Bootstrap wind data to account for autocorrelation and obtain new slope

Hi there,

I have a sample dataset (12783x2) containing the time and wind speed values overs 35 years (6 hour intervals). I have noted that there is a large amount of autocorrelation in the wind data and thus I would like to use bootstrapping re-sampling to perform a new regression on the data with time to find a new slope that describes the long term trend in the wind speeds.

I have been trying a few options with bootstrap but cannot get my polyfit function to output a new slope for the resampled dataset. Instead I get multiple slopes and intercepts.

bootstrp(1000,@polyfit,test(:,1),test(:,2),1);

I know I am writing this code incorrectly. Any idea how I can just get one new slope of the bootstrapped data?

I will also like to perform the wblft() function on the data as well to see if the resampled data with bootstrp has a similar distribution to the original.

Answer 1

[Cloud Blend]

Because 1000 is your first argument, bootstrp is iterating on your data 1000 times, and returning 1000 slopes and 1000 intercepts. You could simply take the mean

mean(bootstrp(1000,@polyfit,test(:,1),test(:,2),1),1);

If your resamples are sparse enough, that may help with your autocorrelation problem. You may want to compute autocorrelation for a number of different time lags and decide what is best using a high p value or a rho that is close to zero:

maxSamples = 1000; %prevents very large correlations from taking too much memory
maxSkip = 1461; %1 year
rhos = NaN(1, maxSkip);
ps = NaN(1, maxSkip);
for frameSkip = 1:maxSkip
  sampleTotal = size(test,1)-frameSkip;
  sampleInterval = floor(sampleTotal / maxSamples);
  bufferSize = min(maxSamples, sampleTotal);
  buffer = NaN(bufferSize,2);
  sourceCounter = 1;
  for destCounter = 1:bufferSize
      buffer(destCounter,1) = test(sourceCounter, 2);
      buffer(destCounter,2) = test(sourceCounter + frameSkip, 2);
      sourceCounter = sourceCounter + sampleInterval;
  end
  [rho, p] = corr(buffer);
  rhos(frameSkip) = rho(2);
  ps(frameSkip) = p(2);
end