Investors have been piling into Japan’s markets, repeatedly pushing them to record highs. The enthusiasm for Japan’s stocks was reflected on Tuesday when its benchmark index Nikkei 225 climbed to a 34-year high. Will its bull run continue though, and how should investors play this Asian market? Here’s what Wall Street and other pros say, and how to invest — including the stocks to buy. Where do Japan stocks go from here? Alongside India, Morgan Stanley says it prefers Japan over emerging markets and China this year. It says there’s a “rising likelihood” of its bull case target of 2,800 for the Topix index coming into play. That would imply an upside of more than 7%. The “fund re-allocations to Japan have been high year to date driving multiple expansion,” the bank wrote in a Jan. 21 note, explaining its bullish call. Tokyo-based advisor Jesper Koll, a director at stockbroker Monex, predicted last week that the Nikkei 225 could surge more than 50% over the next two years. Jeremy Schwartz, global chief investment officer at WisdomTree, told CNBC’s “Squawk Box Asia” on Friday that Japanese stocks are a “catalyst-rich” asset class. He believes that a “new corporate culture” is emerging in Japan, with companies becoming more shareholder friendly. “You’re seeing the combination of dividends and buybacks … a lot of these companies do have a lot of cash on their books,” he said. “I mean, if I look at the average Japanese company, their cash percentage of market cap, it’s something like three to four times higher than the average S & P 500 companies’ capital market cap,” Schwartz said. “So there’s room for dividends, there’s room for buybacks.” Eastspring Investments says a “new phase” for Japanese companies — with much improved focus on price discipline and improving profits — has taken hold. It said the Tokyo Stock Exchange has launched a corporate governance reform campaign on companies to disclose their plans for improvement, spurred by the fact that many are trading at a price-to-book ratio of below one. That means that many stocks are undervalued. “Reassuringly, the forces driving this new phase seem persistent. As such we are observing a more normalised environment today than in recent years, where improving trend fundamentals are driving share prices,” said head of Japan equities Ivailo Dikov and client portfolio manager Oliver Lee. How – and what – to invest Global investors may find it more accessible to invest in Japan markets via exchange-traded funds. Here are some to consider. Meanwhile, for those who wish to stock pick, these are some of the names in Morgan Stanley’s list of productivity and innovation leaders that it believes can outperform the overall Japanese market. Among sectors, Morningstar likes Japan’s consumer stocks set to benefit from rising spending power, and prefers Kao as a name to play it. It also likes industrials, in particular factory automation companies as it anticipates demand for industrial robots improving this year. It sees upside potential for stocks including Fanuc and Harmonic Drive . — CNBC’s Ganesh Rao contributed to this report.