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goPrecisonsamplerTrendCycle.m
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%% Apply precision-based ABC sampler to Common-Trend-cum-VAR(p) models (and simulated data)
%% clean workspace
clear
clc
close all
%% load toolboxes
path(pathdef)
addpath matlabtoolbox/emtools/
addpath matlabtoolbox/emtexbox/
addpath matlabtoolbox/emgibbsbox/
addpath matlabtoolbox/emeconometrics/
addpath matlabtoolbox/emstatespace/
rng(061222); % fix random seed
%#ok<*UNRCH>
%#ok<*NOPTS>
for doSingleThread = [true false]
maxNumCompThreads('automatic');
if doSingleThread
% enforce single threaded computations
usedThreads = 1;
availableThreads = maxNumCompThreads(usedThreads);
fprintf('Using 1 of %d available threads.\n', availableThreads)
else
usedThreads = maxNumCompThreads('automatic');
availableThreads = usedThreads;
fprintf('Using all %d available threads.\n', usedThreads)
end
%% define parameter grid
gridNy = 5 : 5 : 25;
gridT = [200 800];
gridP = [4 8 12 24];
[PStimes, PS0times, PSnoisetimes, PSnoise0times, TCPStimes, TCPS0times, PSyxtimes, PS0yxtimes, DKtimes] = deal(NaN(length(gridP), length(gridNy), length(gridT)));
for iterT = 1 : length(gridT)
T = gridT(iterT)
for iterNy = 1 : length(gridNy)
Ny = gridNy(iterNy)
for iterP = 1 : length(gridP)
p = gridP(iterP)
%% prepare vectorized system
Nx = Ny + Ny;
Nx0 = Nx * p;
NyT = Ny * T;
NxT = Nx * T;
NxTp = Nx * (T + p);
kappa1 = .2^2;
kappa2 = .5^2;
kappa3 = 2;
minnesotaPrior = ones(Ny,Ny);
for i = 1 : Ny
for j = 1 : Ny
if i ~= j
minnesotaPrior(i,j) = kappa2;
end
end
end
minnesotaPrior = kappa1 .* minnesotaPrior;
minnesotaPrior = minnesotaPrior ./ permute(1:p, [1 3 2]).^kappa3;
agap = minnesotaPrior .* randn(Ny,Ny,p);
a = zeros(Nx,Nx,p);
a(1:Ny,1:Ny,1) = eye(Ny);
a(Ny+1:end,Ny+1:end,:) = agap;
b = blkdiag(randn(Ny), randn(Ny)); % trend and cycle assumed orthogonal
c = [eye(Ny) eye(Ny)];
% prior for x0; recall ordering is from x(-p+1) to x(0)
X0 = zeros(Nx0,1);
cholsigX0 = 1e2 * eye(Nx0);
invcholsigX0 = inv(cholsigX0);
% create 3D state space matrices
aaa = repmat(a, 1, 1, 1, T);
ccc = repmat(c, 1, 1, T);
bbb = repmat(b, [1 1 T]);
invbbb = repmat(inv(b), [1 1 T]);
%% construct matrix-form state space
XX0 = sparse(1:Nx0, 1, X0, NxTp, 1);
%% AA
% build sequentially: first unit diagonal
arows1 = 1 : NxTp;
acols1 = 1 : NxTp;
arows2 = repmat((1 : Nx)', 1, Nx * p);
arows2 = Nx0 + arows2 + permute(Nx * (0 : T - 1), [1 3 2]);
acols2 = repmat(1 : Nx * p, Nx,1) + permute(Nx * (0 : T - 1), [1 3 2]);
arows = [arows1(:); arows2(:)];
acols = [acols1(:); acols2(:)];
values1 = ones(NxTp,1);
values2 = -aaa(:,:,p:-1:1,:);
values = [values1(:); values2(:)];
AA = sparse(arows, acols, values);
%% BB
brows0 = repmat((1 : Nx0)', 1 , Nx0);
brows1 = Nx0 + repmat((1 : Nx)', 1 , Nx) + permute(Nx * (0 : T-1), [1 3 2]);
brows = [brows0(:); brows1(:)];
bcols0 = repmat((1 : Nx0), Nx0, 1);
bcols1 = Nx0 + repmat((1 : Nx), Nx, 1) + permute(Nx * (0 : T-1), [1 3 2]);
bcols = [bcols0(:); bcols1(:)];
bvalues = [cholsigX0(:); bbb(:)];
BB = sparse(brows, bcols, bvalues);
invbvalues = [invcholsigX0(:); invbbb(:)];
invBB = sparse(brows, bcols, invbvalues);
%% CC
crows = repmat((1 : Ny)', 1 , Nx, T) + permute(Ny * (0 : T-1), [1 3 2]);
ccols = Nx0 + repmat(1 : NxT, Ny, 1);
CC = sparse(crows(:), ccols(:), ccc(:), NyT, NxTp);
%% simulate data
% prepare
rndStream = getDefaultStream;
xshocks = randn(rndStream, NxTp, 1);
X = AA \ (XX0 + BB * xshocks(:));
Y = CC * X;
%% measure Precision samplers
YXprecsam0 = @() abcYXprecisionsampler(Y,XX0,AA,invBB,CC,rndStream);
[~, QQ, RR1] = YXprecsam0();
YXprecsam = @() abcYXprecisionsampler(Y,XX0,AA,invBB,CC,rndStream,QQ,RR1);
PS0yxtimes(iterP, iterNy, iterT) = timeit(YXprecsam0, 1);
PSyxtimes(iterP, iterNy, iterT) = timeit(YXprecsam, 1);
y = reshape(Y, Ny, T);
aaa = aaa(:,:,p:-1:1,:);
precsam0 = @() ALBCprecisionsampler(aaa,invbbb,ccc,y,X0,invcholsigX0,rndStream);
[~, ~, CC, QQ, RR1, arows, acols, a0ndx, asortndx, brows, bcols, b0ndx, bsortndx] = precsam0();
precsam = @() ALBCprecisionsampler(aaa,invbbb,ccc,y,X0,invcholsigX0,rndStream,CC,QQ,RR1,...
arows, acols,a0ndx,asortndx,brows,bcols,b0ndx,bsortndx);
PS0times(iterP, iterNy, iterT) = timeit(precsam0, 1);
PStimes(iterP, iterNy, iterT) = timeit(precsam, 1);
%% measure precision sampler with (minimal) noise
invnoisevol = repmat(1e5, Ny, T);
precsamnoise0 = @() ALBCnoiseprecisionsampler(aaa,invbbb,ccc,invnoisevol,y,X0,invcholsigX0,rndStream);
[~, ~, ~, arows, acols, asortndx, brows, bcols, crows, ccols] = precsamnoise0();
precsamnoise = @() ALBCnoiseprecisionsampler(aaa,invbbb,ccc,invnoisevol,y,X0,invcholsigX0,rndStream, ...
arows, acols, asortndx, brows, bcols, crows, ccols);
PSnoise0times(iterP, iterNy, iterT) = timeit(precsamnoise0, 1);
PSnoisetimes(iterP, iterNy, iterT) = timeit(precsamnoise, 1);
%% trend-cycle sampler
invbbar = eye(Ny) / b(1:Ny,1:Ny);
invbgap = eye(Ny) / b(Ny+(1:Ny),Ny+(1:Ny));
ybar0 = sparse(Ny,1);
tcsam0 = @() trendcyclePrecisisionsampler(y, agap, invbgap, invbbar, ybar0, rndStream);
[~, ~, Abar, agaprows, agapcols, agapsortndx, brows, bcols] = tcsam0();
tcsam = @() trendcyclePrecisisionsampler(y, agap, invbgap, invbbar, ybar0, rndStream, Abar, agaprows, agapcols, agapsortndx, brows, bcols);
TCPS0times(iterP, iterNy, iterT) = timeit(tcsam0, 2);
TCPStimes(iterP, iterNy, iterT) = timeit(tcsam, 2);
%% DK application
Nw = Ny * 2;
Nstates = Ny + Ny * p;
x0companion = zeros(Nstates,1);
cholsigx0companion = 1e2 * eye(Nstates);
sigx0companion = cholsigx0companion * cholsigx0companion';
Acompanion = zeros(Nstates);
Acompanion(1:Ny,1:Ny) = eye(Ny);
Acompanion(Ny+(1:Ny),Ny+1:end) = reshape(agap, Ny, Ny * p);
Acompanion(Nx+1:Nstates,Ny+(1:Ny*(p-1))) = eye(Ny*(p-1));
Bcompanion = zeros(Nstates,Nw);
Bcompanion(1:Nx,:) = b;
Ccompanion = zeros(Ny, Nstates);
Ccompanion(:,1:Nx) = c;
Acompanion = repmat(Acompanion, [1 1 T]);
Bcompanion = repmat(Bcompanion, [1 1 T]);
Ccompanion = repmat(Ccompanion, [1 1 T]);
dk = @() abcDisturbanceSmoothingSampler1drawSLIM(Acompanion, Bcompanion, Ccompanion, y, x0companion, cholsigx0companion, [], rndStream);
DKtimes(iterP, iterNy, iterT) = timeit(dk, 1);
end % p
end % Ny
end % T
%% store results
thisArch = computer('arch');
thisVer = ver;
if ismac
[~, thisSys] = system('sysctl -a | grep machdep.cpu ', '-echo');
[~, thisBrand] = system('sysctl -a | grep machdep.cpu | grep brand_string ', '-echo');
if contains(thisBrand, 'M1 Pro')
thisBrand = 'AppleSilicon';
else
thisBrand = 'MacOSIntel';
end
elseif isunix
[~, thisSys] = system('cat /proc/cpuinfo ', '-echo');
thisBrand = 'IntelUbuntu';
else % ispc
thisSys = 'Intel(R) Xeon(R) Gold 6320 CPU @ 2.1 GHz';
thisBrand = 'WindowsXeon';
end
varlist = {'grid*', '*times', 'thisArch', 'thisVer', 'thisSys', 'thisBrand', ...
'doSingleThread', 'usedThreads', 'availableThreads'};
matname = sprintf('TRENDCYCLEPStimes%sThreads%dof%d', thisBrand, usedThreads, availableThreads);
save(matname, varlist{:});
end % doSingleThread