Summary: Take the US tech bubble of the 1990s, add the subsequent real estate bubble of the 2000s, multiply by two, and you have a good approximation of the events leading to Japan's stock market crash in 1990.
The Nikkei stock index rose more than 900% in the 15 years before it finally topped. It was a frenzy powered by a belief that Japan Inc. was on its way to taking over nearly every major industry worldwide. The stock market bubble was further fueled by a massive real estate bubble at least twice the size of the one the US experienced in the 2000s. Tokyo alone became more valuable than all the land in the US. In short, it was the product of a tsunami of monumental and concurrent events that are unlike anything present in the US today.
Long advances in the stock market bring out fears that the rise will end in a crash. A current meme is how the US market today is just like the one leading up to the 1987 crash. That same argument was made in 2013, 2014 and 2016, and failed each time. More on that in a recent post here.
Today's stock market is sometimes compared to Japan's main stock index, the Nikkei, in the years leading up to its brutal crash in 1990.
Some might recall the Nikkei's spectacular advance. The index rose 30% in 1989 alone, but this came after a long bull market. Over the last 5 years of that bull market, the Nikkei rose 3.4 times; over the last 15 years, it rose more than 10 times. The rise was relentless.
The long, sustained, uncorrected and ultimately parabolic move in the Nikkei is almost without parallel. The appreciation of the US stock indices leading up to today are nothing like it. The S&P's appreciation over the past 10 years is 1/4th that of the Nikkei into its peak. (The Nikkei comprises the 225 largest companies in Japan; the S&P 500 is the closest comparable index in the US).
But the Nikkei's epic rise is not completely without parallel. Into its peak in 2000, the Nasdaq Composite (COMPQ) crushed even the Nikkei's rise a decade earlier. The S&P's rise was not quite as spectacular, but it was stunning nonetheless.
So, if you are looking for a parallel to Japan's Nikkei in the 1980s, the US in the 1990s ahead of the tech bubble crash is very good. The current bull market is not.
Spectacular stock gains lead to an investing frenzy and bubble that ultimately bursts. In the US in the 1990s, teachers and policemen left their jobs to become day traders. IPOs gained 300-500% on the first day of trading (more on the US's 1990s euphoria here).
The same retail investor euphoria that gripped the US in the 1990s had similarly gripped Japanese investors a decade earlier. Real incomes had more than doubled in just 20 years. By the late 80s, Japan had suddenly become one of the richest countries in the world.