Autocorrelation of residuals Analysis

Hello I am currently working with Non Linear Models and the System Ident. Toolbox in my university. I managed to get a good fit for the data and my model,

however I am not sure how to interpret the Autocorrelation of the residuals for my model, which is shown below. They seem to be okay except for the range of

-10/+10 samples. Do you have any idea how to interpret this results and how I can try to change them? I tried different orders but nothing really changed, just the shape

seemed to move a bit.

I thought it might be because of the data itself. I am measuring temperatures which have a an approx error of -4/+4 C° because of the sensor. Could this be a reason? Also what exactly does this graph mean? I interpret it like this: When looking at big sample quantities of +10 and more my mode is doing fine, however if i look in the near vicinity of my data, lets say sample 293 and its -5/+5 closest neigbours there is a relatively big error in measuring.

Answer 1

[Rajiv Singh]

If the residue curve (solid green) is within the region defined by the dotted green lines, that indicates that any information in the residue is statistically insignificant for those lags. The dotted green lines define a 99% confidence region of statistical insignificance of the data.

The residuals are strongly correlated at lag 0 and hence the top plot value at t=0 is always 1. That is not a problem. You probably have a good model since the residues are not correlated with the input. The residuals themselves show some correlation at small lags. This could mean that the residuals are colored. If capturing the nature of the noise (that is, linear filter that is coloring a white noise disturbance) is important, pick a model structure with higher order for the noise component. For example, if you are using an ARX model, you would consider using an ARMAX model while choosing a sufficiently large value for the order of the C polynomial in the equation A(q)y(t) = B(q)u(t) + C(q) e(t).

[Nils B]

Thanks for your advice! This was very helpful! However what do you mean by "colored residuals" ? I did not find anything on that term in the literature?

[Rajiv Singh]

I meant residual that is colored noise. Colored noise is white noise filtered by a linear filter commonly called a noise component of the identified model in identification literature.