I am a student writing my thesis on default rate modeling. My major is finance, so I'm not really experienced in econometrics. I'm trying to create a model for quarterly corporate default rates (percentage of defaulted corporations in the previous 12 months) with macroeconomical variables (GDP growth, interest rate, debt/GDP, etc.)
My problem is, that according to ADF and KPSS my variables are non-stationary. Differenciating doesn't really help, and second differences hold no explanatory value. The variables are not cointegrated. I'm using a sample of 17 years (60-70 values, depending on the variable lags). They should be stationary on the long term (100 years), but my sample is very narrow.
Because I'm using quaretly data of annual default rates, the dependent variable is also heavily autocorrelated. Using annual data shows no autocorrelation, but 16 variables are few for a model.
My goal is to examine the significance of the independent variables and their lags in different sectors, and also trying out different methods for modeling (linear, linear with lags, log-linear, diffeneciated, and all with Hodrick-Prescott filter).
In real life it is common practice by banks to just use linear regression, which I did, and got awesome results, but it turns out at the end that the data needs to be stationary and non-autocorrelated for this model.
The only appropriate model I found was ARDL which suggests 4 lags and it shows that all four lags of the dependent variable is significant, so it's not really helpful for me.
I'm running out of ideas what kind of models to use or how to explain why I used linear regression.
Please help, I'm getting desperate.
edit: Data used
edit2: I tried to use Newey-West and Hansen-Hodrick Standard Errors to correct the issue of (overlapping) autocorrelation, the coefficients and the Durbin-Watson value did not change, only the p ant t values in a minimal way.
edit3: MY final regression model is ln(hp_DR)= -0,3349+0,0182*hp_debt/GDP(t-2))+ + 0,0639* hp_interest(t-11)- 0,0182* hp_GDP(t-9)+ μ,
DR is the default rate in percentage, debt/GDP is corporate debt/GDP rate in %, and interest rate is government 10 year bond yields. All with Hodrick-Prescott filter (hp) and appropriate lags.