Apple buyers cautiously rejoice, charts favor bulls

(Click for video linked to a searchable transcript of this Mad Money segment)

After a very difficult 12 months, is Apple finally about to resume its march higher? Chart patterns suggest it is.

Apple stock has confounded even the shrewdest investors for quite some time now. After printing $700 in September 2012, the stock slipped below $400 in the spring of 2013.

The sell-off was generated, in part, by skepticism that Apple CEO Tim Cook would be able to drive innovation in the same way as founder Steve Jobs. Sentiment became extremely negative.

Nonetheless, fundamentals seem to favor buying.

Apple is a relatively inexpensive stock, trading at 12 times next year's forward earnings and there's still tremendous growth potential for the iPhone across the emerging world.

In circumstances such as these where an advance would seem just as likely as a decline, pros such as Jim Cramer often turn to technical analysis. And the following technical analysis was provided by Carolyn Boroden of FibonacciQueen.com and a Cramer colleague at RealMoney.com.

Boroden sees a slew of signs and patterns that lead her to conclude that Apple has experienced a momentous trend change. In a nutshell, she thinks Apple is ready to roar.

Angel Naverrete | Bloomberg | Getty Images

As a Fibonacci analyst, Boroden's market insights are based on the work of Leonardo Fibonacci, an Italian mathematician from the middle ages, who discovered a series of ratios that repeat themselves over and over again in nature—23.6%, 38.2%, 61.8% and 100%.

According to Boroden and other Fibonacci analysts, they also show up in stock charts.

Boroden looks at a stock's past swings, and then she looks for retracements of these moves that hit the key Fibonacci levels, or extensions of those moves that do the same.

And what she found in Apple was five Fibonacci price relationships that clustered between $386 and $395. Boroden finds that when you get a cluster of these Fibonacci levels all together, it can mean that a stock is about to change course in a major way.

However, Boroden doesn't only examine Fibonacci relationships in price – she also examines those relationships in time. Again she found a cluster of relationships which suggest to her the stock is about to see a major trend reversal.

Those are two important Fibonacci signs. But there's more.

Boroden also believes Apple made a double bottom when it re-tested the April lows at the end of June. That's positive.

Also she says on July 9th, Apple's 5-day exponential moving average crossed above its 13-day moving average. She also says Apple later crossed above its 50-day moving average, as well as its 200-day moving average. Chart watchers call the patterns a bullish crossover.

In addition, Apple has now rallied further over a longer period of time than in every other rally since the stock peaked last September. This suggests to Boroden that the current move is very different from the previous brief upward swings during a general move lower.

Based on Boroden's Fibonacci calculations, she thinks that Apple could trade up as high as $582. And if the stock can break above that level, Boroden's analysis suggests Apple could ultimately trade $792, that's a new all-time high.

---------------------------------------------------------------
Read More from Mad Money with Jim Cramer
Cramer: Europe about to buoy US market, really!
Sector laggard about to play catch up?
Bottom signal for this industrial metal?
---------------------------------------------------------------

Cramer thinks the analysis warrants serious attention. He believes that developments overseas suggest the economies of Europe are improving at a somewhat rapid clip. "Apple has a gigantic business on the continent," he said.

"Global recovery could generate significant upside for this stock," he said. All told, Cramer thinks these developments are too significant to ignore. "I think you can scale into a position on any weakness. It's a cheap stock."

Disclosure: On Wednesday August 14th, Cramer owned Apple on behalf of his charitable trust.

Call Cramer: 1-800-743-CNBC

Questions for Cramer? madmoney@cnbc.com

Questions, comments, suggestions for the "Mad Money" website? madcap@cnbc.com