Even as U.S. stock indexes hit all-time highs, Warren Buffett predicts they’ll go far higher in the long run.

Right now, he very much favors equities over bonds, warning some investors could lose a lot of money in long-term fixed-income assets when interest rates eventually start to rise.

In a live appearance on CNBC’s Squawk Box Monday morning, Buffett told Becky Quick. You’ll see (stock) numbers a lot higher than this in your lifetime.

Acknowledging that milestones like Dow 15,000 can draw Main Street’s attention to stocks, Buffett said people should pay more attention when indexes cross those milestones on the way down because that’s when stocks are cheaper and more attractive to buy.

While not as cheap as they were a few years ago, Buffett thinks stocks are now reasonably priced and not ridiculously high.

There could be a pullback for stocks at any time, Buffett said, but warned against attempts to time the market. People pay way too much attention to the short term.

Buffett said that bonds are a terrible investment right now because they are priced artificially high due to the Federal Reserve’s massive asset buying program and could lose people a lot of money when inevitably interest rates start to rise. He doesn’t know when that will happen and he doesn’t know how much rates will rise, but he’s certain they will be going up eventually.

While he has bought bonds in the past under different circumstances, he generally prefers productive assets to fixed-income investments.

Buffett also warned that it’s crazy to get enticed into a risky investment because someone promises you a higher yield. I can take you to the waterfront and they’ll promise you 15 percent, he joked.

Buffett said he sees no major changes for the U.S. economy over the past four years. It continues to show gradual improvement. moving forward, but at a slow pace. From his viewpoint, Demand has come back, but slowly. He does see some fairly strong improvement in housing.

He called Fed Chairman Ben Bernanke a gutsy guy who has done very, very well keeping the economy on the right track. Buffett did concede he might have lifted his foot off the accelerator pedal earlier, but he’s not sure how to do that.

Lacy O'Toole | CNBC

Warren Buffett

Buffett also endorsed JP Morgan Jamie Dimon as the bank’s CEO. Asked about efforts by some shareholders to split the chairman and CEO roles, Buffett said Dimon should keep both jobs.

Buffett said each year when the Berkshire board meets, he gives them a chance to talk without him there.