The top plot sure looks familiar. Evidently they plotted the same data that I used.
Interesting part of the article is that for different periods the lag between housing and stocks changes, and the amount of correlation changes. In the 80’s & early 90’s there was some correlation with NO lag. In the late 90’s the lag required to get high correlation was 12 months or more.
The analysis that shows correlation by changing the lag may be data mining. If you take two signals that are out of phase and actually anti-correlated (one rises when the other falls) and lag them by a long enough factor you can show a positive correlation.
When someone changes the lag to demonstrate that two things are correlated, that makes me instantly cautious about how I interpret the results, especially for quantitative predictions.
When the underlying conditions change, statisticians call the process “non-stationary”, to a layman this means that the way these variables (HMI & S&P) relate to eachother changes over time. This makes it difficult or impossible to use this analysis to do any prediciton.
The author in the link even points this out by stating
“The question of whether there is a lag is an important one, of course, because if there is a lag, then the stock market is likely to fall over the next few months based on the recent decline in the HMI. On the other hand, if the lag seen in recent times turns out to be a temporary phenomenon and the S&P 500 reverts to a more coincident relationship with the HMI, then the recent decline in the latter could already have been discounted and provides no indication of the likely direction of the stock market.”
In other words the author says a stock market decline will either follow or it won’t, depending on where you think the lag should be going forward.
