Trying to plot correlogram of time series data

%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)

Answer 1

[Star Strider]

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')

.