how can I speed up this code?

the following code computes daily Value at Risk, from 03/01/2013 to 12/12/2016, but it takes 3 days.How can I speed up?

    Dati=xlsread('port_banche','portafoglio');
VaR95=zeros(1000,1);
VaR99=zeros(1000,1);
VaR999=zeros(1000,1);
for t=1395:size(Dati,1)
  SottoDati=Dati(1:t,:);
  T=size(SottoDati,1);
  model=arima('AR',NaN,'Distribution','t','Variance',garch(1,1));
  nAzioni=size(SottoDati,2);
  residui=NaN(T,nAzioni);
  varianza=NaN(T,nAzioni);
  fit=cell(nAzioni,1);
  options=optimset('fmincon');
  options=optimset(options,'Display','off','Diagnostics','off','Algorithm','sqp','TolCon',1e-07);
  for i=1:nAzioni
      fit{i}=estimate(model,SottoDati(:,i),'print',false,'options',options);
      [residui(:,i),varianza(:,i)]=infer(fit{i},SottoDati(:,i)); 
  end
  residui=residui./sqrt(varianza); 
  soglia=0.05;
  code=cell(nAzioni,1);
  for i=1:nAzioni 
      code{i}=paretotails(residui(:,i),soglia,1-soglia,'kernel');
  end
  U=zeros(size(residui));
  for i=1:nAzioni
      U(:,i)=cdf(code{i},residui(:,i));
  end
  [R]=copulafit('Gaussian',U,'Method','ML');
  s=RandStream.getGlobalStream();
  reset(s)
  nProve=10000;
  orizzonte=1;
  Z=zeros(orizzonte,nProve,nAzioni);
  U=copularnd('Gaussian',R,orizzonte*nProve);
  for j=1:nAzioni
      Z(:,:,j)=reshape(icdf(code{j},U(:,j)),orizzonte,nProve);
  end
  Y0=SottoDati(end,:);
  Z0=residui(end,:);
  V0=varianza(end,:);
  RendSimulati=zeros(orizzonte,nProve,nAzioni);
  for i=1:nAzioni
      RendSimulati(:,:,i)=filter(fit{i},Z(:,:,i),'Y0',Y0(i),'Z0',Z0(i),'V0',V0(i));
  end
  RendSimulati=permute(RendSimulati,[1 3 2]);
  RendCumulati=zeros(nProve,1);
  pesi=repmat(1/nAzioni,nAzioni,1);
  for i=1:nProve
      RendCumulati(i)=sum(log(1+(exp(RendSimulati(:,:,i))-1) *pesi)); 
    end
    VaR95(t-1394,:)=quantile(RendCumulati, 0.05);
    VaR99(t-1394,:)=quantile(RendCumulati, 0.01);
    VaR999(t-1394,:)=quantile(RendCumulati, 0.001);
end

Answer 1

[Jyotish Robin]

Hi Marco,

I would suggest you to use the Profiler to track execution time. Knowing the execution time of your MATLAB code helps you to optimize it. Thereby you can understand which parts of your computation are slow.

Also, Vectorizing your code is worthwhile. Vectorized code often runs much faster than the corresponding code containing loops.

To know more about vectorization, you can take a look at the following link: https://www.mathworks.com/help/matlab/matlab_prog/vectorization.html

Some other suggestions:

• preallocating a chunk of memory for arrays before entering into a loop in loops can significantly speed up your code by . The zeros() and ones() functions are the most common way to do this.
• Since "bsxfun" is multithreaded and can take advantage of multiple CPUs ,using it may be good for performance improvement.
• Try to implement the algorithm more efficiently.
• Try to use most recent versions of MATLAB.

Hope this helps!

[Marco Della Ciana]

Hi Jyotish, thanks for your answer, I used the Profiler to track execution time, and I saw that the part of the code which is slowest is this

    for i=1:nAzioni
      fit{i}=estimate(model,SottoDati(:,i),'print',false,'options',options);
      [residui(:,i),varianza(:,i)]=infer(fit{i},SottoDati(:,i)); 
  end

I preallocated the memory, but I don't know how to vectorizing that part of the code.

[Jyotish Robin]

Maybe you could try changing the "fmincon" algorithm. Currently it is set to 'sqp'. Try changing this and see whether there is performance improvements.

Read this link for more info: https://www.mathworks.com/help/optim/ug/choosing-the-algorithm.html

Also, there are lot of parameters which you could tune corresponding to different algorithms. Try changing these values (for example, tolerance limits) and see their effect on performance.

See the following link for more details:

https://www.mathworks.com/help/optim/ug/fmincon.html#inputarg_options

[James Wiken]

Hi Marco,

Looking at your profiler results, I have a few suggerstions.

1) Look through your code and see if you have any lines in a loop that do not change over iterations. Take these lines and move them outside of the loop. This helps reduce repeated calculations. On a quick look through I found the following lines:

model=arima('AR',NaN,'Distribution','t','Variance',garch(1,1));
options=optimset('fmincon');
options=optimset(options,'Display','off','Diagnostics','off','Algorithm','sqp','TolCon',1e-07);
soglia=0.05;
nProve=10000;
orizzonte=1;

2) Your code is calling 'optimset' a huge amount of times. Looking at the 'estimate' function I saw that the options you were manually setting were identical to the defaults. Comment out the following lines to remove these calls. If I am guessing right, this should roughly half the runtime of your code:

options=optimset('fmincon');
options=optimset(options,'Display','off','Diagnostics','off','Algorithm','sqp','TolCon',1e-07);

3) If you have access to the parallel computing toolbox, it may be worth trying to parallelize this code. The first thing I would try is changing

for i=1:nAzioni
    fit{i}=estimate(model,SottoDati(:,i),'print',false,'options',options);
    [residui(:,i),varianza(:,i)]=infer(fit{i},SottoDati(:,i));
end

to

parfor i=1:nAzioni
      fit{i}=estimate(model,SottoDati(:,i),'print',false,'options',options);
      [residui(:,i),varianza(:,i)]=infer(fit{i},SottoDati(:,i));
end