standardize t distriution and its confidence interval
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I am modeling my data with ARIMA and to check if my model is good I have to compute the residuals and plot the correlation function and partial correlation function of the residuals. If the results of the functions are between [1.96-1/sqrt(sigma) 1.96+1/sqrt(sigma)] that means that the residuals are drawn from Gaussian process, hence my model is good (there are more processes needed to be done to check the model, but I'm not worried about those now).
Now, suppose to model my data I have used ARIMA with innovation comes from t-distribution. If now I compute the residuals and plot the autocorrelation and partial correlation function, does it still need to be between [1.96-1/sqrt(sigma) 1.96+1/sqrt(sigma)].
I guess I have to find what is the 95% confidence of t-distribution and that would be my boundary! Am I right? And the second question is how can I standardize the residuals, knowing that they have t-distribution.
Star Strider on 6 Aug 2014
The t-distribution depends on your degrees-of-freedom (derived from the number of observations in your data set). That information and the tinv function will give you the information you need to calculate the critical values for your data.
The linear regression routines in MATLAB will provide you with Studentized residuals (this link is to the Wikipedia discussion).