Former Federal Reserve Chairman Alan Greenspan is predicting that the stock market will continue to go up — even to record levels.

But based on Greenspan’s history, there may be a reason to worry about his speculation.

“In a sense, we are actually at relatively low stock prices,” Greenspan said in an interview with Sara Eisen on Bloomberg Television yesterday. “So-called equity premiums are still at a very high level, and that means that the momentum of the market is still ultimately up.”

Greenspan pointed out that the stock market is “just barely above 2007” — which he says opens up the possibility for a huge rise.

While the potential for growth is undoubtably real, here is one reason to reconsider (via Gawker):

Greenspan in 2004: “American consumers might benefit if lenders provided greater mortgage product alternatives to the traditional fixed-rate mortgage.”

Greenspan in 2005: “Although a ‘bubble’ in home prices for the nation as a whole does not appear likely, there do appear to be, at a minimum, signs of froth in some local markets.”

Greenspan in 2005: “The resolution of our current account deficit and household debt burdens does not strike me as overly worrisome.”

The housing bubble then burst and the economy tanked.

Greenspan in 2008: ““I still do not fully understand why it happened.”

Greenspan to Bloomberg, 2013: “In a sense, we are actually at relatively low stock prices… [the market has] gone up a huge amount, but it’s not bubbly.”

Based on that history, investors are likely taking Greenspan’s current prediction with a grain of salt.

Meanwhile, the Standard & Poor’s 500 Index increased 23.03% through the year (up through yesterday), so it’s on par with its 23.5% surge in 2009.

This of course comes as insiders say the Fed will put off cuts to its monthly bond purchases until the market improves.