I get it now. The real estate market picked up in late 1992 for one year, but rising unemployment nipped that recovery in the bud, making the market go down in late 1993 to late 1995.
Despite the up and down of sales, median price did not start rising until 1996. Perhaps inventory would explain some of this; maybe sales were increasing in 1992, making it appear that there was a recovery, but rising unemployment was causing inventory to spike as well, making months inventory stay high. Perhaps using months inventory as a predictor would not have given a false signal that the market had turned. I am back to wondering about inventory as a predictor, since the data doesn’t seem to be available.
So my theory is that on the way down, inventory is not as important, as slowing sales indicate the market is turning, and the slower sales pace causes inventory to rise. As the cycle turns down, inventory rises not only due to a fall in sales, but also due to distress and REOs. When sales pick up, there is no correlation with price as long as REOs are still high.
Maybe none of this makes sense, since you already accounted for NODs.