I'm using a CIR short rate model to forecast interest rate paths. I've been thinking and also searching online about different ways of estimating its parameters (a, b and sigma). While there are a number of relatively intuitive ways with their pros and cons (e.g. reshape into a linear regression and do OLS or MLE), I cannot find anywhere how to actually calibrate them and fit them. Is there a way to measure the goodness of fit? From my calculations, the R-squared from the linear regression is meaningless. In what way can you test that your fitted values are similar to your observed values?
To clarify, this question is not about term structures. I'm only interested to see how well it fits to the observed historical time series values before I run simulated paths.
Thanks for any advice!