Long-run properties of trading volume and volatility of equities listed in DJIA index

In this paper, the authors explain the notion of long memory and report their results concerned with the long memory properties of trading volume and the volatility of stock returns (given by absolute returns and alternatively by square returns) of American companies listed in DJIA index. The contributors focus on calculation of long memory parameters and try to answer the question of whether or not the degree of long memory is the same for the trading volume and for the return volatility data and whether these are fractionally cointegrated. Computations are performed on a daily basis for the whole period from January 1990 to November 2005 and in four sub-periods: January 1990 to December 1993, January 1994 to December 1997, January 1998 to December 2001 and January 2002 to November 2005. We established that for the equities listed in the DJIA index the log-volume (the logarithm of trading volume) and returns volatility exhibit long memory. Moreover, these two series have the same long-memory parameters for most of the equities. This common long memory of both series is especially strongly pronounced in the latest data. On the other hand, there is no evidence that log-volume and volatility share the same long memory component. One important question which arises here concerns the source of long memory in the series. The existence of long memory in the series under investigation may reflect the statistical properties of fundamental factors underlying their behaviour or qualitative changes which take place on stock markets. According to empirical investigations, the growing share of stocks by institutional investors is accompanied by an increasing autocorrelation in returns and trading volume data. On the other hand, long memory is related to autocorrelation. Thus, in our opinion the increasing presence of long memory in the latest American trading-volume data may be caused by the growing share of equities by institutional investors.