Against the world’s major currencies, the value of the greenback has been strengthening on signs that the U.S. economy is improving — a development that hasn’t happened in recent years. Who knows what might transpire months from today, but some analysts and traders have taken the recent rally as a sign of the beginning of the end of the dollar’s slump.

On Monday, The Dollar Index, a measure of the U.S. currency against its six major trading partners, rose to 82.7742. This follows gains built on last week’s 2.2% rally — its biggest weekly rise in 19 months. The dollar has been particularly strong against the Japanese yen, rising 3.8% to 97.90 yen last week — the most since the last week of December 2009.

“I would not be surprised if the dollar trended higher over the new three or four years,” says Jens Nordvig, global head of currency at Normura. In a May 29 note to clients, he forecasted a prolonged strengthening of the dollar.

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This would be a significant structural shift for the currency. Since 2003, it has generally declined in value, with a few short-term spikes. Unlike the gains we saw previously, however, the dollar has risen on good rather than bad news.

Since 2009, whenever the currency gained, panicky investors worried the economy was in meltdown. The dollar strengthened in the wake of the financial crisis as banks were reluctant to lend. With a credit crunch and interest rates rising, the dollar rose as U.S. stocks sank. And during the most tumultuous months of Eurozone crisis, traders and investors fled the euro for relatively safer U.S. dollars.

All this has led currency experts like Nordvig and others to believe that this time is different; that the recent rally could last longer, at least well into 2014, if not a few more years.

If that happens, the U.S. would lose the global currency war. Three years ago, Brazilian Prime Minister Guido Mantega warned troubled economies around the world were taking measures to weaken their currencies. While this makes exports more competitive, it potentially spells financial turmoil for global markets. Guido predicted the war would intensify this year as the world economy slows, but perhaps he might want to take another look at the U.S.

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Last week, U.S. Federal Reserve Chairman Ben Bernanke said if the economy continues to do better the central bank could slow down its bond purchases later this year, and possibly stop the program altogether by mid-2014 if the unemployment rate falls to 7% from the current 7.5%. U.S. Treasuries have spiked on the Fed’s outlook as investors anticipating that interest rates could rise further fled their investments in bonds. On Monday, the sell-off picked up steam, as the 10-year note spiked to 2.64% — the highest level since August 2011.

With interest rates rising, the cost of borrowing goes up. So expectations for fewer U.S. dollars circulating in the economy have pushed up the value of the greenback. It also helps that while the U.S. is seeing better economic times, troubled economies in Japan and Europe have weakened the yen and the euro.

If this continues, America would lose the currency war by winning with a stronger greenback.