Japan's main share index finished above its psychologically important 11,000 point mark for the first time in 15 months this week. Tokyo's Nikkei 225 gained 2 percent over the week to close on Friday at 10,938.
Despite the fact that the Tokyo index lost less than 1 percent on Friday in what traders called a 'technical correction,' the Nikkei remained near Thursday's 15-month closing high of 11,033.
Toshihiko Fukui, governor of the Bank of Japan, says Japan's brighter economic outlook is being led by an increase in demand for exports.
But he says he does not think the domestic demand will recover as quickly.
However, UBS's Japan chief economist Hiromichi Shirokawa says that improved confidence in Japan's banking, property and construction sectors added fuel to this week's rally.
"Right now the market is looking at autonomous or internal demand recovery," said Mr. Shirokawa.
Construction shares on Taipei's stock exchange were also stronger Friday, following news of an increase in home buying there.
The Taiex added 2 percent this week to close Friday at 5,758.
Hong Kong's Hang Seng index managed to hold onto 0.5 percent gain, closing Friday at 10,968.
While confidence is returning to Hong Kong's property market, the Hang Seng property sub-index took a battering on Friday, losing more than 400 points in what traders say is profit taking.
South Korea's main share index slipped almost 2.5 percent over the past 5 days as investors dumped top tier stocks such as Samsung electronics.
Analysts say big South Korean companies are not likely to post further gains and their valuations are high at current levels. The Kospi finished at 748 on Friday.