Japan's Nikkei boosted by weaker yen
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Japan's Nikkei share index hit yet another 15-year high on Tuesday after rising for the fifth day in a row.
The move came as the yen weakened against the dollar amid speculation about what US Federal Reserve chair Janet Yellen might say regarding rate rises in the US later in the day.
Tokyo's benchmark Nikkei 225 closed up 0.74% at 18,603.48.
A weaker yen helps big exporting firms in Japan because it makes their goods cheaper overseas.
The dollar rose to 119.22 yen compared with 118.76 yen in New York trading.
Shares in Hitachi fell 0.8% following reports that the company was about to buy the rail business from Italy's Finmeccanica. The deal was confirmed after the market had closed.
In Hong Kong, the Hang Seng index closed down 0.35% at 24,750.07. Markets in the rest of China continued to remain shut for the Chinese New Year holidays.
HSBC's Hong Kong-listed shares fell after the bank reported lower-than-expected profits on Monday.
HSBC said 2014 had been a "challenging year" after reporting a 17% drop in profit to $18.7bn (£12.2bn), blaming the fall on $2.4bn in fines and settlements.
CMC Markets' Singapore-based analyst Nicholas Teo said it was difficult to find a silver lining in the gloomy report.
"Conduct fines and settlements for currency rigging have left a dent in their numbers," he said.
"Even simple operational metrics such as operating costs controls and margins were a disappointment. All this has come at a time when the company is faced with a tax evasion scandal at its Swiss private bank."
BHP Billiton results
In Australia, the benchmark S&P/ASX 200 closed up 0.3% at 5,926.99.
Mining giant BHP Billiton's Sydney-listed shares were trading higher, despite the firm posting a fall in underlying profit for the half-year to 31 December.
The firm, which is the world's biggest mining company, said its profit for the period fell by 31% to $5.35bn (£3.46bn) - but the numbers were better than industry analysts were expecting.
In Korea, the Kospi share index closed up 0.4% at 1,976.12.