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Stocks seeing 'bear market' rally: Peter Boockvar

Stocks overall entered a "bear market months ago," and the gains of late are just a "bear market rally," Lindsey Group analyst Peter Boockvar said Thursday.

"This is just the mega-cap bounce," he told CNBC's "Squawk Box." He said the broader market has not seen the same rate of recovery from the lows of the year in late August, when the S&P 500 first dipped into correction territory. After testing but not breaching those levels over the next month or so, the index since the end of September has gained 11.5 percent as of Wednesday's close. For the year, the S&P 500 was up about 2 percent.

Read MoreMel Karmazin: I've pulled my money out of stocks

Admittedly, Boockvar said he's been a long-time advocate that the Federal Reserve's near-zero percent interest rate policy has boosted asset values "well above" where he thinks they would be otherwise.

"There's no easy way out of this without having some pain, economic speaking and asset-price speaking. So we need to start the process," he said. "Zero interest rates is monetary fantasy land. It's not real world."

Boockvar added: "If [the Fed] were truly data-dependent they would have raised last year. Now I think they're just emotionally dependent because they realize they're stuck at zero and God forbid if we go into a recession next year."

In testimony before a House panel Wednesday, Fed Chair Janet Yellen reiterated the possibility of the first rate hike in nine years coming in December. At an evening event, the No. 2 Fed official, Stanley Fischer, said the central bank could quickly see its 2-percent inflation target met once oil and the dollar stabilize.

Read MoreFischer: Fed may be closer than thought to inflation target

Boockvar was pleased the Fed appears to be ready to hike rates. But he said policymakers keep moving the goalposts:. "They keep lowering the standards that would now meet a rate hike," he said, arguing job growth has slowed recently from the more robust levels of last year.

Also on Thursday, Jim O'Sullivan, chief U.S. economist at High Frequency Economics, stressed the importance of the two government employment reports out before the Fed's mid-December meeting, one of which comes Friday morning. Expectations were calling for nonfarm payroll creation of about 183,000 for October, after the tepid 142,000 gain in September. The October unemployment was seen dropping slightly to 5 percent.

"Ultimately, 150,000 [jobs] a month, if you think that's the trend, is more than enough to keep the unemployment rate coming down," O'Sullivan told "Squawk Box."

Those type of numbers could add to the Fed's case for a hike, he said.

"The presumption now is they probably go unless we get weak numbers really at this stage or there's more turmoil in the markets," he said. "There's still time a lot time between now and December 16th. But we're getting there in terms of the numbers right now."

Ed Keon, managing director at Prudential's Quantitative Management Associates, believes a Fed rate hike would help stocks. But on CNBC, he provided a caveat.

"The best thing for the market, just like I thought in September, is if they'd raise," he argued — adding the Fed should also stress "basically, unless something really extraordinary happens, we're done for about six months or so."

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