The primary goal is to examine the time series of the Japanese equity market over a lengthy period of time to determine aspects of this time series as it moves and what are the factors that may determine its. We study the Index of the Tokyo Exchange over nearly four decades by data analytical methods also known as exploratory data analysis with some principle methods of statistical testing. The aim is to put to rest some arguments concerning the applicability in long range memory modeling some use of methods based serial correlation in the data over this nearly four decades of monthly observations.

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