Trying to plot correlogram of time series data

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%Plot of entire patient one time series
load ('glucose.mat')
glucose_mgdl = glucose * 18;
plot(date1+time,glucose_mgdl),
xlabel('Days'), ylabel('Glucose')
title('Glucose readings vs days/time')
M = mean(glucose_mgdl)
M = 183.4936
S = std(glucose_mgdl)
S = 87.6448
%now get the PDF
figure
[D PD] = allfitdist(glucose_mgdl,'PDF');
Unrecognized function or variable 'allfitdist'.
xlabel('Data (mgdL)');
%now get the CDF
figure
[D PD] = allfitdist(glucose_mgdl,'CDF');
xlabel('Data(mgdL)')
%Plot of correlogram
r = xcorr(date1+time,glucose_mgdl)

Accepted Answer

Star Strider
Star Strider on 19 Dec 2021
Essentially all physiological variables are lognormally distributed. This is inutitively obvious because physiological variables can only take on positive values (so any distributions having infinite support are not applicable), and mathematically obvious by comparing the fit to a normal (or any other) and lognormal distribution, and can be supported mathematically with appropriate goodness-of-fit tests.
Calculating and plotting the autocorrelation is the best I can do with those data.
I also corrected the distribution —
T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/838690/glucose.csv', 'VariableNamingRule','preserve')
T1 = 1438×5 table
date time glucose type comments __________ ________ _______ __________ ________ 2014-10-01 19:14:00 10.3 {'cgm' } NaN 2014-10-01 19:19:00 9.9 {'cgm' } NaN 2014-10-01 19:23:00 9.4 {'manual'} NaN 2014-10-01 19:24:00 9.8 {'cgm' } NaN 2014-10-01 19:29:00 9.6 {'cgm' } NaN 2014-10-01 19:34:00 9.4 {'cgm' } NaN 2014-10-01 19:39:00 9.2 {'cgm' } NaN 2014-10-01 19:44:00 8.9 {'cgm' } NaN 2014-10-01 19:49:00 8.7 {'cgm' } NaN 2014-10-01 19:54:00 8.4 {'cgm' } NaN 2014-10-01 19:59:00 8.2 {'cgm' } NaN 2014-10-01 20:04:00 8 {'cgm' } NaN 2014-10-01 20:09:00 7.9 {'cgm' } NaN 2014-10-01 20:14:00 7.9 {'cgm' } NaN 2014-10-01 20:19:00 7.8 {'cgm' } NaN 2014-10-01 20:24:00 7.8 {'cgm' } NaN
d_t = T1.date+T1.time;
Glc = T1.glucose;
figure
plot(d_t, Glc)
grid
xlabel('Time')
ylabel('Plasma GLucose (m\itM\rm)')
title('Original Data')
Glcmx = Glc == max(Glc); % Detect Saturation ('Railed') Data
Glce = Glc(~Glcmx); % Eliminate Saturation ('Railed') Data
d_te = d_t(~Glcmx); % Eliminate Saturation ('Railed') Data
figure
plot(d_te, Glce, '.')
grid
xlabel('Time')
ylabel('Plasma GLucose (m\itM\rm)')
title('Data Without Saturated Values')
figure
histfit(Glce, ceil(numel(Glce)/10), 'lognormal')
grid
pd = fitdist(Glc, 'lognormal')
pd =
LognormalDistribution Lognormal distribution mu = 2.19456 [2.16697, 2.22215] sigma = 0.533301 [0.514498, 0.553542]
Glcmode = mode(Glce)
Glcmode = 2.2000
Glcmedian = median(Glce)
Glcmedian = 9.5000
[r,lags] = xcorr(Glce,'coeff');
figure
plot(lags, r, '.')
grid
xlabel('Lags')
ylabel('Croorelation Coefficient')
title('Autocorrelation')
.

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