I have a time series that reflects the last twelve months default rate for every month-end since Jan 2001. I also have other exogenous variables like credit quality score etc.
Before proceeding, my intuition suggests that while the LTM Default Rate (y) should have dependency on Credit Quality Score (x), or its lagged values, it should also show case a dependency on its past lagged values y(t-1), y(t-2) etc. (my business intition says, there will be a bunching effect, periods of moderate default rates lead to higher default rates and periods of prolonged high default rates lead to low default rates in the future).
What might be the right model to go about modelling this behavior? I am expecting such a model, should have good predictive ability a few datasteps ahead.