According to Austrian Business Cycle Theory the prices of capital goods (= asset price inflation) increase first in the course of an inflationary process, while consumer price inflation (= rising consumer prices) only ensues later. The asset price inflation that is currently in train can be identified by a multitude of symptoms. Prices for antiques, expensive wines, vintage cars, but also real estate and especially stocks recently increased strongly.
This quote is actually a very interesting one, because it can be added to our collection of correlations. Whenever you look at the trend in art, stocks, real estate (capital goods), you can predict the CPI. Because capital goods asset prices will always increase first and when this money flows into the economy, the CPI will increase afterwards. Note that art, stocks are not included in the CPI, that's why the CPI doesn't show inflation yet.
Peter Schiff has explained this too in one of his radio shows. He says that the QE that we see now is boosting asset prices. Eventually all these earnings will flow to the consumer and that's when we will see the CPI go up.
So in the graphs below, you will first see the red (art), yellow (stocks) and blue line (real estate) go up and afterwards the CPI will increase. That's why I believe that stocks can go down, while the CPI keeps going up, because we have this delay.