In a CNBC interview, the longtime central bank chief said the prolonged period of low interest rates is about to end and, with it, a bull market in fixed income that has lasted more than three decades.
"The current level of interest rates is abnormally low and there's only one direction in which they can go, and when they start they will be rather rapid, " Greenspan said on "Squawk Box."
Greenspan did not criticize the policies of the current Fed. But he warned that the low rate environment can't last forever and will have severe consequences once it ends.
"I have no time frame on the forecast, " he said. "I have a chart which goes back to the 1800s and I can tell you that this particular period sticks out. But you have no way of knowing in advance when it will actually trigger."
One point he did make about timing is it likely will be quick and take the market by surprise.
"It looks stronger just before it isn't stronger, " he said. Anyone who thinks they can forecast when the bubble will break is "in for a disastrous" experience."
In addition to his general work at the Fed, which also featured an extended period of low rates though nowhere near their current position, Greenspan is widely known for the "irrational exuberance" speech he gave at the American Enterprise Institute in 1996. The speech warned about asset prices and said it is difficult to tell when a bubble is about to burst.
Those remarks foreshadowed the popping of the dot-com bubble, and the phrase has found a permanent place in the Wall Street lexicon.