HAC confidence interval for the response

Hello. One can use Matlab's predict to get estimates of the response or dependent variable and its confidence interval for a desired value of the predictor or independent variable. Can we do somehow the same upon using hac? I'm interested in the default value of the option 'Prediction' being 'curve'.

Answer 1

[Tamas Bodai]

Maybe the following works. I don't accept this answer because i'm not sure if we can use mdl.DFE.

% Define your own data vectors 'y', 't' first, and then make a table
tbl = table(y,t);
% Fit the linear model to have mdl.DFE
mdl = fitlm(tbl,'y ~ t');
% Consider the response in the middle of the interval
%[ypred,yci] = predict(mdl,t(T/2)); % instead of this, do as follows
[EstCov, se, coeff] = hac(t,y);
[ypred,yci] = mypredict(t(T/2),coeff,EstCov,mdl.DFE,0.05);

% This is a stripped down version of function 'predci' called in function
% 'predictDesign' in CompactLinearModel.m.
function [ypred,yCI] = mypredict(X,beta,Sigma,dfe,alpha)

X = [1 X];

% Compute the predicted values at the new X.
ypred = X * beta;

% confi interval for fitted curve
varpred = sum((X*Sigma) .* X,2);

% pointwise
crit = tinv(1-alpha/2,dfe);

delta = sqrt(varpred) * crit;
yCI = [ypred-delta ypred+delta];

end

[Tamas Bodai]

I have found an answer here:

https://www.mathworks.com/help/econ/correct-ols-coefficient-covariance-estimate.html

From the function nlpredci, you can read out the degree of freedom of the t-distribution applied. Mind, however, that for small sample size, it is not a t-distribution, it appears to me, or, the approximate t-distribution is of a different degree of freedom.