plot.forLCmulti: Function to plot the parameters of the multi-population mortality models

Description

Function to plot different results of the forecasting process of multi-population mortality models, five different options which are obtained using the forecast.fitLCmulti() function. In fact, the function will show the trend parameters kt fitted for the in-sample periods and its forecast results. Similarly, the behavior of the logit mortality rate for the mean in-sample age and the out-of-sample forecast will be shown for all the populations 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 show the single population version of the Lee-Carter model, the classical one.

Usage

# S3 method for forLCmulti
plot(x, ...)

Value

plot the trend parameter kt fitted for the in-sample periods and its forecast results for the multi-population mortality models. Similarly, the behavior of the logit mortality rate for the mean in-sample age and the out-of-sample forecast will be shown for all the populations considered.

Arguments

x: x developed using function forecast.fitLCmulti() which are objects of the fortLCmulti class.
...: additional arguments to show in the plot appearance.

References

Carter, L.R. and Lee, R.D. (1992). Modeling and forecasting US sex differentials in mortality. International Journal of Forecasting, 8(3), 393–411.

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.

Li, N. and Lee, R.D. (2005). Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42(3), 575–594.

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

Villegas, A. M., Haberman, S., Kaishev, V. K., & Millossovich, P. (2017). A comparative study of two-population models for the assessment of basis risk in longevity hedges. ASTIN Bulletin, 47(3), 631-679.

Examples

Run this code

#The example takes more than 5 seconds because it includes
#several fitting and forecasting process and hence all
#the process is included in donttest
# \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)
#1. 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")

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)

#2. 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")

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)

#3. COMMON-FACTOR MULTI-POPULATION MORTALITY MODEL
#In the case, the user wants to fit the common-factor multi-population mortality model
cfm_Spainmales <- fitLCmulti(model = "CFM",
                             qxt = SpainRegions$qx_male,
                             periods = c(1991:2020),
                             ages = c(ages),
                             nPop = 18,
                             lxt = SpainRegions$lx_male)

cfm_Spainmales

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

#Once, we have fit the data, it is possible to forecast the multipopulation
#mortality model several years ahead, for example 10.
#In this case, we apply another ktmethod = arimauser which implies to specify
#by the user the order of the trend parameters as follows:
fut_cfm_Spainmales <- forecast(object = cfm_Spainmales, nahead = 10,
                               ktmethod = "arimauser", order = c(0,1,0))

fut_cfm_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_cfm_Spainmales)

#4. AUGMENTED-COMMON-FACTOR MULTI-POPULATION MORTALITY MODEL
#In the case, the user wants to fit the augmented-common-factor multi-population mortality model
acfm_Spainmales <- fitLCmulti(model = "ACFM",
                              qxt = SpainRegions$qx_male,
                              periods = c(1991:2020),
                              ages = c(ages),
                              nPop = 18,
                              lxt = SpainRegions$lx_male)

acfm_Spainmales

#Once, we have fit the data, it is possible to see the ax, bx, kt, and It
#provided parameters for the fitting.
plot(acfm_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_acfm_Spainmales <- forecast(object = acfm_Spainmales, nahead = 10,
                               ktmethod = "arimapdq")

fut_acfm_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_acfm_Spainmales)

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

jointk_Spainmales

#Once, we have fit the data, it is possible to see the ax, bx, kt, and It
#provided parameters for the fitting.
plot(jointk_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_jointk_Spainmales <- forecast(object = jointk_Spainmales, nahead = 10,
                               ktmethod = "arimapdq")

fut_jointk_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_jointk_Spainmales)

#6. 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,
                              model = "additive",
                              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")

#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)

# }