulated rates to generate Bt (x),
DFt (x, x + 1), DM
t (x, x + 1) for t = n + 1, . . . , n + h,
assuming deaths and births are Poisson.
Functional time series with applications in demography
8. Stochastic population forecasting
21
Stochastic population forecasts
Component models
Data: age/sex-specific mortality rates, fertility
rates and net migration.
Models: Functional time series models for
mortality (M/F), fertility and net migration (M/F)
assuming independence between components
and coherence between sexes.
Generate random sample paths of each
component conditional on observed data.
Use simulated rates to generate Bt (x),
DFt (x, x + 1), DM
t (x, x + 1) for t = n + 1, . . . , n + h,
assuming deaths and births are Poisson.
Functional time series with applications in demography
8. Stochastic population forecasting
21
Stochastic population forecasts
Component models
Data: age/sex-specific mortality rates, fertility
rates and net migration.
Models: Functional time series models for
mortality (M/F), fertility and net migration (M/F)
assuming independence between components
and coherence between sexes.
Generate random sample paths of each
component conditional on observed data.
Use simulated rates to generate Bt (x),
DFt (x, x + 1), DM
t (x, x + 1) for t = n + 1, . . . , n + h,
assuming deaths and births are Poisson.
Functional time series with applications in demography
8. Stochastic population forecasting
21
Stochastic population forecasts
Component models
Data: age/sex-specific mortality rates, fertility
rates and net migration.
Models: Functional time series models for
mortality (M/F), fertility and net migration (M/F)
assuming independence between components
and coherence between sexes.
Generate random sample paths of each
component conditional on observed data.
Use simulated rates to generate Bt (x),
DFt (x, x + 1), DM
t (x, x + 1) for t = n + 1, . . . , n + h,
assuming deaths and births are Poisson.
Functional time series with applications in demography
8. Stochastic population forecasting
21
Simulation
Demographic growth-balance equation used to get
population sample paths.
Demographic growth-balance equation
Pt+1 (x + 1) = Pt (x) − Dt (x, x + 1) + Gt (x, x + 1)
Pt+1 (0) = Bt
x = 0, 1, 2, . . . .
− Dt (B, 0)
+ Gt (B, 0)
10000 sample paths of population Pt (x), deaths Dt (x)
and births Bt (x) generated for t = 2010, . . . , 2059 and
x = 0, 1, 2, . . . ,.
This allows the computation of the empirical forecast
distribution of any demographic quantity that is based on
births, deaths and population numbers.
Functional time series with applications in demography
8. Stochastic population forecasting
22
Simulation
Demographic growth-balance equation used to get
population sample paths.
Demographic growth-balance equation
Pt+1 (x + 1) = Pt (x) − Dt (x, x + 1) + Gt (x, x + 1)
Pt+1 (0) = Bt
x = 0, 1, 2, . . . .
− Dt (B, 0)
+ Gt (B, 0)
10000 sample paths of population Pt (x), deaths Dt (x)
and births Bt (x) generated for t = 2010, . . . , 2059 and
x = 0, 1, 2, . . . ,.
This allows the computation of the empirical forecast
distribution of any demographic quantity that is based on
births, deaths and population numbers.
Functional time series with applications in demography
8. Stochastic population forecasting
22
Simulation
Demographic growth-balance equation used to get
population sample paths.
Demographic growth-balance equation
Pt+1 (x + 1) = Pt (x) − Dt (x, x + 1) + Gt (x, x + 1)
Pt+1 (0) = Bt
x = 0, 1, 2, . . . .
− Dt (B, 0)
+ Gt (B, 0)
10000 sample paths of population Pt (x), deaths Dt (x)
and births Bt (x) generated for t = 2010, . . . , 2059 and
x = 0, 1, 2, . . . ,.
This allows the computation of the empirical forecast
distribution of any demographic quantity that is based on
births, deaths and population numbers.
Functional time series with applications in demography
8. Stochastic population forecasting
22
Simulation
Functional time series with applications in demography
8. Stochastic population forecasting
23
Simulation
2010
0
2010
200
150
100
50
0
50
100
150
200
Population ('000)
Functional time series with applications in demography
8. Stochastic population forecasting
24
Age
Female
10 20 30 40 50 60 70 80 90 100
10 20 30 40 50 60 70 80 90 100
Male
0
Age
Forecast population: 2030
Simulation
2000
2020
Year
2040
2060
12
14
16
18
1980
10
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8
8
10
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Functional time series with applications in demography
Population (millions)
16
14
12
Population (millions)
18
20
Total males
20
Total females
1980
2000
2020
2040
2060
Year
8. Stochastic population forecasting
25
Forecasts of life expectancy at age 0
70
75
80
85
90
Forecasts from FDM model
1960
1980
2000
Functional time series with applications in demography
2020
2040
8. Stochastic population forecasting
2060
26
Forecasts of TFR
3500
Forecasts from FDM model
1000
1500
2000
2500
3000
Total Fertility Rate
Average number of children
born to a woman over her
lifetime if fertility rates
unchanged.
1960
1980
2000
Functional time series with applications in demography
2020
2040
8. Stochastic population forecasting
2060
27
Old-age dependency ratio
Functional time series with applications in demography
8. Stochastic population forecasting
28
Old-age dependency ratio
0.3
0.1
0.2
ratio
0.4
0.5
Old Aged Dependency Ratio forecasts with pension age=65
1920
1940
1960
1980
2000
2020
2040
2060
year
Functional time series with applications in demography
8. Stochastic population forecasting
29
70
Pension age
68
67
65
66
Age of retirement
69
Current pension age
Approved change
Proposed further change
2010
2020
2030
2040
2050
2060
Year
Functional time series with applications in demography
8. Stochastic population forecasting
30
Pension age
0.5
Old−age dependency ratio forecasts
0.3
0.1
0.2
ratio
0.4
Current pension age
Approved change
Proposed further change
1920
1940
1960
1980
2000
2020
2040
2060
Year
Functional time series with applications in demography
8. Stochastic population forecasting
30
Pension age
0.5
Old−age dependency ratio forecasts
0.3
ratio
0.4
Current pension age
Approved change
Proposed further change
0.1
0.2
Target OADR
1920
1940
1960
1980
2000
2020
2040
2060
Year
Functional time series with applications in demography
8. Stochastic population forecasting
30
Pension age
76
Pension age schemes
72
70
66
68
Age of retirement
74
Current pension age
Approved change
Proposed further change
Pension age to give OADR=0.22
1960
1980
2000
2020
2040
2060
Year
Functional time series with applications in demography
8. Stochastic population forecasting
30
Pension age
0.5
Old−age dependency ratio forecasts
0.3
ratio
0.4
Current pension age
Approved change
Proposed further change
OADR target=0.22
0.1
0.2
Target OADR
1920
1940
1960
1980
2000
2020
2040
2060
Year
Functional time series with applications in demography
8. Stochastic population forecasting
30
Advantages of stochastic simulation approach
Functional data analysis provides a way of
forecasting age-specific mortality, fertility and net
migration.
Stochastic age-specific component simulation
provides a way of forecasting many demographic
quantities with prediction intervals.
No need to select combinations of assumed rates.
True prediction intervals with specified coverage for
population and all derived variables (TFR, life
expectancy, old-age dependencies, etc.)
Economic planning is better based on prediction
intervals rather than mean or median forecasts.
Stochastic models allow true policy analysis to be
carried out.
Functional time series with applications in demography
8. Stochastic population forecasting
31
Advantages of stochastic simulation approach
Functional data analysis provides a way of
forecasting age-specific mortality, fertility and net
migration.
Stochastic age-specific component simulation
provides a way of forecasting many demographic
quantities with prediction intervals.
No need to select combinations of assumed rates.
True prediction intervals with specified coverage for
population and all derived variables (TFR, life
expectancy, old-age dependencies, etc.)
Economic planning is better based on prediction
intervals rather than mean or median forecasts.
Stochastic models allow true policy analysis to be
carried out.
Functional time series with applications in demography
8. Stochastic population forecasting
31
Advantages of stochastic simulation approach
Functional data analysis provides a way of
forecasting age-specific mortality, fertility and net
migration.
Stochastic age-specific component simulation
provides a way of forecasting many demographic
quantities with prediction intervals.
No need to select combinations of assumed rates.
True prediction intervals with specified coverage for
population and all derived variables (TFR, life
expectancy, old-age dependencies, etc.)
Economic planning is better based on prediction
intervals rather than mean or median forecasts.
Stochastic models allow true policy analysis to be
carried out.
Functional time series with applications in demography
8. Stochastic population forecasting
31
Advantages of stochastic simulation approach
Functional data analysis provides a way of
forecasting age-specific mortality, fertility and net
migration.
Stochastic age-specific component simulation
provides a way of forecasting many demographic
quantities with prediction intervals.
No need to select combinations of assumed rates.
True prediction intervals with specified coverage for
population and all derived variables (TFR, life
expectancy, old-age dependencies, etc.)
Economic planning is better based on prediction
intervals rather than mean or median forecasts.
Stochastic models allow true policy analysis to be
carried out.
Functional time series with applications in demography
8. Stochastic population forecasting
31
Advantages of stochastic simulation approach
Functional data analysis provides a way of
forecasting age-specific mortality, fertility and net
migration.
Stochastic age-specific component simulation
provides a way of forecasting many demographic
quantities with prediction intervals.
No need to select combinations of assumed rates.
True prediction intervals with specified coverage for
population and all derived variables (TFR, life
expectancy, old-age dependencies, etc.)
Economic planning is better based on prediction
intervals rather than mean or median forecasts.
Stochastic models allow true policy analysis to be
carried out.
Functional time series with applications in demography
8. Stochastic population forecasting
31
Advantages of stochastic simulation approach
Functional data analysis provides a way of
forecasting age-specific mortality, fertility and net
migration.
Stochastic age-specific component simulation
provides a way of forecasting many demographic
quantities with prediction intervals.
No need to select combinations of assumed rates.
True prediction intervals with specified coverage for
population and all derived variables (TFR, life
expectancy, old-age dependencies, etc.)
Economic planning is better based on prediction
intervals rather than mean or median forecasts.
Stochastic models allow true policy analysis to be
carried out.
Functional time series with applications in demography
8. Stochastic population forecasting
31
Model extensions
allow cohort effects
allow fertility to be modelled using parity data
allow interaction between fertility and
migration?
allow interaction between mortality and
migration?
allow interaction between mortality and
fertility?
Functional time series with applications in demography
8. Stochastic population forecasting
32
Model extensions
allow cohort effects
allow fertility to be modelled using parity data
allow interaction between fertility and
migration?
allow interaction between mortality and
migration?
allow interaction between mortality and
fertility?
Functional time series with applications in demography
8. Stochastic population forecasting
32
Model extensions
allow cohort effects
allow fertility to be modelled using parity data
allow interaction between fertility and
migration?
allow interaction between mortality and
migration?
allow interaction between mortality and
fertility?
Functional time series with applications in demography
8. Stochastic population forecasting
32
Model extensions
allow cohort effects
allow fertility to be modelled using parity data
allow interaction between fertility and
migration?
allow interaction between mortality and
migration?
allow interaction between mortality and
fertility?
Functional time series with applications in demography
8. Stochastic population forecasting
32
Model extensions
allow cohort effects
allow fertility to be modelled using parity data
allow interaction between fertility and
migration?
allow interaction between mortality and
migration?
allow interaction between mortality and
fertility?
Functional time series with applications in demography
8. Stochastic population forecasting
32
Selected references
Hyndman, Booth (2008). “Stochastic
population forecasts using functional data
models for mortality, fertility and migration”.
International Journal of Forecasting 24(3),
323–342
Hyndman, Booth, Yasmeen (2013). “Coherent
mortality forecasting: the product-ratio method
with functional time series models”.
Demography 50(1), 261–283.
Hyndman (2014). demography: Forecasting
mortality, fertility, migration and population
data.
cran.r-project.org/package=demography
Functional time series with applications in demography
8. Stochastic population forecasting
33