Suppose that we have bankruptcy data representative for Small and Medium-sized enterprises in a country. We can therefore calculate default rates. Furthermore suppose that we found that GDP, unemployment rates and interest rates seem to be significant macro economic factors that could explain there default rates.
Now we use regression to fit the macro economic variables to the observed default rates. My question now follows: If I suppose to have a portfolio of SME companies with only default rates from the last year. How could I using the above backward extrapolate these default rates, using the macro economic factors?