Why does the function ploterrcorr display a graph with the values of autocorrelation that are much more than 1?

It is quite strange that the values of autocorrelation of each delay displayed in the graph are much greater than 1, and I don't know the reason and I wonder if there is someone that has ever found this case. I'm Chinese and my expression may be not quite clear and approriate, hope you could forgive me.

[dpb]

Your English is quite good...

Would need to see actual code to see exactly, I don't have the TB so can't play around -- the doc is of little (as in no) use here -- it says

ploterrcorr(errors,'outputIndex',outIdx) uses the optional property name/value pair to define 
which output error autocorrelation is plotted. The default is 1.

but there's no list of the possible values nor which actual statistic the numeric index correlates with. VERY bad documenation; unusual for TMW doc although the TB doc in general is far from the standard set for the base product I've noted -- and seems to be getting worse with newer releases.

[志顺 常]

@dpb Thanks for your praise. I have seen the doc of the function, and I am also confused about the part that you have displayed.

The reason why I need to use the function is that I am trying to use BPNN model to forecast the values of a given time series as accurately as possible and I need to check the autocorrelation graph. If you need, here are my code and the given time series:

k=36;
lag=k;
x=readmatrix('x.xlsx','Range','B1:B408');
n=length(x);
traindata=zeros(lag,n-lag);
for i=1:n-lag
    traindata(:,i)=x(i:i+lag-1);
end
results=x(lag+1:end).';
[traindata1,~]=mapminmax(traindata);
[results1,rs]=mapminmax(results);

net=newff(traindata1,results1,[20,1]);
net.trainParam.epochs=1000;
net.trainParam.goal=1e-6;
net.trainParam.lr=0.01;
net.divideParam.trainRatio = 80/100;
net.divideParam.valRatio = 10/100;
net.divideParam.testRatio = 10/100;
[net,tr] = train(net,traindata1,results1);
trainresults=sim(net,traindata1);
trainresults=mapminmax('reverse',trainresults,rs);

close all
figure, plotperform(tr)          
res=trainresults-results;
figure, ploterrcorr(res)        
figure, parcorr(res)             
[h,pValue]= lbqtest(res);        
figure,plotresponse(con2seq(results),con2seq(trainresults)) 

writematrix(trainresults.','x.xlsx','Range',['C',num2str(lag+1),':C408']);

Thanks for your attention.

[dpb]

I don't have any more insight -- and not having the TB can't go look myself.

Is the function ploterrcorr an m-file in the TB, perchance? What does

which ploterrcorr

return at command line? If it's an m-file, then you can open it in the editor and see if you can tell how it is computing or what it is using to compute the correlation values it plots.

You could also just use the builtin base correslation functions in MATLAB and forego the fancy plot to compare....you might find there's a fixed normalization factor that could be applied to scale the results.

Or, the various optional values of the selection must be listed in the input processing of the function; you could at least see what those are and hope for some additional comments in the file.

After that, it would seem worthy of a "Quality of Implementation" bug report that the doc is so incomplete -- if you're not in the US, I'm not sure the protocol to submit; in the US it's just email to the support link.

[志顺 常]

@dpb Thank you very much indeed, I have not learnt how to find the m-file of some function until you told me. I'm trying to check the code, although it is quite long. If I could find the bug, I will try to submit it to the official. And finally, I need to express my gratitude to you for your helpful advice.

[dpb]

Don't misunderstand; I don't think there's an actual bug in the code; I expect it is working as is intended just that what is intended isn't documented as to what it is actually computing.

Note that you can simply type

edit ploterrcorr

at the command line and the m-file will be opened in the code editor automatically, presuming the function exists, of course, and is in the MATLABPATH such that it is accessible to run. When you do this, be VERY careful to not accidentally make any changes in the file that could corrupt it.

You'll see that even builtin functions like mean have an m-file stub that contains the help text although the code isn't displayed; just a note it's a builtin function.

What you're looking for here is simply to see if there are enough comments in the file to identify the particular correlation functions it is using and what options are available.

On the latter, you can always just pass in a sequence of integers from 1 on up as the optional 'outputIndex',outIdx argument and see what the results are and how many indices it will take. Perhaps (probably?) one of those will be recognizable as the normalized version you're wanting.

[志顺 常]

@dpb Sorry，I misunderstood your meaning. And I found that the code is quite difficult to understand, and I only found this part of the code which mentions the item 'Output Index':

function info = get_info
  info = nnfcnPlot(mfilename,getString(message('nnet:nnplots:PlotErrCorrName')),7.0,[...
  nnetParamInfo('outputIndex','Output Index','nntype.pos_int_scalar',1,...
      'Index of error element to plot.'), ...
  ]);
end

and it has no comments in the m-file... Additionally, I have tried some integers but it doesn't work.It seems that 1 is the only appropriate input, but the initial problem is still not solved.

[dpb]

I'm guessing it's outputting the raw, unscaled estimator which, remember, is

Rxx(m)=E{x(n+m)x(n)}

Use

R=xcorr(res,20)
plot([-20:20],R)

and see if you don't get same result.

See xcorr doc for scaling options, it is

R=xcorr(res,20,'coeff');

that is the one you're expecting -- you'll also see it's nothing but the raw one divided by the actual R(0) so it's simple-enough to fixup your case by normalizing yourself.

Answer 1

[nick]

Hi 志顺 常,

I understand that you are facing an issue in figuring out the reason for “ploterrcorr” to display a graph with the values of autocorrelation greater than 1 at no time lag.

The autocorrelation at lag 0 is equal to the mean squared error and is not normalised. There are two common conventions for error autocorrelation plots:

Either the mean correlation is plotted directly, in which case the height at 0 lag will be the mean squared error, or the correlations are normalized by mean squared error so the lag 0 height is 1. The relative heights and relative confidence band, are the same with either convention. In ploterrcorr it is showing the former, as it shows the additional information of MSE. This is also a common convention for signal processing and control systems.

Kindly refer to “help ploterrcorr” in MATLAB command window to know more about “ploterrcorr”.

Hope it helps.

Regards,

Neelanshu.

[志顺 常]

Hi Neelanshu,

I really appretiate your detailed reply to my answer, it has been a long time since I posed this question so that I almost forget the definitions of these concepts. But just now, I took some time to try to improve my code again and I found that it did work as long as I added one line of code that performs normalization by mean squared error! The image is posted below:

just as you mentioned, I drew the figures without normalizing the data by mean squared error. By now, I think this question is completely resolved. At last, thank for your help again!