I am trying to investigate the stability of spread between two short-term interest rates by the example of 1M and 12M Euribor.
I don't think only looking at correlations over time is statisically enough to infer the stability of the spread.
My first thought would be to use a regression framework in which I regress 12M euribor (Y) on 1M (X) and suppress the intercept, because the difference between Y and X will be then only the residual and thus the spread.
Then, it could be tested whether the regression coefficient (Beta) = 1 and whether has remained 1 over time (implying that 12M - 1M is the term spread), and tested whether the residual (term spread) is stationary implying constant spread over time.
I was thinking to use the Engle Granger cointegration test. However, I don't know if it will test what I am aiming at.
My question is:
Does my line of reasoning (regressing, testing beta over time and residual stationarity) make sense? If so, which methods are suitable?