simulate.bootStMoMo: Simulate future sample paths from a Bootstrapped Stochastic...
In StMoMo: Stochastic Mortality Modelling

Description Usage Arguments Details Value See Also Examples

Simulate future sample paths from a Bootstrapped 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.

## S3 method for class 'bootStMoMo'
simulate(object, nsim = 1, 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, ...)

`object`	an object of class `"bootStMoMo"` with the bootstrapped parameters of a stochastic mortality model.
`nsim`	number of sample paths to simulate from each bootstrapped sample. Thus if there are `nBoot` bootstrapped samples the total number of paths will be `nsim * nBoot`.
`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 array/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.

For further details see simulate.fitStMoMo.

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 indices of the model. This is a list with the simulated paths of κ_t (`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 simulated paths of γ_c (`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 (and bootstrapped).
`jumpchoice`	Jump-off method used in the simulation.
`kt.method`	method used in the modelling of the period index.
`model`	the bootstrapped model from which the simulations were produced.

bootstrap.fitStMoMo, simulate.fitStMoMo

#Long computing times
## Not run: 
#Lee-Carter: Compare projection with and without parameter uncertainty
library(fanplot)
LCfit <- fit(lc(), data = EWMaleData)
LCResBoot <- bootstrap(LCfit, nBoot = 500)
LCResBootsim <- simulate(LCResBoot)
LCsim <- simulate(LCfit, nsim = 500) 
plot(LCfit$years, log(LCfit$Dxt / LCfit$Ext)["10", ], 
     xlim = range(LCfit$years, LCsim$years),
     ylim = range(log(LCfit$Dxt / LCfit$Ext)["10", ], 
                  log(LCsim$rates["10", , ])),
     type = "l", xlab = "year", ylab = "log rate", 
     main = "Mortality rate projection at age 10 with and without parameter uncertainty") 
fan(t(log(LCResBootsim$rates["10", , ])),start = LCResBootsim$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)
fan(t(log(LCsim$rates["10", 1:(length(LCsim$years) - 3), ])),
    start = LCsim$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)

## End(Not run)