NEW YORK (TheStreet) -- Ironic. Let me explain.

There's a bit of grumbling going on about Janet Yellen and her comments yesterday about stock prices being "quite high." Jim Cramer even went so far as to suggest Yellen keep her stock opinions to herself.

While it's worth pointing out just why her statements were not worthwhile (and we'll get to that a bit later on), what needs to be pointed out is the extreme irony of a central banker talking about high stock valuations. When it comes to U.S. equities, the Federal Reserve helped create the high valuations.

And that's just the tip of the iceberg.

A 2014 report by the Official Monetary and Financial Institutions Forum claims that central banks around the world -- including the Fed itself -- own close to half of all global equities. The report is available in hard copy at the OMFIF website for £100 ($153).

The Fed isn't the only central bank buying stocks around the world. The Swiss National Bank, for example, is open about holding 18% of its balance sheet in foreign equities. In fact, in its public filings with the SEC, it lists an astonishing $1.1 billion stake in Apple (AAPL) - Get Report, $627 million stake in Exxon Mobil (XOM) - Get Report, $513 million in Johnson & Johnson (JNJ) - Get Report, and $508 million in Microsoft (MSFT) - Get Report. The SNB owns a total of 2,548 companies all the way down to micro-caps like Resolute Energy Corp. (REN) , which it graced with a $34,000 investment.

The Bank of Japan is another example of a central bank open about buying equities. The Nikkei is still straddling recent highs.

And where do central banks get the money to sink into equities? They print it. And it goes into the stock market. Much of the quantitative easing the Federal Reserve engaged in through the Great Recession and after has helped inflate equities prices. And then the head of that organization warns of high prices -- irony of ironies!

Beyond that, Yellen and other supposed experts have been terrible at predicting the market.

The "irrational exuberance" quote by Alan Greenspan has been well referenced this week. He was off by about 300%, give or take a point or two. Or we can take this gem from former Chair Bernanke from July 2005 commenting on the possibility of a nationwide housing decline:

"It's a pretty unlikely possibility. We've never had a decline in house prices on a nationwide basis. So what I think is more likely is that house prices will slow, maybe stabilize: might slow consumption spending a bit. I don't think it's going to drive the economy too far from its full employment path, though."

You can watch a litany of Bernanke blunders here. Grab some popcorn.

If we want to have some more fun and broaden our horizons a bit to include other economic giants sharing their wisdom, there's Irving Fisher, who infamously quipped that stock prices have "reached a permanently high plateau" six days before Black Tuesday in October 1929. Slingshot forward to 2014 and we're back with Yellen again, who commented in July that small- to mid-cap biotechs "appear substantially stretched." Since then, the SPDR Biotech ETF (XBI) - Get Report, which is an equally-weighted fund, is up 62%.

Conversely, those who purport to know almost nothing about the market are sometimes right when making predictions. Guess which public figure handed in the most accurate bottom prediction in the past decade, perhaps even the past half century? It was Barack Obama, who has no economics degree, but back on March 3, 2009 was inspired to opine the following:

"What you're now seeing is profit and earnings ratios are starting to get to the point where buying stocks is a potentially good deal, if you've got a long-term perspective on it."

The bottom in the S&P came in on March 6. Obama was within 4% of calling it perfectly, almost to the day.

So what? Should the president be running the Fed? Should we all take our cue from him? Of course not. One should always take it with a grain of salt when market predictions are offered, no matter who they come from. And when those predictions come from the head of the Federal Reserve? Add a dash of irony to that grain of salt.

This article is commentary by an independent contributor. At the time of publication, the author held XOM.