Abstract
The aim of this paper is to show new empirical results on the statistical properties of absolute log returns, defined as the absolute value of the log return, in a stock market. We used the daily data of the Nikkei 225 index of the 28-year period from January of 1975 to December of 2002, and compared the statistical properties of the return and absolute log returns in the inflationary (bubble) period with those in the deflationary (anti-bubble) period. Our results show that the distribution of absolute log returns is approximated by the q-exponential distribution where q = 1.14 , that is, a power-law distribution, in the inflationary period from January of 1975 to December of 1989, and it is accurately described by the q-exponential distribution where q = 1 , that is, an exponential distribution, in the deflationary period from January of 1990 to December of 2002.
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