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doVAR.m
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%% estimate a single VAR models for a given sample
% select modeltype in third cell below
% Carriero, Clark, Marcellino and Mertens (forthcoming, REStat)
%#ok<*NOSEL>
%#ok<*DISPLAYPROG>
%#ok<*UNRCH>
%% load em toolboxes
warning('off','MATLAB:handle_graphics:exceptions:SceneNode')
path(pathdef)
addpath matlabtoolbox/emtools/
addpath matlabtoolbox/emtexbox/
addpath matlabtoolbox/emgibbsbox/
addpath matlabtoolbox/emeconometrics/
addpath matlabtoolbox/emstatespace/
%% Initial operations
clear; close all; clc;
Nstreams = max(1,getparpoolsize);
rndStreams = initRandStreams(Nstreams, [], 1);
%% set parameters for VAR and MCMC
modeltype = 'SVO';
jumpoffDate = datenum(2021,03,1);
% jumpoffDate = datenum(2020,04,1);
% jumpoffDate = datenum(1975,01,1);
% jumpoffDate = datenum(2019,12,1);
SVOmaxscale = 20;
datalabel = 'fredMD16-2021-04';
% datalabel = 'fredMD16levels-2021-04';
doQuarterly = false;
MCMCdraws = 1e3; % Final number of MCMC draws after burn in
fcstNdraws = 100 * MCMCdraws; % draws sampled from predictive density
doCensorYields = true;
samStart = []; % datenum(1988,12,1); % truncate start of sample if desired (leave empty if otherwise)
% SED-PARAMETERS-HERE
MCMCdraws = 1e2; % Final number of MCMC draws after burn in
fcstNdraws = MCMCdraws; % draws sampled from predictive density
doStoreXL = false; %#ok<*NASGU>
check_stationarity = 0; % Truncate nonstationary draws? (1=yes)
Compute_diagnostics = false; % compute Inefficiency Factors and Potential
doRobustPrior = false;
if doCensorYields
ELBbound = .25;
else
ELBbound = [];
end
if doQuarterly
p = 4;
np = 4; % number of periods per year, used for calibrating priors
datalabel = strcat(datalabel, '-quarterly');
else
p = 12;
np = 12;
end
%% load data
% load CSV file
dum=importdata(sprintf('%s.csv', datalabel),',');
ydates=dum.data(3:end,1);
% Variable names
ncode=dum.textdata(1,2:end);
% Transformation codes (data are already transformed)
tcode =dum.data(1,2:end);
cumcode=logical(dum.data(2,2:end));
% Data
data=dum.data(3:end,2:end);
% define index of yields that need to obey ELB (out of sample)
if doCensorYields
ndxYIELDS = find(ismember(ncode, {'FEDFUNDS', 'GS1', 'GS5', 'GS10'}));
else
ndxOTHERYIELDS = [];
end
Tdata = length(ydates);
Ylabels = fredMDprettylabel(ncode);
Ylabelslong = Ylabels;
Ylabelslong(ismember(tcode, [2 5])) = strcat(Ylabelslong(ismember(tcode, [2 5])), ' (APR growth)');
%% process settings
N = size(data,2);
doTightPrior = false; % N >= 10;
Kbvar = N * p + 1; % number of regressors per equation
K = Kbvar;
% truncate start of sample (if desired)
if ~isempty(samStart)
ndx = ydates >= samStart;
data = data(ndx,:);
ydates = ydates(ndx);
Tdata = length(ydates);
end
% define oos jump offs
thisT = find(ydates == jumpoffDate);
% other settings
fractiles = [5, normcdf(-1) * 100, 100 - normcdf(-1) * 100, 95]; % legacy, used for some plots
setQuantiles = [.5, 2.5, 5, normcdf(-1) * 100, 25 , 75, (1 - normcdf(-1)) * 100, 95, 97.5, 99.5];
Nquantiles = length(setQuantiles);
ndxCI = ismember(setQuantiles, fractiles);
%% mean for Minnesota prior: zero (diff) or RW (level)
if contains(lower(datalabel), 'levels')
minnesotaPriorMean = ones(N,1);
else
minnesotaPriorMean = NaN(N,1);
for n = 1 : N
switch ncode{n}
case {'CUMFNS', 'UNRATE', ...
'WPSFD49207', 'PPICMM', 'PCEPI', ...
'FEDFUNDS', 'HOUST', 'GS1', 'GS5', 'GS10', 'BAAFFM', 'WUXIASHADOWRATE',...
'GDPCTPI', 'PCECTPI', 'GPDICTPI'}
minnesotaPriorMean(n) = 1;
otherwise
minnesotaPriorMean(n) = 0;
end
end
end
%% allocate memory for out-of-sample forecasts
fcstNhorizons = 24; % number of steps forecasted (1:fcstNhorizon)
yearStart = year(ydates(1));
yearStop = year(ydates(end)) + 9;
if doQuarterly
fcstdates = genrQdates(yearStart, yearStop);
else
fcstdates = genrMdates(yearStart, yearStop, 1);
end
ndx = find(fcstdates == ydates(1));
if isempty(ndx)
error houston
end
fcstdates = fcstdates(ndx:end);
%% start latexwrapper to collect results
titlename=sprintf('%s-p%d', datalabel, p);
if ~isempty(samStart)
titlename = strcat(titlename, '-', datestr(samStart, 'yyyymmm'));
end
titlename = strcat(titlename, '-', modeltype);
if contains(modeltype, 'SVO')
titlename=strcat(titlename, sprintf('maxscale%d', SVOmaxscale));
end
if doQuarterly
titlename = strcat(titlename, '-', datestr(ydates(thisT), 'yyyyQQ'), '-since', datestr(ydates(1), 'yyyyQQ'));
else
titlename = strcat(titlename, '-', datestr(ydates(thisT), 'yyyymmm'), '-since', datestr(ydates(1), 'yyyymmm'));
end
wrap = [];
% initwrap
%% plot input data
% thesedates = ydates(1:thisT);
% Ofactor = 5;
%
% for n = 1 : N
%
% dev = abs(data(1:thisT,n) - median(data(1:thisT,n)));
% iqr = range(prctile(data(1:thisT,n), [25 75]));
% outndx = dev > Ofactor * iqr;
%
% this = figure;
% hold on
% plot(thesedates, data(1:thisT,n))
% xtickdates(thesedates)
%
% plot(thesedates(outndx), data(outndx,n), 'rd', 'linewidth', 2)
%
% % title('full sample')
%
% % subplot(2,1,2)
% % bar(ydates(thisT-23:thisT), data(thisT-23:thisT,n))
% % xtickdates([ydates(thisT-24:thisT); ydates(thisT+1) + mean(diff(ydates))])
% % datetick('x', 28, 'keeplimits')
% %
% % title('most recent data')
%
% sgtitle(Ylabelslong{n})
%
% wrapthisfigure(this, sprintf('data%s', ncode{n}), wrap)
% end
%% setup forecast origin
TID = parid;
T = thisT - p;
% collect realized values
yrealized = NaN(N, fcstNhorizons);
for h = 1 : fcstNhorizons
if thisT + h < Tdata
yrealized(:,h) = data(thisT+h,:)';
end
end
% set Funds Rate equal to ELB when at ELB
% (Note: ELB may be set higher than actual funds rate readings, e.g.
% 25p)
if ~isempty(ELBbound)
yieldsrealized = yrealized(ndxYIELDS,:);
ndx = yieldsrealized < ELBbound;
yieldsrealized(ndx) = ELBbound;
yrealized(ndxYIELDS,:) = yieldsrealized;
end
% cumulate realizations and predictions if necessary
yrealized(cumcode,:) = cumsum(yrealized(cumcode,:),2);
%% MCMC sampler
tic
switch modeltype
case 'CONST'
[PAI_all, SIGMA_all, ~, ...
ydraws, yhat, yhatRB] ...
= mcmcVARconstvcv(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
case 'CONSTnanO'
Ofactor = 5;
[PAI_all, SIGMA_all, ~, Ydatadraws, Ynan, ...
ydraws, yhat, yhatRB] ...
= mcmcVARconstvcvNaNoutlier(thisT, MCMCdraws, Ofactor, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
case 'CONSTsansCOVID'
[PAI_all, SIGMA_all, ~, ...
ydraws, yhat, yhatRB] ...
= mcmcVARconstvcvSansCOVID(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
case 'CONSTdummy'
dummyPrecision = 0;
[PAI_all, SIGMA_all, ~, ...
ydraws, yhat, yhatRB] ...
= mcmcVARconstvcvDummy(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, dummyPrecision, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
K = size(PAI_all,1);
case 'SVdummy'
dummyPrecision = 0;
[PAI_all, PHI_all, invA_all, sqrtht_all, ...
ydraws, yhat, yhatRB] ...
= mcmcVARSVdummy(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, dummyPrecision, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
case 'SV'
[PAI_all, PHI_all, invA_all, sqrtht_all, ...
ydraws, yhat, yhatRB, ~, logscoredraws] ...
= mcmcVARSV(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
yrealized,...
fcstNdraws, fcstNhorizons, rndStreams{TID}, true);
case 'SVar1'
[PAI_all, PHI_all, invA_all, SVrho_all, sqrtht_all, ...
ydraws, yhat, yhatRB] ...
= mcmcVARSVar1(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID}, true);
case 'SVnanO'
Ofactor = 5;
[PAI_all, PHI_all, invA_all, sqrtht_all, Ydatadraws, Ynan, ...
ydraws, yhat, yhatRB, ~, ydraws2, yhat2, logscoredraws] ...
= mcmcVARSVnanOutlier(thisT, MCMCdraws, Ofactor, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
yrealized, ...
fcstNdraws, fcstNhorizons, rndStreams{TID}, true);
case 'SVt'
tdofGrid = 3 : 40;
[PAI_all, PHI_all, invA_all, sqrtht_all, ...
SVtscalelog2_all, SVtdof_all, ...
ydraws, yhat, yhatRB, fcstSVdraws, logscoredraws] ...
= mcmcVARSVt(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
tdofGrid, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
yrealized, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
case 'SVtar1'
tdofGrid = 3 : 40;
[PAI_all, PHI_all, invA_all, SVrho_all, sqrtht_all, ...
SVtscalelog2_all, SVtdof_all, ...
ydraws, yhat, yhatRB, fcstSVdraws] ...
= mcmcVARSVtar1(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
tdofGrid, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
case 'SVOt'
SVOpriorobs = 10 * np;
SVOalpha = 1 / (10 * np) * SVOpriorobs; % 10 years of data with 1 outlier every 10 years
SVObeta = SVOpriorobs - SVOalpha;
tdofGrid = 3 : 40;
[PAI_all, PHI_all, invA_all, sqrtht_all, ...
SVOprob_all, SVOscale_all, ...
SVtscalelog2_all, SVtdof_all, ...
ydraws, yhat, yhatRB, fcstSVdraws, fcstSVoutliers] ...
= mcmcVARSVOt(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
SVOalpha, SVObeta, SVOmaxscale, ...
tdofGrid, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
case 'SVOtar1'
SVOpriorobs = 10 * np;
SVOalpha = 1 / (10 * np) * SVOpriorobs; % 10 years of data with 1 outlier every 10 years
SVObeta = SVOpriorobs - SVOalpha;
tdofGrid = 3 : 40;
[PAI_all, PHI_all, invA_all, SVrho_all, sqrtht_all, ...
SVOprob_all, SVOscale_all, ...
SVtscalelog2_all, SVtdof_all, ...
ydraws, yhat, yhatRB, fcstSVdraws, fcstSVoutliers] ...
= mcmcVARSVOtar1(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
SVOalpha, SVObeta, SVOmaxscale, ...
tdofGrid, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
case 'SVobar'
SVobarpriorobs = 10 * np;
SVobaralpha = 1 / (4 * np) * SVobarpriorobs; % 10 years of data with 1 outlier every 4 years
SVobarbeta = SVobarpriorobs - SVobaralpha;
[PAI_all, PHI_all, invA_all, sqrtht_all, ...
SVobarprob_all, SVobarscale_all, ...
ydraws, yhat, yhatRB, fcstSVdraws] ...
= mcmcVARSVObar(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
SVobaralpha, SVobarbeta, SVOmaxscale, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
case 'SVOobar'
SVOpriorobs = 10 * np;
SVOalpha = 1 / (4 * np) * SVOpriorobs; % 10 years of data with 1 outlier every 4 years
SVObeta = SVOpriorobs - SVOalpha;
SVobarpriorobs = 10 * np;
SVobaralpha = 1 / (4 * np) * SVobarpriorobs; % 10 years of data with 1 outlier every 4 years
SVobarbeta = SVobarpriorobs - SVobaralpha;
[PAI_all, PHI_all, invA_all, sqrtht_all, ...
SVOprob_all, SVOscale_all, ...
SVobarprob_all, SVobarscale_all, ...
ydraws, yhat, yhatRB, fcstSVdraws] ...
= mcmcVARSVOobar(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
SVOalpha, SVObeta, SVOmaxscale, ...
SVobaralpha, SVobarbeta, SVOmaxscale, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID});
case 'SVO'
SVOpriorobs = 10 * np;
SVOalpha = 1 / (4 * np) * SVOpriorobs; % 10 years of data with 1 outlier every 4 years
SVOalpha = repmat(SVOalpha, N, 1);
SVObeta = SVOpriorobs - SVOalpha;
[PAI_all, PHI_all, invA_all, sqrtht_all, ...
SVOprob_all, SVOscale_all, ...
ydraws, yhat, yhatRB, fcstSVdraws, fcstSVoutliers, logscoredraws] ...
= mcmcVARSVO(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
SVOalpha, SVObeta, SVOmaxscale, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
yrealized, ...
fcstNdraws, fcstNhorizons, rndStreams{TID},true);
case 'SVOar1'
SVOpriorobs = 10 * np;
SVOalpha = 1 / (4 * np) * SVOpriorobs; % 10 years of data with 1 outlier every 4 years
SVOalpha = repmat(SVOalpha, N, 1);
SVObeta = SVOpriorobs - SVOalpha;
[PAI_all, PHI_all, invA_all, SVrho_all, sqrtht_all, ...
SVOprob_all, SVOscale_all, ...
ydraws, yhat, yhatRB, fcstSVdraws, fcstSVoutliers] ...
= mcmcVARSVOar1(thisT, MCMCdraws, p, np, data, ydates, ...
minnesotaPriorMean, doTightPrior, doRobustPrior, ...
SVOalpha, SVObeta, SVOmaxscale, ...
ndxYIELDS, ELBbound, ...
check_stationarity, ...
fcstNdraws, fcstNhorizons, rndStreams{TID},true);
otherwise
error('modeltype <<%s>> not reognized')
end
toc
%% LOGSCORE
offsetlogscoredraw = max(logscoredraws);
figure
subplot(2,1,1)
histogram(exp(logscoredraws - offsetlogscoredraw))
title('exp(log score draws)')
subplot(2,1,2)
histogram(logscoredraws - offsetlogscoredraw)
title('log score draws')
yLogscore = log(mean(exp(logscoredraws - offsetlogscoredraw))) + offsetlogscoredraw;
fprintf('Logscore: %6.4f\n', yLogscore)
%MV logscore
thesedraws = squeeze(ydraws(:,1,:));
MU = mean(thesedraws, 2);
Sigma = cov(thesedraws', 1); % normalize variance by N
sqrtSigma = chol(Sigma)';
logdetSigma = 2 * sum(log(diag(sqrtSigma)));
dev = sqrtSigma \ (yrealized(:,1) - MU);
SSR = dev' * dev;
yMVlogscore = -.5 * (N * log(2 * pi) + logdetSigma + SSR);
fprintf('Mean-variance Logscore: %6.4f\n', yMVlogscore)
%% Diagnostics
if Compute_diagnostics
if contains(lower(modeltype), 'const')
DiagnosticsCONST(PAI_all,SIGMA_all,N,K,MCMCdraws);
else
Diagnostics(sqrtht_all,invA_all,PAI_all,PHI_all,N,K,MCMCdraws);
end
end
%% compute out-of-sample forecasts
ydraws(cumcode,:,:) = cumsum(ydraws(cumcode,:,:),2);
yhat(cumcode,:) = cumsum(yhat(cumcode,:),2);
yhatRB(cumcode,:) = cumsum(yhatRB(cumcode,:),2);
% compute median
ymed = median(ydraws,3);
%% collect (missing) data draws
switch modeltype
case {'SVnanO', 'CONSTnanO'}
Ymid = median(Ydatadraws, 3);
Ytails = prctile(Ydatadraws, fractiles, 3);
ydraws2(cumcode,:,:) = cumsum(ydraws2(cumcode,:,:),2);
yhat2(cumcode,:) = cumsum(yhat2(cumcode,:),2);
ymed2 = median(ydraws2,3);
for n = 1 : N
thisfig = figure;
hold on
% plot(ydates(p+1:thisT),Ymid(:,n), 'k-', 'linewidth', 2);
% plot(ydates(p+1:thisT),squeeze(Ytails(:,n, [2 3])), 'k--', 'linewidth', 1);
% plot(ydates(p+1:thisT),squeeze(Ytails(:,n, [1 4])), 'k:', 'linewidth', 1);
plotCI(Ymid(:,n), squeeze(Ytails(:,n, :)), ydates(p+1:thisT),[], 'k-', 'linewidth', 2);
xtickdates(ydates)
nanmid = Ymid(:,n);
nanmid(~Ynan(:,n)) = NaN;
plot(ydates(p+1:thisT), nanmid, 'rd', 'linewidth', 3)
wrapthisfigure(thisfig, sprintf('dataX-%s', ncode{n}), wrap)
end
end
%% plot outmiss predictive densities per Jumpoff for Outmiss
switch modeltype
case {'SVnanO', 'CONSTnanO'}
jj = find(fcstdates == ydates(thisT));
if jj ~= thisT
error houston
end
allthesedates = fcstdates(jj-np:jj+fcstNhorizons);
theseFcstdates = fcstdates(jj+(1:fcstNhorizons));
theseJumpoffdates = fcstdates(jj+(-np:0));
for n = 1 : N
hanni = NaN(7,1);
thesedraws = squeeze(ydraws(n,:,:));
thisfig = figure;
fcstMid = mean(thesedraws, 2);
fcstMed = median(thesedraws, 2);
fcstTails = prctile(thesedraws, fractiles, 2);
thesedraws2 = squeeze(ydraws2(n,:,:));
fcstMid2 = mean(thesedraws2, 2);
fcstTails2 = prctile(thesedraws2, fractiles, 2);
% subplot(2,1,1)
hold on
hanni(1) = plot(theseFcstdates,fcstMid, 'k-', 'linewidth', 3);
% hanni(2) = plot(theseFcstdates,yhatRB(n,:), 'bd', 'linewidth', 3);
% hanni(3) = plot(theseFcstdates,fcstMed, 'r-.', 'linewidth', 3);
hanni(4:5) = plot(theseFcstdates,fcstTails(:, [2 3]), 'k--', 'linewidth', 2);
% hanni(6:7) = plot(theseFcstdates,fcstTails(:, [1 4]), 'k:', 'linewidth', 2);
hanni(9) = plot(theseFcstdates,fcstMid2, 'r-', 'linewidth', 3);
plot(theseFcstdates,fcstTails2(:, [2 3]), 'r:', 'linewidth', 2);
hanni(8) = plot(theseJumpoffdates, data(jj+(-np:0),n), 'g-', 'linewidth', 2);
if min(ylim) < 0 && max(ylim) > 0, plotOrigin, end
xtickdates(allthesedates)
title(sprintf('%s \n per %s', Ylabelslong{n}, datestr(ydates(thisT))))
legend(hanni([8 1 9]), 'data', 'mean', 'YhatMiss', ...
'location', 'best')
% subplot(2,1,2)
% hold on
% hanni(1) = plot(theseFcstdates,fcstMid, 'k-', 'linewidth', 3);
% hanni(2) = plot(theseFcstdates,yhatRB(n,:), 'bd', 'linewidth', 3);
% hanni(3) = plot(theseFcstdates,fcstMed, 'r-.', 'linewidth', 3);
% plot(theseJumpoffdates, data(jj+(-np:0),n), 'g-', 'linewidth', 2);
% if min(ylim) < 0 && max(ylim) > 0, plotOrigin, end
% xtickdates(allthesedates)
wrapthisfigure(thisfig, sprintf('outmisspredictiveDensity-%s', ncode{n}), wrap)
end
end
%% plot predictive densities per Jumpoff
jj = find(fcstdates == ydates(thisT));
if jj ~= thisT
error houston
end
allthesedates = fcstdates(jj-np:jj+fcstNhorizons);
theseFcstdates = fcstdates(jj+(1:fcstNhorizons));
theseJumpoffdates = fcstdates(jj+(-np:0));
for n = 1 : N
hanni = NaN(7,1);
thesedraws = squeeze(ydraws(n,:,:));
thisfig = figure;
fcstMid = mean(thesedraws, 2);
fcstMed = median(thesedraws, 2);
fcstTails = prctile(thesedraws, fractiles, 2);
% subplot(2,1,1)
hold on
hanni(1) = plot(theseFcstdates,fcstMid, 'k-', 'linewidth', 3);
% hanni(2) = plot(theseFcstdates,yhatRB(n,:), 'bd', 'linewidth', 3);
hanni(3) = plot(theseFcstdates,fcstMed, 'r-.', 'linewidth', 3);
hanni(4:5) = plot(theseFcstdates,fcstTails(:, [2 3]), 'k--', 'linewidth', 2);
hanni(6:7) = plot(theseFcstdates,fcstTails(:, [1 4]), 'k:', 'linewidth', 2);
hanni(8) = plot(theseJumpoffdates, data(jj+(-np:0),n), 'g-', 'linewidth', 2);
if min(ylim) < 0 && max(ylim) > 0, plotOrigin, end
xtickdates(allthesedates)
title(sprintf('%s \n per %s', Ylabelslong{n}, datestr(ydates(thisT))))
legend(hanni([8 1 3 4 6]), 'data', 'mean', 'Median', '68% band', '90% band', ...
'location', 'best')
% subplot(2,1,2)
% hold on
% hanni(1) = plot(theseFcstdates,fcstMid, 'k-', 'linewidth', 3);
% hanni(2) = plot(theseFcstdates,yhatRB(n,:), 'bd', 'linewidth', 3);
% hanni(3) = plot(theseFcstdates,fcstMed, 'r-.', 'linewidth', 3);
% plot(theseJumpoffdates, data(jj+(-np:0),n), 'g-', 'linewidth', 2);
% if min(ylim) < 0 && max(ylim) > 0, plotOrigin, end
% xtickdates(allthesedates)
wrapthisfigure(thisfig, sprintf('predictiveDensity-%s', ncode{n}), wrap)
end
%% report Ainv
if exist('invA_all', 'var')
medAinv = median(invA_all,3);
meanAinv = mean(invA_all,3);
ubound = 5;
thisfig = figure;
bar3(abs(medAinv))
hold on
[row, col] = find(abs(medAinv) > 5);
plot3(col, row, repmat(ubound, length(row), 1), 'rd', 'linewidth', 5)
xlim([0 N+1])
ylim([0 N+1])
zlim([0 5])
xticks(2 : 2 : N);
yticks(2 : 2 : N);
xticks('manual')
yticks('manual')
title(sprintf('%s model: median(|A^{-1}|)', modeltype))
wrapthisfigure(thisfig, sprintf('medAinv-%s', modeltype), wrap)
thisfig = figure;
bar3(abs(meanAinv))
hold on
[row, col] = find(abs(meanAinv) > 5);
plot3(col, row, repmat(ubound, length(row), 1), 'rd', 'linewidth', 5)
xlim([0 N+1])
ylim([0 N+1])
zlim([0 5])
xticks(2 : 2 : N);
yticks(2 : 2 : N);
xticks('manual')
yticks('manual')
title(sprintf('%s model: mean(|A^{-1}|)', modeltype))
wrapthisfigure(thisfig, sprintf('midAinv-%s', modeltype), wrap)
end
%% SV Graphs
switch modeltype
case {'SV', 'SVdummy', 'SVar1', 'SVnanO'}
SVdraws = NaN(N,thisT,MCMCdraws);
parfor m=1:MCMCdraws
invA = invA_all(:,:,m);
thisSV = NaN(N,thisT);
thisSV(:,p+1:end) = sqrtht_all(:,:,m);
thisSVdraw = NaN(N,thisT);
for t=p+1:thisT
thisSVdraw(:,t) = sqrt(diag(invA*diag(thisSV(:,t).^2)*invA'));
end
SVdraws(:,:,m) = thisSVdraw;
end
SVmid = mean(SVdraws,3);
SVtails = prctile(SVdraws, [5 95], 3);
for n = 1 : N
thisfig = figure;
hold on
h1 = plot(ydates(1:thisT), SVmid(n,:), 'k-', 'linewidth', 2);
plot(ydates(1:thisT), squeeze(SVtails(n,:,:)), 'k-', 'linewidth', 1)
title(sprintf('%s', Ylabels{n}))
xtickdates(ydates(1:thisT))
wrapthisfigure(thisfig, sprintf('SV%s', ncode{n}), wrap)
end
case {'SVt', 'SVtdof', 'SVtar1'}
SVtdraws = NaN(N,thisT,MCMCdraws);
parfor m=1:MCMCdraws
invA = invA_all(:,:,m);
thisSV = NaN(N,thisT);
thisSV(:,p+1:end) = sqrtht_all(:,:,m);
thisSVdraw = NaN(N,thisT);
for t=p+1:thisT
thisSVdraw(:,t) = sqrt(diag(invA*diag(thisSV(:,t).^2)*invA'));
end
SVtdraws(:,:,m) = thisSVdraw;
end
SVtmid = mean(SVtdraws,3);
SVttails = prctile(SVtdraws, [5 95], 3);
% compute SV sans outliers
stochvol = sqrtht_all .* exp(-.5 * SVtscalelog2_all);
SVdraws = NaN(N,thisT,MCMCdraws);
parfor m=1:MCMCdraws
invA = invA_all(:,:,m);
thisSV = NaN(N,thisT);
thisSV(:,p+1:end) = stochvol(:,:,m);
thisSVdraw = NaN(N,thisT);
for t=p+1:thisT
thisSVdraw(:,t) = sqrt(diag(invA*diag(thisSV(:,t).^2)*invA'));
end
SVdraws(:,:,m) = thisSVdraw;
end
SVmid = mean(SVdraws,3);
SVtails = prctile(SVdraws, [5 95], 3);
for n = 1 : N
thisfig = figure;
hold on
h1 = plot(ydates(1:thisT), SVtmid(n,:), 'r-', 'linewidth', 2);
% plot(ydates(1:thisT), squeeze(SVOtails(n,:,:)), 'r-', 'linewidth', 1)
h2 = plot(ydates(1:thisT), SVmid(n,:), 'k-.', 'linewidth', 2);
title(sprintf('%s', Ylabels{n}))
xtickdates(ydates(1:thisT))
legend([h1 h2], 'SV (incl. t outlier)', 'SV (proper)', 'location', 'best')
wrapthisfigure(thisfig, sprintf('SV-%s-%s', modeltype, ncode{n}), wrap)
end
% plot density of SVt scale
oscales = permute(exp(SVtscalelog2_all / 2), [3 2 1]);
ogrid = 0 : .1 : 20;
outlierpdf = NaN(length(ogrid),T,N);
parfor n = 1 : N
for t = 1 : T
outlierpdf(:,t,n) = ksdensity(oscales(:,t,n), ogrid);
end
end
for n = 1 : N
thisfig = figure;
surf(ydates(p+1:thisT), ogrid, outlierpdf(:,:,n));
shading interp
datetick('x')
title(sprintf('%s -- SV-t scale', Ylabels{n}))
view(88,33)
wrapthisfigure(thisfig, sprintf('SVtscale-%s', ncode{n}),wrap)
end
case {'SVO', 'SVOar1'}
SVOdraws = NaN(N,thisT,MCMCdraws);
parfor m=1:MCMCdraws
invA = invA_all(:,:,m);
thisSV = NaN(N,thisT);
thisSV(:,p+1:end) = sqrtht_all(:,:,m);
thisSVdraw = NaN(N,thisT);
for t=p+1:thisT
thisSVdraw(:,t) = sqrt(diag(invA*diag(thisSV(:,t).^2)*invA'));
end
SVOdraws(:,:,m) = thisSVdraw;
end
SVOmid = mean(SVOdraws,3);
SVOtails = prctile(SVOdraws, [5 95], 3);
% compute SV sans outliers
stochvol = sqrtht_all ./ SVOscale_all;
SVdraws = NaN(N,thisT,MCMCdraws);
parfor m=1:MCMCdraws
invA = invA_all(:,:,m);
thisSV = NaN(N,thisT);
thisSV(:,p+1:end) = stochvol(:,:,m);
thisSVdraw = NaN(N,thisT);
for t=p+1:thisT
thisSVdraw(:,t) = sqrt(diag(invA*diag(thisSV(:,t).^2)*invA'));
end
SVdraws(:,:,m) = thisSVdraw;
end
SVmid = mean(SVdraws,3);
SVtails = prctile(SVdraws, [5 95], 3);
for n = 1 : N
thisfig = figure;
hold on
h1 = plot(ydates(1:thisT), SVOmid(n,:), 'r-', 'linewidth', 2);
% plot(ydates(1:thisT), squeeze(SVOtails(n,:,:)), 'r-', 'linewidth', 1)
h2 = plot(ydates(1:thisT), SVmid(n,:), 'k-.', 'linewidth', 2);
title(sprintf('%s', Ylabels{n}))
xtickdates(ydates(1:thisT))
legend([h1 h2], 'SV', 'SV w/o outlier', 'location', 'best')
wrapthisfigure(thisfig, sprintf('SV%s', ncode{n}), wrap)
end
% plot density of SVO scale (for comparison against SVt)
oscales = permute(SVOscale_all, [3 2 1]);
ogrid = 0 : .1 : 20;
outlierpdf = NaN(length(ogrid),T,N);
parfor n = 1 : N
for t = 1 : T
outlierpdf(:,t,n) = ksdensity(oscales(:,t,n), ogrid);
end
end
for n = 1 : N
thisfig = figure;
surf(ydates(p+1:thisT), ogrid, outlierpdf(:,:,n));
shading interp
datetick('x')
title(sprintf('%s -- SVO scale', Ylabels{n}))
view(88,33)
wrapthisfigure(thisfig, sprintf('SVOfullscale-%s', ncode{n}),wrap)
end
% plot density of SVO scale
if strcmpi(modeltype, 'SVO')
SVOgrid = 1 : SVOmaxscale;
else
SVOgrid = [1, 2, 3, 4, 5, 6, 8, 10, 15, 20];
end
outlierpdf = NaN(SVOmaxscale,T,N);
for t = 1 : T
for n = 1 : N
outlierpdf(:,t,n) = histcounts(squeeze(SVOscale_all(n,t,:)), 1:SVOmaxscale+1, 'Normalization', 'probability');
end
end
for n = 1 : N
thisfig = figure;
subplot(1,2,1)
surf(ydates(p+1:thisT), 2:SVOmaxscale, outlierpdf(2:end,:,n));
shading interp
if length(SVOgrid) > 10
yticks(SVOgrid(2:2:end))
else
yticks(SVOgrid)
end
datetick('x')
thisZlim = zlim;
zlim([0 max(thisZlim(2), .01)])
title('SV-O scale')
priordraws = betadraw(SVOalpha(n), SVObeta(n), 1e4);
[priorpdf, priorx] = ksdensity(priordraws, 'Support', 'positive');
subplot(1,2,2)
[posteriorpdf, posteriorx] = ksdensity(SVOprob_all(n,:), 'Support', 'positive');
hold on
h1 = plot(priorx, priorpdf, 'k-.');
h2 = plot(posteriorx, posteriorpdf, 'r-');
legend([h1 h2], 'prior', 'posterior')
title('SV-O prob')
wrapthisfigure(thisfig, sprintf('SVOscale-%s', ncode{n}),wrap)
sgtitle(Ylabels{n})
wrapthisfigure(thisfig, sprintf('SVOscale-%s-WITHTITLE', ncode{n}),wrap)
end
%% outlier prob, standalone
for n = 1 : N
priordraws = betadraw(SVOalpha(n), SVObeta(n), 1e4);
[priorpdf, priorx] = ksdensity(priordraws, 'Support', 'positive');
thisfig = figure;
set(gca, 'fontsize', 20)
[posteriorpdf, posteriorx] = ksdensity(SVOprob_all(n,:), 0 : .001 : .1, 'Support', 'positive');
hold on
h1 = plot(priorx, priorpdf, 'k-.', 'linewidth', 3);
h2 = plot(posteriorx, posteriorpdf, 'r-', 'linewidth', 3);
xlim([0 .1])
wrapthisfigure(thisfig, sprintf('SVOprob-%s', ncode{n}),wrap, [], [], [], [], true);
legend([h1 h2], 'prior', 'posterior')
wrapthisfigure(thisfig, sprintf('SVOprob-%s-WITHLEGEND', ncode{n}),wrap, [], [], [], [], true);
title(Ylabels{n})
wrapthisfigure(thisfig, sprintf('SVOprob-%s-WITHTITLE', ncode{n}),wrap)
end
case {'SVobar'}
SVOdraws = NaN(N,thisT,MCMCdraws);
parfor m=1:MCMCdraws
invA = invA_all(:,:,m);
thisSV = NaN(N,thisT);
thisSV(:,p+1:end) = sqrtht_all(:,:,m);
thisSVdraw = NaN(N,thisT);
for t=p+1:thisT
thisSVdraw(:,t) = sqrt(diag(invA*diag(thisSV(:,t).^2)*invA'));
end
SVOdraws(:,:,m) = thisSVdraw;
end
SVOmid = mean(SVOdraws,3);
SVOtails = prctile(SVOdraws, [5 95], 3);