I'm working on the following task:
Given quarterly data:
- a time series representing the 1-year realized (10 years of data) rates of default on a portfolio of mortgages
- a slew of realized (10 years of data) macroeconomic time series. Each time series may or may not be relevant
- A stressed scenario of those same macroeconomic time series for 2 years
Estimate the probability of default using the stressed data.
I don't actually know anything about underlying distributions. The only data I have for inference are these time series.
My initial approach was something like this: I would first make every time series stationary. Then eliminate macroeconomic variables that were not significantly correlated with my dependent variable. Then use a stepwise method to determine the best variables to use in a linear regression. Then I would include those exogenous variables while fitting an ARIMA model. Along the way I would do several tests (e.g., autocorrelation, multicollinearity, stationarity, etc.). Then use that model for prediction.
Note that I actually have several different "portfolios" which I am fitting. Using my above procedure, some of the stressed scenarios appear unreasonable. So, I began looking for totally different alternatives. Are there any suggestions?
I realize this is an unreasonably broad question. To narrow the scope, I've done some brief research and believe some viable alternatives might include:
- Calibrating some dynamic transition densities using Bayesian inference and MCMC
- Calibrating a conditional Vasicek model that allows of autocorrelation
The problem is, I'm not too familiar with these methods and would want to make efficient use of my time.
Would you suggest I attempt implementing these alternatives? Or some other alternative?
Do you have any advice for implementation in R?