FMHDFTS

This is the repo for paper "Factor Modelling for High-dimensional Functional Time Series", and this README file provides procedure for reproducing numerical results presented in the paper.

Simulation

Before you start, you install the package FMfts by running the following code in R. install.packages("youpath/FMHDFTS/FMfts_1.0.0.tar.gz", repos = NULL, type = "source") Besides, the dependencies also include the following packages. foreach, doRNG, doSNOW.

To generate simualtion results, you should collect key outputs by running the following code in command line. nohup Rscript simulation.R 100 1 0 >./print.log 2>./error.log

The first parameter (100) is the dimension p of factor model. The second parameter (1) denotes the simulation scenario from 1-5. The last parameter (0) indicates whether the simulation is for a strong signal or a weak signal. By using different combinations of the three parameters, you can gather all the necessary results to reproduce Figure 1/2/5/6/7 of the article.

If you are not familiar with command line, you can uncomment the following code and run it directly in R, but doing so will be more time-consuming and resource-intensive.

# for(type in 1:5){
#     p_seq = c(50,100,200)
#     w_seq = c(0,1)
#     if(type == 3) {w_seq=c(0)}
#     if(type == 5) {p_seq = c(100) w_seq=c(0)}
#     for(p in p_seq){
#         for(if_weak in w_seq){
#             simulation(p, type, if_weak)
#         }
#     }
# }

To generate Figure 8 or Table 4, you only need to run additional/robustness_verify.R and utils/simulation_sparse.R respectively. Once you finish, you should turn to utils/visualization where three files contain key code to plot the figures. The code is self-explanatory, so we will not go into the details here.

Empirical

For UK temperature data, empirical/UKtemperature/data_collect.R is code for data collection and empirical/UKtemperature/plot_loading_uk.R is for Figure 3.

For Japanese mortality data, empirical/JapanMortality/plot_loading_japan.R is for Figure 4/9, while empirical/JapanMortality/mortality_predict_final.R contains all code to compare various methods for forecasting. You should run this script first and you will obtain 6 different ``.RData'' files. After that, you should run empirical/JapanMortality/mortality_sum.R to generate the results of Table 2.