83 lines
2.9 KiB
Matlab
83 lines
2.9 KiB
Matlab
function generate_trend_stationary_AR1(fname)
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n_periods=10000;
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rho_y=0.5;
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rho_p=0.5;
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g_y=0.0001;
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g_p=-0.0001;
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const_y=2;
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const_p=2;
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sigma_y=0.001;
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sigma_p=0.001;
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orig_params=[rho_y rho_p g_y g_p sigma_y sigma_p]';
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param_names={'rho_y'; 'rho_p'; 'g_y'; 'g_p'; 'sigma_y'; 'sigma_p'};
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save([fname '_orig_params_prefilter.mat'],'orig_params','param_names')
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orig_params = [rho_y rho_p g_y g_p const_y const_p sigma_y sigma_p]';
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param_names = {'rho_y'; 'rho_p'; 'g_y'; 'g_p'; 'const_y'; 'const_p'; 'sigma_y'; 'sigma_p'};
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save([fname '_orig_params.mat'],'orig_params','param_names')
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jumping_covariance=diag([1e-8; 1e-8; 1e-16; 1e-16; 1e-8; 1e-8; 1e-12; 1e-12;])^-1;
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save([fname '_MCMC_jump_covar.mat'],'jumping_covariance');
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jumping_covariance=diag([1e-8; 1e-8; 1e-16; 1e-16; 1e-12; 1e-12;])^-1;
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save([fname '_MCMC_jump_covar_prefilter.mat'],'jumping_covariance');
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%% data without constant
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log_P=zeros(1,n_periods);
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log_Y=zeros(1,n_periods);
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junk2_orig=zeros(1,n_periods);
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for ii=2:n_periods
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log_P(ii)=rho_p*log_P(ii-1)+sigma_p*randn;
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log_Y(ii)=rho_y*log_Y(ii-1)+sigma_y*randn;
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junk2_orig(ii)=0.9*junk2_orig(ii-1)+randn;
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end
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%add trend
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log_P=log_P+g_p*(1:n_periods);
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log_Y=log_Y+g_y*(1:n_periods);
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Y_obs=exp(log_Y);
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P_obs=exp(log_P);
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junk2=exp(junk2_orig);
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save([fname '_Exp_AR1_trend_data_no_constant.mat'],'Y_obs','P_obs','junk2')
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%
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% [b_p,~,~,~,stats_p] = regress(log(P_obs(2:end))',[ones(n_periods-1,1) (2:n_periods)' log(P_obs(1:end-1)')]);
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% [b_y,~,~,~,stats_y] = regress(log(Y_obs(2:end))',[ones(n_periods-1,1) (2:n_periods)' log(Y_obs(1:end-1)')]);
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Y_obs=log_Y;
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P_obs=log_P;
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junk2=junk2_orig;
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save([fname '_AR1_trend_data_no_constant.mat'],'Y_obs','P_obs','junk2')
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% [b_p,~,~,~,stats_p] = regress((P_obs(2:end))',[ones(n_periods-1,1) (2:n_periods)' (P_obs(1:end-1)')]);
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% [b_y,~,~,~,stats_y] = regress((Y_obs(2:end))',[ones(n_periods-1,1) (2:n_periods)' (Y_obs(1:end-1)')]);
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%% data with constant
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log_P=zeros(1,n_periods);
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log_Y=zeros(1,n_periods);
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log_P(1,1)=const_p;
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log_Y(1,1)=const_y;
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for ii=2:n_periods
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log_P(ii)=(1-rho_p)*const_p+rho_p*log_P(ii-1)+sigma_p*randn;
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log_Y(ii)=(1-rho_y)*const_y+rho_y*log_Y(ii-1)+sigma_y*randn;
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end
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%add trend
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log_P=log_P+g_p*(1:n_periods);
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log_Y=log_Y+g_y*(1:n_periods);
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Y_obs=exp(log_Y);
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P_obs=exp(log_P);
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junk2=exp(junk2_orig);
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save([fname '_Exp_AR1_trend_data_with_constant.mat'],'Y_obs','P_obs','junk2')
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% [b,bint,r,rint,stats] = regress(log(P_obs(2:end))',[ones(n_periods-1,1) (2:n_periods)' log(P_obs(1:end-1)')]);
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% [b,bint,r,rint,stats] = regress(log(Y_obs(2:end))',[ones(n_periods-1,1) (2:n_periods)' log(Y_obs(1:end-1)')]);
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Y_obs=log_Y;
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P_obs=log_P;
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junk2=junk2_orig;
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save([fname '_AR1_trend_data_with_constant.mat'],'Y_obs','P_obs','junk2')
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% [b_p,~,~,~,stats_p] = regress((P_obs(2:end))',[ones(n_periods-1,1) (2:n_periods)' (P_obs(1:end-1)')]);
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% [b_y,~,~,~,stats_y] = regress((Y_obs(2:end))',[ones(n_periods-1,1) (2:n_periods)' (Y_obs(1:end-1)')]); |