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Optimizing code for HAC Weight matrix generation - How to be faster?

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Hi everyone,
I am re-creating Newey-West procedure for a heteroskedasticity and autocorrelation consistent standard errors (HAC) from scratch.
In order to compute the sandwich matrix V(b), I need to generate the weight matrix W
Since I have to run that test thousands of times, I need to optimize the code. Right now, I have this:
%% Weight matrix generation for HAC
T = length(Dependant_Variable);
k = length(Coeff);
df = T-k;
Optimal_Lags = floor(4*(T/100)^(2/9));
Residual_correlation = Residual*Residual';
Weight_correlation = zeros(size(Residual_correlation));
for i = 1:size(Weight_correlation,1)
for j = 1:size(Weight_correlation,2)
if abs(i-j)>Optimal_Lags
Weight_correlation(i,j)=0;
else
Weight_correlation(i,j)=(T/df)*Residual_correlation(i,j)*(1-abs(j-i)/(Optimal_Lags+1));
end
end
end
Question:
How can I get the same result without using loops?
Thanks and best regards,

Answers (1)

Alan Stevens
Alan Stevens on 18 Mar 2024
Try replacing the loops with something like this:
i = (1:size(Weight_correlation,1))';
j = 1:size(Weight_correlation,2);
c = ones(1,size(Weight_correlation,2));
r = ones(size(Weight_correlation,1),1);
lags = abs(i*c-r*j);
ind1 = lags>Optimal_Lags;
ind2 = lags<=Optimal_Lags;
Weight_correlation(ind1)=0;
Weight_correlation(ind2)=(T/df)*Residual_correlation(ind2).*(1-lags(ind2)/(Optimal_Lags+1));
Check carefully, as I can't really test it properly, not having your data.
  2 Comments
Vic
Vic on 20 Mar 2024
You are right. This does not work.
close all; clearvars;clc;
Variables = rand(10,10);
Companies = rand(10,1);
Coeff = (Variables'*Variables)\Variables'*Companies;
Expected = Variables*Coeff;
Residual = Companies-Expected;
T = length(Companies);
k = length(Coeff);
df = T-k;
Optimal_Lags = floor(4*(T/100)^(2/9));
Residual_correlation = Residual*Residual';
Weight_correlation = zeros(size(Residual_correlation));
for i = 1:size(Weight_correlation,1)
for j = 1:size(Weight_correlation,2)
if abs(i-j)>Optimal_Lags
Weight_correlation(i,j)=0;
else
Weight_correlation(i,j)=Residual_correlation(i,j)*(1-abs(j-i)/(Optimal_Lags+1));
end
end
end
i = (1:size(Weight_correlation,1))';
j = 1:size(Weight_correlation,2);
c = ones(1,size(Weight_correlation,2));
r = ones(size(Weight_correlation,1),1);
lags = abs(i*c-r*j);
ind1 = lags>Optimal_Lags;
ind2 = lags<=Optimal_Lags;
Weight_corr(ind1)=0;
Weight_corr(ind2)=(T/df)*Residual_correlation(ind2).*(1-lags(ind2)/(Optimal_Lags+1));
Check = Weight_correlation - Weight_corr;
Arrays have incompatible sizes for this operation.
Weight_correlation is (10x10) and Weight_corr is (1x100). I reshaped the outcome of this code but here is the result:
Any idea?
Alan Stevens
Alan Stevens on 20 Mar 2024
Edited: Alan Stevens on 20 Mar 2024
Try this:
Variables = rand(10,10);
Companies = rand(10,1);
Coeff = (Variables'*Variables)\Variables'*Companies;
Expected = Variables*Coeff;
Residual = Companies-Expected;
T = length(Companies);
k = length(Coeff);
df = T-k;
Optimal_Lags = floor(4*(T/100)^(2/9));
Residual_correlation = Residual*Residual';
Weight_correlation = zeros(size(Residual_correlation));
for i = 1:size(Weight_correlation,1)
for j = 1:size(Weight_correlation,2)
if abs(i-j)>Optimal_Lags
Weight_correlation(i,j)=0;
else
Weight_correlation(i,j)=Residual_correlation(i,j)*(1-abs(j-i)/(Optimal_Lags+1));
end
end
end
i = (1:size(Weight_correlation,1))';
j = 1:size(Weight_correlation,2);
c = ones(1,size(Weight_correlation,2));
r = ones(size(Weight_correlation,1),1);
lags = abs(i*c-r*j);
ind2 = lags<=Optimal_Lags;
Weight_corr = ind2.*Residual_correlation.*(1-lags/(Optimal_Lags+1));
Check = Weight_correlation - Weight_corr;
disp(Check)
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(I note that you removed the T/df term which gave the inf values!).

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