How to do autocorrelation with a given data

Hi, Could you help me please? I have data (t,A). t stands for time, A for Absorbance, and i have it in txt file. I'd like to analyze it with autocorrelation function. I tried writing the code, I did just like how i understand what i read the mathworks site 'Autocorr'. But simply saying, i'm afraid the data 't' that i have is not included in the process with my coding. Could I get more explanation, or a validation maybe? thank you.

just for example the data is

t = 3:3:30

A = 3.523;3.523;3.43;3.323;3.43;3.43;3.323;2.923;2.723;2.923;

[t,A]=textread('Data.txt')
[acf,lags]=autocorr(A)

Answer 1

[Pavl M.]

clc
clear all
close all

stdv = 4;
norm_option = 'normalized'; %unbiasd, biased

t = 3:3:30;
A = [3.523;3.523;3.43;3.323;3.43;3.43;3.323;2.923;2.723;2.923];

%OR:

% [t,A]=textread('Data.txt')

subplot(2, 1, 1);
plot(t, A, 'b-', 'LineWidth', 2);
grid on;
xlabel('t');
ylabel('A')
title('Original Data')

%Next will incorporate in full 't' in the process:
[autoCorrA,l] = autocorr(A,NumLags=length(t)-1,NumSTD=stdv);
autocorrB = xcorr(A,norm_option)

autocorrB = 19×1

0.0965 0.1864 0.2804 0.3848 0.4957 0.6058 0.7092 0.8057 0.9005 1.0000

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autoCorrA

autoCorrA = 10×1

1.0000 0.6892 0.1810 -0.0982 -0.0910 -0.1166 -0.2491 -0.3870 -0.3094 -0.1189

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l

l = 10×1

0 1 2 3 4 5 6 7 8 9

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subplot(2, 1, 2);
%original time included
plot(t,autoCorrA, 'b-', 'LineWidth', 2);
grid on;
xlabel('Index');
ylabel('ACF')
title('ACF')

figure
plot(t,autocorrB(1:2:length(autocorrB)), 'b-', 'LineWidth', 2);
grid on;
xlabel('Index');
ylabel('XCorr')
title('Raw normalized auto cross-correlation')

%Constructed from needing help code by
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    %[phone]
    %https://diag.net/u/u6r3ondjie0w0l8138bafm095b
    %https://github.com/goodengineer
    %https://orcid.org/0000-0001-8184-8166
    %https://willwork781147312.wordpress.com/portfolio/cp/
    %https://www.youtube.com/channel/UCC__7jMOAHak0MVkUFtmO-w
    %https://nanohub.org/members/130066
    %https://pangian.com/user/hiretoserve/
    %https://substack.com/profile/191772642-paul-m

[Sasha]

Thanks for your explanation, it's really helpful, but actually I'm a little bit confused why did you pick '4' as stdv. I read it the default number for NumSTD is 2. Thank you.

Answer 2

[Image Analyst]

I don't have the Econometric Toolbox so I can't use autocorr but I can use the regular xcorr. Maybe this will help you:

t = 3:3:30;
A = [3.523;3.523;3.43;3.323;3.43;3.43;3.323;2.923;2.723;2.923];
subplot(2, 1, 1);
plot(t, A, 'b-', 'LineWidth', 2);
grid on;
xlabel('t');
ylabel('A')
title('Original Data')
% [t,A]=textread('Data.txt')
% [acf,lags]=autocorr(A)
autoCorrA = xcorr(A);
subplot(2, 1, 2);
plot(autoCorrA, 'b-', 'LineWidth', 2);
grid on;
xlabel('Index');
ylabel('Autocorrelation Value')
title('Autocorrelation Signal')

[Sasha]

Thank you for you explanation, since i still can't understand the difference between autocorr and xcorr usage, so actually I needed it with autocorrelation function. Do you mind give me a simple hint? like when I should use autocorr and when it's better with xcorr..

[Image Analyst]

I'm not really familiar with the autocorrelation function. It seems different than the usual one we all know. They say

"

The autocorrelation function measures the correlation between the univariate time series yt and yt + k, where k = 0,...,K and yt is a stochastic process.

According to [1], the autocorrelation for lag k is

rk=ckc0,

where

• ck=1TT−k∑t=1(yt−‾y)(yt+k−‾y).
• c0 is the sample variance of the time series.

Suppose that q is the lag beyond which the theoretical ACF is effectively 0. Then, the estimated standard error of the autocorrelation at lag k > q is

SE(rk)=⎹⎷1T(1+2q∑j=1r2j).

If the series is completely random, then the standard error reduces to 1/√T.

"

You probably know more about that function than me. Sorry but I don't really know when you'd use that. I'm guessing it's something special for econometrics applications.