predict.fitStMoMo: Predict method for Stochastic Mortality Models fits

Description

Obtain predictions from a Stochastic Mortality Model fit.

Usage

# S3 method for fitStMoMo
predict(object, years, kt = NULL, gc = NULL,
  oxt = NULL, type = c("link", "rates"), ...)

Arguments

object

an object of class "fitStMoMo" with the fitted parameters of a stochastic mortality model.

years

vector of years for which a prediction is required.

matrix of values of the period indexes to use for the prediction. If the model has any age-period term this argument needs to be provided and the number of rows in kt must be equal to the number of age-period terms in the model and the number of columns in kt must correspond to the length of years. If the Stochastic Mortality Model doesn't have any age-period terms this argument is ignored and needs not be provided.

vector of values of the cohort indexes to use for the prediction. If the model has a cohort effect this argument needs to be provided. In this case the length of gc must be equal to the number of cohorts for which a prediction is being produced, namely, length(object$ages) + length(years) - 1. If the Stochastic Mortality Model doesn't have a cohort effect this argument is ignored and needs not be provided.

oxt

optional matrix/vector or scalar of known offset to be used in the prediction.

type

the type of the predicted values that should be returned. The alternatives are "link"(default) and "rates".

...

other arguments.

Value

A matrix with the predicted values.

Details

This function evaluates $$\hat{\eta}_{xt} = o_{xt} + \alpha_x + \sum_{i=1}^N \beta_x^{(i)}\kappa_t^{(i)} + \beta_x^{(0)}\gamma_{t-x}$$ for a fitted Stochastic Mortality model. In producing a prediction the static age function, $\alpha_x$, and the age-modulating parameters, $\beta_x^{(i)}, i=0, ..., N$, are taken from the fitted model in object while the period indexes, $\kappa_t^{(i)}, i=1,..., N$, and cohort index, $\gamma_{t-x}$, are taken from the function arguments.

This function can be useful, for instance, in producing forecasts of mortality rates using time series models different to those available in forecast.fitStMoMo (See examples below).

Examples

Run this code

# NOT RUN {
# }
# NOT RUN {
##M6 Forecast using VARIMA(1,1) model
library(MTS)

# fit m6
years <- EWMaleData$years
ages.fit <- 55:89
M6 <- m6(link = "log")
M6fit <- fit(M6, data = EWMaleData, ages.fit = ages.fit)

# Forecast kt using VARIMA(1,1) model from MTS
h <- 50
kt.M6 <- t(M6fit$kt) 
kt.M6.diff <- apply(kt.M6, 2, diff)
fit.kt.M6.11 <- VARMA(kt.M6.diff, p = 1, q = 1)
pred.ktdiff.M6.11 <- VARMApred(fit.kt.M6.11, h = h)
pred.kt.M6.11 <- apply(rbind(tail(kt.M6, n = 1),
                             pred.ktdiff.M6.11$pred), 
                       2, cumsum)[-1, ]

# set row names
years.forecast <- seq(tail(years, 1) + 1, length.out = h)
rownames(pred.kt.M6.11) <- years.forecast

# plot kt1
plot(x = c(years, years.forecast),
     y = c(kt.M6[, 1], pred.kt.M6.11[, 1]),
     col = rep(c("black", "red"), times = c(length(years), h)),
     xlab = "time",
     ylab = "k1")

plot(x = c(years, years.forecast),
     y = c(kt.M6[, 2], pred.kt.M6.11[, 2]),
     col = rep(c("black", "red"), times = c(length(years), h)),
     xlab = "time",
     ylab = "k2")

# forecast cohort effect
# the following cohorts are required:
# from 2012 - 89 = 1923
# to 2061 - 55 = 2006
pred.gc.M6 <- forecast(auto.arima(M6fit$gc, max.d = 1), h = h)

# use predict to get rates
pred.qxt.M6.11 <- predict(object = M6fit,
                          years = years.forecast,
                          kt = t(pred.kt.M6.11),
                          gc = c(tail(M6fit$gc, 34), pred.gc.M6$mean),
                          type = "rates")

qxthatM6 <- fitted(M6fit, type = "rates")

# plot mortality profile at age 60, 70 and 80
matplot(1961 : 2061,
        t(cbind(qxthatM6, pred.qxt.M6.11)[c("60", "70", "80"), ]),
        type = "l", col = "black", xlab = "years", ylab = "rates",
        lwd = 1.5)
# }