I know it's obvious what's going on with phi_22 from the formula, but I'm having trouble answering in a more conceptual, intuitive way. I guess I'm thinking the question is more like, why should the Corr(Y_t, Y_t-2|Y_t-1) become negative when Corr(Y_t, Y_t-1) increases? Am I making this more complicated than it is?
[NEAS: When the correlation for lag 1 increases, more of the correlation for lag 2 is explained by the correlation for lag 1.]