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I'm working on the following task:

Given quarterly data:

  1. a time series representing the 1-year realized (10 years of data) rates of default on a portfolio of mortgages
  2. a slew of realized (10 years of data) macroeconomic time series. Each time series may or may not be relevant
  3. 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?

Thank you!

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  • $\begingroup$ If you don't know the underlying distributions then it sounds like you need to do some exploratory data analysis before anything else. You're trying to drive across the country without first checking if there's gas in the car . . . $\endgroup$ – Unknown Coder Dec 19 '14 at 16:01
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I would suggest you to add spreads to the implied hazard rates, spreads that you regress on the macroeconomic factors. Then you stress by calculating the spreads corresponding to the stressed factors.

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