Autocorrelation computation fails for floats equal to integers

Hi all,

I found a peculiar behavior of autocorr function. If I have a row of arbitrary float numbers (which are not integer), it works totally fine. However, if I assign it to an integer value (like 4.0), it fails. Apparently, it looks like matlab stores the value internally as an integer, which causes some out-of-the-range value for float.

Is there any way to avoid such behavior?

Thanks!

figure(1)
subplot(1,2,1)
z(1:500) = 1.9;
autocorr(z)
title({"ACF for 1.9, 500 values:","z(1:500) = 1.9;","autocorr(z)"});
ylabel("ACF");
subplot(1,2,2)
z(1:500) = 4.0; % explicit convertation with cast(4.0,'double') does not help
autocorr(z) % explicit convertation with autocorr(cast(z,'double')) does not help
title({"ACF for 4.0, 500 values:","z(1:500) = 4.0;","autocorr(z)"});
ylabel("ACF");

Answer 1

[Alexandre Turenne]

This is how the autocorr is computed is real life.

1.You find the mean of your series --> mean(z)

2. You find the variance --> var(z)

3.You find the covariance for each lag --> covar(i) = sum((z(i+1:end)-avg.*(z(1:end-i)-avg)/(50-i) where i is the number of lag

4. You calculate the corr with --> covar(i)/var(z)

the covar should always be zero but matlab since to have problems with float numbers which make the function instable returning a variance of 1.8112e-30 and a cov of 1.7749e-30 thats why it gives something close to 1. But in reality it should be NaN like with the integers since the 4th equation for the corr is 0/0.

Code:

avg = mean(z) %0

variance = var(z) %0

for i =1: 20

covar(i) = 1/(50-i)*sum((z(i+1:end)-avg).*(z(1:end-i)-avg)) %0

correl(i) = covar(i)/variance

end

[Ilya Fomin]

Thank you for expalantion! That makes everything very clear. I need to add a manual check for the variance