gblc: Boosted Lee-Carter

gblc provides a novel methodology for multi-population mortality forecasting proposed by Li Li, Han Li, and Anastasios Panagiotelis. They uses well-known stochastic mortality models as weak learners in gradient boosting rather than trees, and includes a penalty that shrinks the forecasts of mortality in adjacent age groups and nearby geographical regions closer together.

Data

The proposed method demonstrates superior forecasting performance based on US male mortality data from 1969 to 2019.

Usage

• For point forecasts, use gb_forecast and gb_forecast_state functions for national and state levels respectively.
• For prediction intervals, use gb_forecast_pi and gb_forecast_pi_ss functions for national and state levels respectively.
• The input mortality data should be organized as a T*n matrix. T denotes years and n denotes ages (for each state).

Quick Demo for national point forecasts

Data preparation

data = read.table(".../Mortality_national_male.txt",head=T)
data_y = data[data[,"Year"]%in%c(1969:2019),]
data_pop = read.table(".../Population_national.txt",head=T)
data_pop_y = data_pop[data_pop[,"Year"]%in%c(1969:2019),]

# T*n matrix
matrix_motality_male = c()
for (i in 1969:2019) {
  row =  data_y[(data_y[,"Year"]==i & data_y[,"Age"]%in%c(0:84)),"Male"]
  row_pop = data_pop_y[(data_pop_y[,"Year"]==i & data_y[,"Age"]%in%c(0:84)),"Male"]
  motality_comb = data_y[(data_y[,"Year"]==i & !data_y[,"Age"]%in%c(0:84)),"Male"]
  pop_comb = data_pop_y[(data_pop_y[,"Year"]==i & !data_pop_y[,"Age"]%in%c(0:84)),"Male"]
  age_comb = sum(motality_comb*pop_comb)/sum(pop_comb)
  row_comb = c(row, age_comb)
  matrix_motality_male = rbind(matrix_motality_male, row_comb)
}
colnames(matrix_motality_male) = c(0:84,"85+")
rownames(matrix_motality_male) = c(1969:2019)

W matrix that captures the age structure

matrix_W=diag(c(0,1,rep(2,82),1,0))
for (i in 2:85) {
  for (j in 2:85) {
    if(abs(i-j)==1){
      matrix_W[i,j]=-1
    }
  }
}

Forecast 2010 to 2019

  matrix_motality_train = matrix_motality_male[c(1:41),]
  matrix_motality_test = matrix_motality_male[c(42:51),]
  # GBLC: set lambda=0;
  # GBLC-age: set lambda>0;
  fore_GB_lca = gb_forecast(matrix_input=matrix_motality_train, 
                            matrix_W = matrix_W, 
                            lambda=0, h=10,
                            max.interation=100,scale=F,threshold=1e-06)
  mase_gblc = c()
  for (h in 1:10) {
    mase = get_mase(fore_GB_lca$final_forecast[c(1:h),], 
                    matrix(matrix_motality_test[c(1:h),],nrow=h), 
                    matrix_motality_train) 
    mase_gblc = c(mase_gblc,mase)
  }
  print("Out-of-sample mortality forecasts for years 2010-2019")
  fore_GB_lca$final_forecast
  print("MASE for horizons 1-10")
  mase_gblc