appendix_C_kStep.m

%% This script replicates the results in Appendix C of the paper  
% Created 21 Jun 2021, 20:03 BST.
% Script last revised 21 Nov 2022
% @author: Arman Hassanniakalager GitHub: https://github.com/hkalager
% Common disclaimers apply. Subject to change at all time.
clear;
clc;
if ispc
    act_fld=[pwd,'\'];
    addpath([act_fld,'\Dataset_ETFS']);
    addpath([act_fld,'\kfwe']);
elseif ismac
    act_fld=[pwd,'/'];
    addpath([act_fld,'/Dataset_ETFS']);
    addpath([act_fld,'/kfwe']);
end
%tickerlistaa={'SPY','QQQ','SHV','LQD','GLD','USO'};
main_ticker={'SPY','QQQ','GLD','USO'};
loss_b_range=[-5,-2,0,1];
Benchmark={'GARCH','GJR-GARCH','HAR'};
freq=5; %mins
%oos_period_range_end=oos_period_range_test+oos_per-1;
try
    Spec_data=load('RV_Pool_325_Spec_tbl.mat');
catch
    record_mdlspec;
    Spec_data=load('RV_Pool_325_Spec_tbl.mat');
end
Bsize=1000;
Bwindow=10;
%% Study period
oos_period_range_test=2014:2020;

%% Liang specification
Max_lambda=0.95;
N_bins=20;
gamma_range=.05:.05:.95;
%% FDR setting
fdrtarget=0.1;
rng(0);
%% Setting for RSW
gamma_rsw=.1;

%% The benchmark indexes
bench_ind=zeros(size(Benchmark));
family_class=Spec_data.Mdl_Class;
for s=1:numel(bench_ind)
    sel_bench=Benchmark{s};
    idx_bench=find(strcmp(family_class,sel_bench));
    bench_ind(s)=idx_bench(1);
    
end
for IS_per=[91,182,252] % number of days for training
    perf_table=table();
    iter=0;
    for t=1:numel(main_ticker)
        flname=[act_fld,main_ticker{t},'_Pool_M',num2str(freq),...
            '_OOS_2014_2020_',num2str(IS_per),'.mat'];
        load(flname,'oosdate','oos_ser','TF1SMP','TF2SMP','tbl0');
        oosdate_red=oosdate;
        oosdate_red(weekday(oosdate_red)==1)=[];
        disp(['Calculations started for ',main_ticker{t}]);
        
        oos_ser(oos_ser>.01)=.01;
        oos_ser(oos_ser<1e-8)=1e-8;
        oos_ser(isnan(oos_ser))=.01;
        
        oos_ser_tested=oos_ser;
        modelscount=size(oos_ser_tested,2);
        tic;
        poolset_ser=oos_ser_tested;
        target=tbl0{TF1SMP:end,'RVDaily'};
        
        %sigma2=tbl0{TF1SMP+poolsetind(1)-1:TF1SMP+poolsetind(end)-1,4+voltyp};
        indices=stationary_bootstrap((1:size(poolset_ser,1))',Bsize,Bwindow);
        Perf=zeros(1,modelscount);
        Perf_B=zeros(Bsize,modelscount);
        for l=1:numel(loss_b_range)
            iter=iter+1;
            perf_table{iter,'Asset'}=main_ticker(t);
            perf_table{iter,'Year'}={'2014-2020'};
            perf_table{iter,'Robust_b'}=loss_b_range(l);
            [Perf,loss_ser]=robust_loss_fn(poolset_ser,target,loss_b_range(l));
            for b=1:Bsize
                bsdata=poolset_ser(indices(:,b),:);
                bstarget=target(indices(:,b),:);
                Perf_B(b,:)=robust_loss_fn(bsdata,bstarget,loss_b_range(l));
            end
     
            for bi=1:numel(Benchmark)
                
                Bench_Perf=Perf(bench_ind(bi));
                [~,maxind]=max(Perf);
                Bench_Perf_B=Perf_B(:,bench_ind(bi));
                
                % SPA set
                n=size(poolset_ser,1);
                d_bar=Bench_Perf-Perf';
                d_bar_B=(Bench_Perf_B-Perf_B);
                omega_hat=var((n^.5)*d_bar_B)';
                I_val=((n^.5)*d_bar./omega_hat<=-(2*log10(log10(n)))^.5);
                mu_k=I_val.*d_bar;
                reject_set=find(mu_k>0);
                %SPA_PVal=bsds(loss_ser(:,bench_ind(bi)),loss_ser,Bsize,Bwindow,'STANDARD','STATIONARY');
                lbl_column_spa=['SPA_',Benchmark{bi}];
                perf_table{iter,lbl_column_spa}=numel(reject_set);
                
                % RSW test
                reject_set_rsw1=kfwe(Bench_Perf-Perf,(Perf_B-Perf),1,fdrtarget,modelscount);
                
                lbl_column_rsw1=['KStepM1_',Benchmark{bi}];
                perf_table{iter,lbl_column_rsw1}=numel(reject_set_rsw1);
                
                
                reject_set_rsw5=kfwe(Bench_Perf-Perf,(Perf_B-Perf),5,fdrtarget,modelscount);
                
                lbl_column_rsw5=['KStepM5_',Benchmark{bi}];
                perf_table{iter,lbl_column_rsw5}=numel(reject_set_rsw5);
                
                reject_set_rsw10=kfwe(Bench_Perf-Perf,(Perf_B-Perf),10,fdrtarget,modelscount);
                
                lbl_column_rsw10=['KStepM10_',Benchmark{bi}];
                perf_table{iter,lbl_column_rsw10}=numel(reject_set_rsw10);
                
                k_rsw=1;
                reject_set_rsw_fdp=kfwe(Bench_Perf-Perf,(Perf_B-Perf),k_rsw,fdrtarget,modelscount);
                while numel(reject_set_rsw_fdp)>=(k_rsw/gamma_rsw-1)
                    k_rsw=k_rsw+1;
                    reject_set_rsw_fdp=kfwe(Bench_Perf-Perf,(Perf_B-Perf),k_rsw,fdrtarget,modelscount);
                end
                
                lbl_column_rsw_fdp=['kStepM_FDP_',Benchmark{bi}];
                perf_table{iter,lbl_column_rsw_fdp}=numel(reject_set_rsw_fdp);
                
                disp(['Number of significant models with SPA and benchmark ',...
                    Benchmark{bi},' is ', num2str(numel(reject_set))]);
                disp(['Number of significant models with kStepM-FDP and benchmark ',...
                    Benchmark{bi},' is ', num2str(numel(reject_set_rsw_fdp))]);
    
            end
        end
        toc;
        
        
    end
    
    fl_lbl=['AllAssets_',num2str(oos_period_range_test(1)),...
            '_',num2str(oos_period_range_test(end)),'_M',num2str(freq),...
            '_',num2str(IS_per),'_OnePiece_FWE.csv'];
        writetable(perf_table,fl_lbl);
end