simulate.fitStMoMo: Simulate future sample paths from a Stochastic Mortality...
In StMoMo: Stochastic Mortality Modelling
Description
Usage
Arguments
Details
Value
See Also
Examples
View source: R/simulatefitStMoMo.R
Description
Simulate future sample paths from a Stochastic Mortality Model.
The period indexes κ_t^{(i)}, i = 1,..N, are modelled
using ether a Multivariate Random Walk with Drift (MRWD) or
N independent ARIMA(p, d, q) models. The cohort index
γ_{t-x} is modelled using an ARIMA(p, d, q).
By default an ARIMA(1, 1, 0) with a constant is used.
Usage
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## S3 method for class 'fitStMoMo'
simulate(object, nsim = 1000, seed = NULL, h = 50,
oxt = NULL, gc.order = c(1, 1, 0), gc.include.constant = TRUE,
jumpchoice = c("fit", "actual"), kt.method = c("mrwd", "iarima"),
kt.order = NULL, kt.include.constant = TRUE, kt.lookback = NULL,
gc.lookback = NULL, ...)
Arguments
object
an object of class "fitStMoMo" with the fitted
parameters of a stochastic mortality model.
nsim
number of sample paths to simulate.
seed
either NULL or an integer that will be used in a
call to set.seed before simulating the time series.
The default, NULL will not change the random generator state.
h
number of years ahead to forecast.
oxt
optional matrix/vector or scalar of known offset to be
added in the simulations. This can be used to specify any a priori
known component to be added to the simulated predictor.
gc.order
a specification of the ARIMA model for the cohort effect:
the three components (p, d, q) are the AR order, the degree of
differencing, and the MA. The default is an ARIMA(1, 1, 0).
gc.include.constant
a logical value indicating if the ARIMA model
should include a constant value. The default is TRUE.
jumpchoice
option to select the jump-off rates, i.e. the rates
from the final year of observation, to use in projections of mortality
rates. "fit"(default) uses the fitted rates and "actual"
uses the actual rates from the final year.
kt.method
optional forecasting method for the period index.
The alternatives are "mrwd"(default) and "iarima". See details.
kt.order
an optional matrix with one row per period index
specifying the ARIMA models: for the ith row (ith period index) the three
components (p, d, q) are the AR order, the degree of differencing,
and the MA order. If absent the arima models are fitted using
auto.arima. This argument is only used when
kt.method is "iarima".
kt.include.constant
an optional vector of logical values
indicating if the ARIMA model for the ith period index should include a
constant value. The default is TRUE. This argument is only used
when kt.method is "iarima".
kt.lookback
optional argument to specify the look-back window to use
in the estimation of the time series model for the period indexes. By
default all the estimated values are used. If
kt.lookback is provided then the last kt.lookback
years of κ_t^{(i)}, i = 1,..N, are used.
gc.lookback
optional argument to specify the look-back window to use
in the estimation of the ARIMA model for the cohort effect. By
default all the estimated values are used in estimating the ARIMA
model. If gc.lookback is provided then the last
gc.lookback years of γ_{t-x} are used.
...
other arguments.
Details
If kt.method is "mrwd", fitting and simulation of
the time series model for the period indexes is done with a
Multivariate Random Walk with Drift using the function
mrwd.
If kt.method is "iarima", fitting and simulation of
the time series model for the period indexes is done with N
independent arima models using the function iarima.
See this latter function for details on input arguments
kt.order and kt.include.constant.
Fitting and simulation of the ARIMA model for the cohort index
is done with function Arima from package
forecast. See the latter function for further details on
input arguments gc.order and gc.include.constant.
Note that in some cases simulations of the
cohort effects may be needed for a horizon longer than h.
This is the case when in the fitted model the most recent cohorts
have been zero weighted. The simulated cohorts can be seen in
gc.s$cohorts.
Value
A list of class "simStMoMo" with components:
rates
a three dimensional array with the future simulated rates.
ages
vector of ages corresponding to the first dimension of
rates.
years
vector of years for which a simulations has been produced.
This corresponds to the second dimension of rates.
kt.s
information on the simulated paths of the period indexes
of the model. This is a list with the model fitted to
κ_t; the simulated paths (sim); and the years
for which simulations were produced. If the mortality model does not
have any age-period terms (i.e. N=0) this is set to NULL.
gc.s
information on the simulated paths of the cohort index of
the model. This is a list with the model fitted to γ_c;
the simulated paths (sim); and the cohorts for which
simulations were produced. If the mortality model does not have a cohort
effect this is set to NULL.
oxt.s
a three dimensional array with the offset used in the
simulations.
fitted
a three dimensional array with the in-sample rates of
the model for the years for which the mortality model was fitted.
jumpchoice
Jump-off method used in the simulation.
kt.method
method used in the modelling of the period index.
model
the model fit from which the simulations were produced.
See Also
Examples
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#Lee-Carter
LCfit <- fit(lc(), data = EWMaleData, ages.fit = 55:89)
LCsim.mrwd <- simulate(LCfit, nsim = 100)
LCsim.iarima <- simulate(LCfit, nsim = 100, kt.method = "iarima",
kt.order = c(1, 1, 2))
par(mfrow=c(2, 2))
plot(LCfit$years, LCfit$kt[1, ], xlim = range(LCfit$years, LCsim.mrwd$kt.s$years),
ylim = range(LCfit$kt, LCsim.mrwd$kt.s$sim), type = "l",
xlab = "year", ylab = "kt",
main = "Lee-Carter: Simulated paths of the period index kt (mrwd)")
matlines(LCsim.mrwd$kt.s$years, LCsim.mrwd$kt.s$sim[1, , ], type = "l", lty = 1)
plot(LCfit$years, (LCfit$Dxt / LCfit$Ext)["65", ],
xlim = range(LCfit$years, LCsim.mrwd$years),
ylim = range((LCfit$Dxt / LCfit$Ext)["65", ], LCsim.mrwd$rates["65", , ]),
type = "l", xlab = "year", ylab = "rate",
main = "Lee-Carter: Simulated mortality rates at age 65")
matlines(LCsim.mrwd$years, LCsim.mrwd$rates["65", , ], type = "l", lty = 1)
plot(LCfit$years, LCfit$kt[1, ], xlim = range(LCfit$years, LCsim.iarima$kt.s$years),
ylim = range(LCfit$kt, LCsim.iarima$kt.s$sim), type = "l",
xlab = "year", ylab = "kt",
main = "Lee-Carter: Simulated paths of the period index kt (ARIMA(1, 1, 2))")
matlines(LCsim.iarima$kt.s$years, LCsim.iarima$kt.s$sim[1, , ], type = "l", lty = 1)
plot(LCfit$years, (LCfit$Dxt / LCfit$Ext)["65", ],
xlim = range(LCfit$years, LCsim.iarima$years),
ylim = range((LCfit$Dxt / LCfit$Ext)["65", ], LCsim.iarima$rates["65", , ]),
type = "l", xlab = "year", ylab = "rate",
main = "Lee-Carter: Simulated mortality rates at age 65 (ARIMA(1, 1, 2))")
matlines(LCsim.iarima$years, LCsim.iarima$rates["65", , ], type = "l", lty = 1)
#APC
par(mfrow=c(1, 3))
wxt <- genWeightMat(55:89, EWMaleData$years, clip = 3)
APCfit <- fit(apc(), data = EWMaleData, ages.fit = 55:89, wxt = wxt)
APCsim <- simulate(APCfit, nsim = 100, gc.order = c(1, 1, 0))
plot(APCfit$years, APCfit$kt[1, ],
xlim = range(APCfit$years, APCsim$kt.s$years),
ylim = range(APCfit$kt, APCsim$kt.s$sim), type = "l",
xlab = "year", ylab = "kt",
main = "APC: Simulated paths of the period index kt")
matlines(APCsim$kt.s$years, APCsim$kt.s$sim[1, , ], type = "l", lty = 1)
plot(APCfit$cohorts, APCfit$gc,
xlim = range(APCfit$cohorts, APCsim$gc.s$cohorts),
ylim = range(APCfit$gc, APCsim$gc.s$sim, na.rm = TRUE), type = "l",
xlab = "year", ylab = "kt",
main = "APC: Simulated paths of the cohort index (ARIMA(1,1,0))")
matlines(APCsim$gc.s$cohorts, APCsim$gc.s$sim, type = "l", lty = 1)
plot(APCfit$years, (APCfit$Dxt / APCfit$Ext)["65", ],
xlim = range(APCfit$years, APCsim$years),
ylim = range((APCfit$Dxt/APCfit$Ext)["65", ], APCsim$rates["65", , ]),
type = "l", xlab = "year", ylab = "rate",
main = "APC: Simulated of mortality rates at age 65")
matlines(APCsim$years, APCsim$rates["65", , ], type = "l", lty = 1)
#Compare LC and APC
library(fanplot)
par(mfrow=c(1, 1))
plot(LCfit$years, (LCfit$Dxt / LCfit$Ext)["65", ],
xlim = range(LCfit$years, LCsim.mrwd$years),
ylim = range((LCfit$Dxt / LCfit$Ext)["65", ], LCsim.mrwd$rates["65", , ],
APCsim$rates["65", , ]), type = "l", xlab = "year", ylab = "rate",
main = "Fan chart of mortality rates at age 65 (LC vs. APC)")
fan(t(LCsim.mrwd$rates["65", , ]), start = LCsim.mrwd$years[1],
probs = c(2.5, 10, 25, 50, 75, 90, 97.5), n.fan = 4,
fan.col = colorRampPalette(c(rgb(1, 0, 0), rgb(1, 1, 1))), ln = NULL)
fan(t(APCsim$rates["65", 1:(length(APCsim$years) - 3), ]),
start = APCsim$years[1], probs = c(2.5, 10, 25, 50, 75, 90, 97.5),
n.fan = 4, fan.col = colorRampPalette(c(rgb(0, 0, 1), rgb(1, 1, 1))),
ln = NULL)
Example output
Loading required package: gnm
Loading required package: forecast
StMoMo: Start fitting with gnm
Initialising
Running start-up iterations..
Running main iterations.....
Done
StMoMo: Finish fitting with gnm
StMoMo: The following cohorts have been zero weigthed: 1872 1873 1874 1954 1955 1956
StMoMo: Start fitting with gnm
StMoMo: Finish fitting with gnm
StMoMo documentation built on May 2, 2019, 11:42 a.m.
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Description Usage Arguments Details Value See Also Examples
View source: R/simulatefitStMoMo.R
Description
Simulate future sample paths from a Stochastic Mortality Model. The period indexes κ_t^{(i)}, i = 1,..N, are modelled using ether a Multivariate Random Walk with Drift (MRWD) or N independent ARIMA(p, d, q) models. The cohort index γ_{t-x} is modelled using an ARIMA(p, d, q). By default an ARIMA(1, 1, 0) with a constant is used.
Usage
1 2 3 4 5 6 | ## S3 method for class 'fitStMoMo'
simulate(object, nsim = 1000, seed = NULL, h = 50,
oxt = NULL, gc.order = c(1, 1, 0), gc.include.constant = TRUE,
jumpchoice = c("fit", "actual"), kt.method = c("mrwd", "iarima"),
kt.order = NULL, kt.include.constant = TRUE, kt.lookback = NULL,
gc.lookback = NULL, ...)
|
Arguments
object |
an object of class |
nsim |
number of sample paths to simulate. |
seed |
either |
h |
number of years ahead to forecast. |
oxt |
optional matrix/vector or scalar of known offset to be added in the simulations. This can be used to specify any a priori known component to be added to the simulated predictor. |
gc.order |
a specification of the ARIMA model for the cohort effect: the three components (p, d, q) are the AR order, the degree of differencing, and the MA. The default is an ARIMA(1, 1, 0). |
gc.include.constant |
a logical value indicating if the ARIMA model
should include a constant value. The default is |
jumpchoice |
option to select the jump-off rates, i.e. the rates
from the final year of observation, to use in projections of mortality
rates. |
kt.method |
optional forecasting method for the period index.
The alternatives are |
kt.order |
an optional matrix with one row per period index
specifying the ARIMA models: for the ith row (ith period index) the three
components (p, d, q) are the AR order, the degree of differencing,
and the MA order. If absent the arima models are fitted using
|
kt.include.constant |
an optional vector of logical values
indicating if the ARIMA model for the ith period index should include a
constant value. The default is |
kt.lookback |
optional argument to specify the look-back window to use
in the estimation of the time series model for the period indexes. By
default all the estimated values are used. If
|
gc.lookback |
optional argument to specify the look-back window to use
in the estimation of the ARIMA model for the cohort effect. By
default all the estimated values are used in estimating the ARIMA
model. If |
... |
other arguments. |
Details
If kt.method is "mrwd", fitting and simulation of
the time series model for the period indexes is done with a
Multivariate Random Walk with Drift using the function
mrwd.
If kt.method is "iarima", fitting and simulation of
the time series model for the period indexes is done with N
independent arima models using the function iarima.
See this latter function for details on input arguments
kt.order and kt.include.constant.
Fitting and simulation of the ARIMA model for the cohort index
is done with function Arima from package
forecast. See the latter function for further details on
input arguments gc.order and gc.include.constant.
Note that in some cases simulations of the
cohort effects may be needed for a horizon longer than h.
This is the case when in the fitted model the most recent cohorts
have been zero weighted. The simulated cohorts can be seen in
gc.s$cohorts.
Value
A list of class "simStMoMo" with components:
rates |
a three dimensional array with the future simulated rates. |
ages |
vector of ages corresponding to the first dimension of
|
years |
vector of years for which a simulations has been produced.
This corresponds to the second dimension of |
kt.s |
information on the simulated paths of the period indexes
of the model. This is a list with the |
gc.s |
information on the simulated paths of the cohort index of
the model. This is a list with the |
oxt.s |
a three dimensional array with the offset used in the simulations. |
fitted |
a three dimensional array with the in-sample rates of the model for the years for which the mortality model was fitted. |
jumpchoice |
Jump-off method used in the simulation. |
kt.method |
method used in the modelling of the period index. |
model |
the model fit from which the simulations were produced. |
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 | #Lee-Carter
LCfit <- fit(lc(), data = EWMaleData, ages.fit = 55:89)
LCsim.mrwd <- simulate(LCfit, nsim = 100)
LCsim.iarima <- simulate(LCfit, nsim = 100, kt.method = "iarima",
kt.order = c(1, 1, 2))
par(mfrow=c(2, 2))
plot(LCfit$years, LCfit$kt[1, ], xlim = range(LCfit$years, LCsim.mrwd$kt.s$years),
ylim = range(LCfit$kt, LCsim.mrwd$kt.s$sim), type = "l",
xlab = "year", ylab = "kt",
main = "Lee-Carter: Simulated paths of the period index kt (mrwd)")
matlines(LCsim.mrwd$kt.s$years, LCsim.mrwd$kt.s$sim[1, , ], type = "l", lty = 1)
plot(LCfit$years, (LCfit$Dxt / LCfit$Ext)["65", ],
xlim = range(LCfit$years, LCsim.mrwd$years),
ylim = range((LCfit$Dxt / LCfit$Ext)["65", ], LCsim.mrwd$rates["65", , ]),
type = "l", xlab = "year", ylab = "rate",
main = "Lee-Carter: Simulated mortality rates at age 65")
matlines(LCsim.mrwd$years, LCsim.mrwd$rates["65", , ], type = "l", lty = 1)
plot(LCfit$years, LCfit$kt[1, ], xlim = range(LCfit$years, LCsim.iarima$kt.s$years),
ylim = range(LCfit$kt, LCsim.iarima$kt.s$sim), type = "l",
xlab = "year", ylab = "kt",
main = "Lee-Carter: Simulated paths of the period index kt (ARIMA(1, 1, 2))")
matlines(LCsim.iarima$kt.s$years, LCsim.iarima$kt.s$sim[1, , ], type = "l", lty = 1)
plot(LCfit$years, (LCfit$Dxt / LCfit$Ext)["65", ],
xlim = range(LCfit$years, LCsim.iarima$years),
ylim = range((LCfit$Dxt / LCfit$Ext)["65", ], LCsim.iarima$rates["65", , ]),
type = "l", xlab = "year", ylab = "rate",
main = "Lee-Carter: Simulated mortality rates at age 65 (ARIMA(1, 1, 2))")
matlines(LCsim.iarima$years, LCsim.iarima$rates["65", , ], type = "l", lty = 1)
#APC
par(mfrow=c(1, 3))
wxt <- genWeightMat(55:89, EWMaleData$years, clip = 3)
APCfit <- fit(apc(), data = EWMaleData, ages.fit = 55:89, wxt = wxt)
APCsim <- simulate(APCfit, nsim = 100, gc.order = c(1, 1, 0))
plot(APCfit$years, APCfit$kt[1, ],
xlim = range(APCfit$years, APCsim$kt.s$years),
ylim = range(APCfit$kt, APCsim$kt.s$sim), type = "l",
xlab = "year", ylab = "kt",
main = "APC: Simulated paths of the period index kt")
matlines(APCsim$kt.s$years, APCsim$kt.s$sim[1, , ], type = "l", lty = 1)
plot(APCfit$cohorts, APCfit$gc,
xlim = range(APCfit$cohorts, APCsim$gc.s$cohorts),
ylim = range(APCfit$gc, APCsim$gc.s$sim, na.rm = TRUE), type = "l",
xlab = "year", ylab = "kt",
main = "APC: Simulated paths of the cohort index (ARIMA(1,1,0))")
matlines(APCsim$gc.s$cohorts, APCsim$gc.s$sim, type = "l", lty = 1)
plot(APCfit$years, (APCfit$Dxt / APCfit$Ext)["65", ],
xlim = range(APCfit$years, APCsim$years),
ylim = range((APCfit$Dxt/APCfit$Ext)["65", ], APCsim$rates["65", , ]),
type = "l", xlab = "year", ylab = "rate",
main = "APC: Simulated of mortality rates at age 65")
matlines(APCsim$years, APCsim$rates["65", , ], type = "l", lty = 1)
#Compare LC and APC
library(fanplot)
par(mfrow=c(1, 1))
plot(LCfit$years, (LCfit$Dxt / LCfit$Ext)["65", ],
xlim = range(LCfit$years, LCsim.mrwd$years),
ylim = range((LCfit$Dxt / LCfit$Ext)["65", ], LCsim.mrwd$rates["65", , ],
APCsim$rates["65", , ]), type = "l", xlab = "year", ylab = "rate",
main = "Fan chart of mortality rates at age 65 (LC vs. APC)")
fan(t(LCsim.mrwd$rates["65", , ]), start = LCsim.mrwd$years[1],
probs = c(2.5, 10, 25, 50, 75, 90, 97.5), n.fan = 4,
fan.col = colorRampPalette(c(rgb(1, 0, 0), rgb(1, 1, 1))), ln = NULL)
fan(t(APCsim$rates["65", 1:(length(APCsim$years) - 3), ]),
start = APCsim$years[1], probs = c(2.5, 10, 25, 50, 75, 90, 97.5),
n.fan = 4, fan.col = colorRampPalette(c(rgb(0, 0, 1), rgb(1, 1, 1))),
ln = NULL)
|
Example output
Loading required package: gnm
Loading required package: forecast
StMoMo: Start fitting with gnm
Initialising
Running start-up iterations..
Running main iterations.....
Done
StMoMo: Finish fitting with gnm
StMoMo: The following cohorts have been zero weigthed: 1872 1873 1874 1954 1955 1956
StMoMo: Start fitting with gnm
StMoMo: Finish fitting with gnm
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