great site!
I have collected monthly deals data for how new ships are being finance from 2005-2012. The data consists of "deals" made by different shipping companies and the amount raised in each deal. The deals can split into the following categories: Bank Loans, Bonds, IPOs and FOs.
Bank loans has been the premier financing option, accounting for 70-80% of total capital raised pre-2008. I am therefore looking to do a time series analysis to see if there has been a structural break (chow test) in the use of bank loans, and that other forms of financing such as Bonds, IPOs and FOs has increased post the financial crisis (2008).
My question is, will I have to conduct a chow test for each variable to prove the structural break or can I somehow incorporate all variables into one analysis?
Thanks in advance!
Best Answer
You could go ahead and just add all these "alternatives" giving you a single vector. It tells you nothing about the interaction of those terms but if you are just looking into wether there was a structural break because of different investments it should suffice (as long as you have data for all alternatives, that is).
Otherwise you'd probably have to use multiple dummies and interactions. On the one hand it is a good idea to have one non-interaction dummy for your slope just because you never know what you missed. On the other hand you'll have a shitload of multilinearity in such a model.
It really depends on how you are approaching this. If you already have a concrete, single day for all those other variables then you can just go ahead and do an F/Chow test on that date for all simultaneously. If that is significant, you can start testing combinations. Once again, multicollinearity will make this a bitch.
On the other hand if you do not know a predetermined date, you'll have to start with a QLR test anyway. I have written on this previously but it turns out to be an optimization problem.
I'd just write a program to test QLR test all dates and dummys and pick the combinations with the highest probability, then go from there.
To answer your question: There is no easy way to test for the correct combination of dummys and dates other than to test around it. Technically if you are really having trouble finding any significance, you'll have to make sure you use modified critical values (Quandt likelihood ratio test criticals) as well.
But all of this depends on the validity of your model. Because those series you mentioned might not behave very well anyways. From personal experience fitting a heavy dummied model to these kinds of price timeseries, it ain't gonna be pretty.