# Regression on default data and backward extrapolation

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?

• I think you may need to be much more precise about your analysis to get better advice. Using regression just is too broad a description: is this panel data, etc.? The bottom lines include (a) no model is guaranteed to perform well with quite different inputs (b) you may not have practical alternatives. – Nick Cox Jan 15 '16 at 12:58
• If you want details; I used a brute force regressions (univariate) to find macroeconomic factors that seem significant for certain default rate sets ($R^2$ big). One can use different kind of regression methods (say log transform) to regress default rates on GDP, unemployment rates, interest rates (significant factors) to find coefficients etc. But say we assume this default set is representative of a smaller portfolio (which only has few observations) could one using this knowledge to extrapolate to obtain more historical default rates? – user100783 Jan 15 '16 at 14:13

Reverse your data set i.e. set the first observation equal to the most recent (true observation), the second observation to the penultimate one ( next to last most recent true observation) ,... the last observation to the true first observation. Develop a transfer function and forecast. These forecasts can then be used as the "lost values" or "unavailable values" .

• OP does not appear to be using time series analysis at all. No doubt your view is that (s)he should be! – Nick Cox Jan 15 '16 at 12:46
• Yes .. but to me everything is a nail and I have a hammer . This "GDP, unemployment rates and interest rates seem to be significant macro economic factors " suggested to me that the OP was using historical data thus time series tools seemed relevant .... – IrishStat Jan 15 '16 at 12:55
• I indeed try to use time series tools as much as possible. I tried to make my question as general as possible. Going into time series details would only make it more complex to answer in my opinion. Is there any literature I could read that applies this method? Seems like a reasonable method. – user100783 Jan 15 '16 at 14:08
• I take full credit ( grin ! ) for having first invented/suggested this reasonable scheme to predict earlier points although others may have also suggested it using the term backcasting. If I were you and I wanted to avoid the pitfalls/challenges/opportunities/improvements available from using time series I would just use OLS regression BUT you are still going to have to provide the values for the X's ( the eXogenous series) . – IrishStat Jan 15 '16 at 15:20
• As a mathematician myself I would prefer the more elegant approach. OLS does not seem a challenge. I do wonder if there is some specific literature that already applied such methods? Thanks for the help though! – user100783 Jan 15 '16 at 21:14