After four months of steady declines in value, Groupon (Nasdaq: GRPN) is finally having a day shareholders can enjoy. Is it time for Groupon owners to breathe a much-needed sigh of relief? No, the damage caused by a share price 80% below Groupon's IPO runs too deep for such a quick turnaround in sentiment. But the nearly 8% spike in stock price on Sept. 11 is certainly a positive for long-suffering Groupon aficionados, including myself.

But there's an underlying concern that should gnaw at Groupon fans: Why the run-up? Without a fundamental basis, it's likely the jump in Groupon stock price is nothing more than a short-term whim for day traders and bargain hunters. That's fine for now, but it does nothing for the long-term investor.

Groupon's decline
At the posting of my last Groupon article lamenting all the negativity surrounding the online coupon leader, the stock was trading at $4.54 a share. Turns out the downward spiral hadn't quite run its course, as Groupon would bottom out around $4.18 the first week in September. At the time, there were two primary reasons for the steady share-price drop.

No. 1, Groupon had recently announced the first-ever decline in quarter-vs.-quarter gross billings for its traditional coupon business. This, according to the naysayers, was evidence of a saturated market and difficult global economics. There are two points worth mentioning here.

First, the gross billings figure neglected to count Groupon's efforts to expand product lines by selling directly the consumer. When added to gross billings, the retail business line management refers to as Groupon Goods actually bumped its Q2 revenues up 1.6% over the prior quarter. And secondly, total revenues climbed 45% over Q2 of 2011. There aren't too many businesses that would complain about a 45% increase in revenues year-over-year in today's economy.

No. 2, Groupon suffers from what one analyst referred to as "online fatigue." Competition from the likes of Amazon.com (Nasdaq: AMZN), with its ownership stake in LivingSocial, was always going to be a factor. If Groupon management needed a reminder that Amazon's for real, the recent Starbucks deal --which has already sold out in many markets, after a tidy 1.5 million coupons were purchased -- was a proverbial slap in the face.

As for Google (Nasdaq: GOOG) and its Offers program, hoping it will be too busy developing iRobot-like artificial intelligence technologies and forget about online coupons isn't likely. Google has been, and remains, a serious competitor of Groupon.

What's happened since
Groupon's accounting woes are old news but still haunt the company to this day. The hope is that naming ex-KMPG finance guru Brian Stevens as its new accounting chief will finally lay those concerns to rest. But does new, financial oversight within Groupon warrant an 8% (give or take) increase in share price? Unfortunately, no. So the search for a fundamental basis behind the bullish sentiment continues.

Direct investors aren't the only ones on board with Groupon right now. Recent options activity has dramatically shifted away from the bears, siding with investors betting that Groupon hit bottom recently in the low $4-per-share range. If the options folks are right, Groupon has significant upside -- possibly as high as $8 a share in the next year. The basis for their optimism? Short-term gains? Possibly hedging against future losses? Again, nothing for Groupon bulls to hang their hats on for the long term.

While I'd love for the Sept. 11 run-up to be sustainable -- hey, I'm on record as a Groupon groupie -- the lack of a fundamental basis for the rise in stock price concerns me. Naming a new accounting chief is nice, but not 8% appreciation nice.

Does Groupon still warrant consideration as part of your aggressive-growth portfolio? You bet. Just be careful running with the Groupon bulls. I don't think they even know why they're so giddy, at least not yet.

Like Google, Amazon has a lot more irons in the fire than online coupon deals. As the leading Internet retailer in the world, Amazon offers investors an intriguing investment opportunity. To get a better handle on the upside, and the risks, of Amazon ownership, take a look at the Fool's premium report.