Question for Expert Forum:

I am working on a Regime-Switching Monte Carlo Simulation for EURIBOR interest rates, where I

1. Estimate separate ARIMA models for three identified regimes (Hiking, Cutting, Stable).
2. Estimate separate GARCH(1,1) models for volatility clustering in each regime.
3. Compute a Markov transition matrix using historical EURIBOR data to determine regime-switching probabilities.
4. Perform Monte Carlo simulations where:
   • At each step, a regime is selected based on the transition matrix.
   • The corresponding ARIMA-GARCH model for that regime generates the next EURIBOR value.
   • This is repeated over multiple paths to explore possible future interest rate scenarios.

I have three specific questions:

1. What is the most appropriate distribution for interest rates? Should I assume normality, log-normal, or something else given the characteristics of financial time series?
2. Is taking the first difference a proper technique to stationarize interest rate data? Given that interest rates are often persistent, is differencing sufficient, or should I consider fractional differencing or alternative transformations?
3. Does this process violate any modeling assumptions? Specifically:
   • Using separate ARIMA-GARCH models per regime, does it introduce biases or violate statistical assumptions?
   • Is it methodologically sound to simulate regime transitions within Monte Carlo, rather than pre-classifying data into fixed regimes before simulation?

I appreciate any insights or literature references that could refine this methodology!

I am currently inexperienced with the topic and I will update when I finished the code. I just needed some advice beforehand.