forecast.fitLCmulti {CvmortalityMult}

Function to forecast multi-population mortality model

Description

R function for forecasting additive and multiplicative multi-population mortality model developed by: Debon et al (2011) and Russolillo et al. (2011), respectively. This model follows the structure of the well-known Lee-Carter model (Lee and Carter, 1992) but including an additive or multiplicative parameter to capture the behavior of each population considered. This parameter seeks to capture the individual behavior of every population considered. It should be mentioned that this function is developed for fitting several populations. However, in case you only consider one population, the function will fit the single population version of the Lee-Carter model, the classical one.

Usage

## S3 method for class 'fitLCmulti'
forecast(
  object,
  nahead,
  ktmethod = c("Arimapdq", "arima010"),
  kt_include.cte = TRUE,
  ...
)

Arguments

object

object "fitLCmulti" developed using function fitLCmulti(). With this object the function will determine the multi-population fitted with the function fitLCmulti().

nahead

number of periods ahead to forecast.

ktmethod

method used to forecast the value of kt Arima(p,d,q) or ARIMA(0,1,0); c("Arimapdq", "arima010").

kt_include.cte

if you want that kt include constant in the arima process.

...

other arguments for iarima.

Value

A list with class "forLCmulti" including different components of the forecasting process:

• ax parameter that captures the average shape of the mortality curve in all considered populations.

• bx parameter that explains the age effect x with respect to the general trend kt in the mortality rates of all considered populations.

• arimakt the arima selected for the kt time series.

• kt.fitted obtained values for the tendency behavior captured by kt.

• kt.fut projected values of kt for the nahead periods ahead.

• kt.futintervals arima selected and future values of kt with the different intervals, lower and upper, 80\

• Ii parameter that captures the differences in the pattern of mortality in any region i with respect to Region 1.

• ktmethod method selected to forecast the value of kt Arima(p,d,q) or ARIMA(0,1,0); c("Arimapdq", "arima010").

• kt_include.cte the decision regarding the inclusion of constant in the kt arima process.

• formula additive multi-population mortality formula used to fit the mortality rates.

• model provided the model selected in every case.

• qxt.real real mortality rates.

• qxt.fitted fitted mortality rates using the additive multi-population mortality model.

• logit.qxt.fitted fitted mortality rates in logit way estimated with the additive multi-population mortality model.

• qxt.future future mortality rates estimated with the additive multi-population mortality model.

• logit.qxt.future future mortality rates in logit way estimated with the additive multi-population mortality model.

• nPop provided number of populations to fit the periods.

References

Debon, A., Montes, F., & Martinez-Ruiz, F. (2011). Statistical methods to compare mortality for a group with non-divergent populations: an application to Spanish regions. European Actuarial Journal, 1, 291-308.

Lee, R.D. & Carter, L.R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659–671.

Russolillo, M., Giordano, G., & Haberman, S. (2011). Extending the Lee–Carter model: a three-way decomposition. Scandinavian Actuarial Journal, 2011(2), 96-117.

See Also

fitLCmulti, plot.fitLCmulti, plot.forLCmulti, multipopulation_cv, multipopulation_loocv, iarima

Examples

#The example takes more than 5 seconds because it includes
#several fitting and forecasting process and hence all
#the process is included in donttest

#First, we present the data that we are going to use
SpainRegions
ages <- c(0, 1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90)

library(gnm)
library(forecast)
#ADDITIVE MULTI-POPULATION MORTALITY MODEL
#In the case, the user wants to fit the additive multi-population mortality model
additive_Spainmales <- fitLCmulti(model = "additive",
                              qxt = SpainRegions$qx_male,
                              periods = c(1991:2020),
                              ages = c(ages),
                              nPop = 18,
                              lxt = SpainRegions$lx_male)

additive_Spainmales

#If the user does not provide the model inside the function fitLCmult()
#the multi-population mortality model applied will be additive one.

#Once, we have fit the data, it is possible to see the ax, bx, kt, and Ii
#provided parameters for the fitting.
plot(additive_Spainmales)

#Once, we have fit the data, it is possible to forecast the multipopulation
#mortality model several years ahead, for example 10, as follows:
fut_additive_Spainmales <- forecast(object = additive_Spainmales, nahead = 10,
                                    ktmethod = "Arimapdq", kt_include.cte = TRUE)

fut_additive_Spainmales
#Once the data have been adjusted, it is possible to display the fitted kt and
#its out-of-sample forecasting. In addition, the function shows
#the logit mortality adjusted in-sample and projected out-of-sample
#for the mean age of the data considered in all populations.
plot(fut_additive_Spainmales)

#MULTIPLICATIVE MULTI-POPULATION MORTALITY MODEL
#In the case, the user wants to fit the multiplicative multi-population mortality model
multiplicative_Spainmales <- fitLCmulti(model = "multiplicative",
                              qxt = SpainRegions$qx_male,
                              periods = c(1991:2020),
                              ages = c(ages),
                              nPop = 18,
                              lxt = SpainRegions$lx_male)

multiplicative_Spainmales

#Once, we have fit the data, it is possible to see the ax, bx, kt, and It
#provided parameters for the fitting.
plot(multiplicative_Spainmales)

#Once, we have fit the data, it is possible to forecast the multipopulation
#mortality model several years ahead, for example 10, as follows:
fut_multi_Spainmales <- forecast(object = multiplicative_Spainmales, nahead = 10,
                                 ktmethod = "Arimapdq", kt_include.cte = TRUE)

fut_multi_Spainmales
#Once the data have been adjusted, it is possible to display the fitted kt and
#its out-of-sample forecasting. In addition, the function shows
#the logit mortality adjusted in-sample and projected out-of-sample
#for the mean age of the data considered in all populations.
plot(fut_multi_Spainmales)

#LEE-CARTER FOR SINGLE-POPULATION
#As we mentioned in the details of the function, if we only provide the data
#from one-population the function fitLCmulti()
#will fit the Lee-Carter model for single populations.
LC_Spainmales <- fitLCmulti(qxt = SpainNat$qx_male,
                              periods = c(1991:2020),
                              ages = ages,
                              nPop = 1)

LC_Spainmales

#Once, we have fit the data, it is possible to see the ax, bx, and kt
#parameters provided for the single version of the LC.
plot(LC_Spainmales)

#Once, we have fit the data, it is possible to forecast the multipopulation
#mortality model several years ahead, for example 10, as follows:
fut_LC_Spainmales <- forecast(object = LC_Spainmales, nahead = 10,
                              ktmethod = "Arimapdq", kt_include.cte = TRUE)

#Once the data have been adjusted, it is possible to display the fitted kt and
#its out-of-sample forecasting. In addition, the function shows
#the logit mortality adjusted in-sample and projected out-of-sample
#for the mean age of the data considered in all populations.
plot(fut_LC_Spainmales)