Tensor-mortality-prediction

This directory provides codes to reproduce the results in the following paper:

Dong, Y., Huang, F., Yu, H., & Haberman, S. (2019). Muti-population mortality forecasting using tensor decomposition, Working paper.

Software Dependency

The plots/tables were produced under the following software

1. MATLAB R2018b
2. Operating system: Windows 10

[Important Notes]:

1. "Tensor Toolbox" is used to do the tensor decomposition. The homepage is http://www.sandia.gov/~tgkolda/TensorToolbox/.
   "DSP System Toolbox" is used to calculate the RMSE/RMSFE. It can be downloaded in MATLAB.
   "Econometrics Toolbox" is used to the fit time series model. It can be downloaded in MATLAB.
   "Parallel Computing Toolbox" is used to do the parfor loop. It can be downloaded in MATLAB.

2. The MATLAB code for the Lee-Carter model is refered from the Appendix (figure 9) of this paper https://pdfs.semanticscholar.org/427c/09210feca24b4b2cabc0d351231a0ffaa2a5.pdf.
   You can also use other software to fit the Lee-Carter model since it is a famous model. Due to the copyright, we don't provide the code for Lee-Carter model.

3. The data used here are central mortality rates (Mx_1x1), which should be downloaded and processed from The Human Mortality Database (https://www.mortality.org/). For convenience, we arrange the data to ".mat" format.

Guidlines for Reproduction

We use the 10 European countries as an example to show how codes work. The codes for Frame A and Frame B are separate. e.g. "CPD_A_Eur" is the CPD method for 10 European countries in Frame A. "CPD_B_Eur" is the CPD method for 10 European countries in Frame B.

#################################################################

For CPD method, there is one rank to be determined.
You only need to change "qq=5" at the begining, which is the length of validation set/testing set.
Short-term forecsat: qq=5
Mid-term forecsat: qq=10
Long-term forecsat: qq=20
Extra-term forecsat: qq=30
The rank determined in the validation set is recorded in the "rank_validation".
The decomposed vectors(year/age/countries) are recorded in "CP_new". e.g. "CP_new{1}.U{1}" is the year vector.
The country-specific RMSFEs from CPD model are recorded in the "RMSE_countries".

##################################################################

For the Tucker method, there are three ranks to be determined, so we split the whole task into 2 steps.

• First Step:
  Open the "Tucker_abc_A_Eur", which is the code to determine the three ranks. In this file, you only need to change the "qq=5".
  For Tucker(aaa) model, "a" is recorded in the "Tucker_aaa_a".
  For Tucker(aab) model, "a" is recorded in the "Tucker_aab_a", "b" is recorded in the "Tucker_aab_b".
  For Tucker(abc) model, "a" is recorded in the "Tucker_abc_a", "b" is recorded in the "Tucker_abc_b", "c" is recorded in the "Tucker_abc_c".

• Second Step:
  Open the "Tucker_testing_A_Eur", which is the code to forecast mortality.
  In this file, you need to change both "rank=[8 14 9]" and "qq=5".
  Remember the "rank" is determined in the * First Step.
  The decomposed vectors(year/age/countries) are recorded in "CP_new". e.g. "CP_new{1}.U{1}" is the year vector.
  The country-specific RMSFEs from Tucker model are recorded in the "RMSE_countries".