What would be the proper way to determine statistically significant changes between time periods within a time series (between Yn and Yn+1)? I thought about taking the first difference and calculating the z value for the difference value.
With provided details I think a self-extracting threshold model might server your purpose. If you are an R programming language user you can use
tsDyn package. The
setar function in the package can fit model to different regimes determined by significant change.