An autoregressive model to get the future evolution a non-jumpy evolution of the interest rates seems a good option , but not taking into account the possible future variations in credit rate states decreases its forecasting power.
Using a split in the R actual rate, into a rate P which is always positive (floored at 0) and a second rate N, taking negative values, including zero does not make sense as well. One could use (see the approach of RiskMetrics after the negative interest in Switzerland appeared) an empirical approach: R=P+N to model a set of the instruments, gives the option to use either R or P for an other part of instruments and uses strictly P to model the remaining part of instruments; but this is inconsistent. Otherwise, one could use a two-factor model, based on the same spit of R into P and N; but this is based on the assumption that the market price for short interest rate risk is zero which is not true, taking into account that the negative interest rates in France / USA are not supported by a triple A rating, and that Germany might loose its triple A as well.
As an overall quesstion, should one split or not the modelling of observed negative interest rates in modelling a theoretical positive interest rate supperposed to an always negative theoretical interest rate?
