Inflation and deflation in stock markets

The aim of this paper is to compare statistical properties of a bubble period with those of the anti-bubble period in stock markets. We investigate the statistical properties of daily data for the Nikkei 225 index in the 28-year period from January 1975 to April 2003, corresponded to the periods of bubbles and anti-bubbles. We divide the time series into two parts, the period of inflation (or bubbles) from January 1975 to December 2002 and the period of deflation (or anti-bubbles) from January 1990 to December 2002. We find that the volatility in the inflationary period is approximated by the q-exponential distribution with q = 1.14 while the volatility distribution in the deflationary period is accurately described by an exponential distribution, that is, the q-exponential distribution with q → 1. Our empirical findings suggest that the momentous structural changes have occurred at the beginning of 1990 when the speculative bubble was collapsed in the Japan’s stock markets.