Many empirical studies show that both equity volatility and its trading volume have long range dependence and can be modeled as fractional integrated processes. The objective of this study is to investigate relationship between volatility and volume.We adopt four estimators of volatility, which includes the squared log returns, historical volatility, iterative t estimators and $GARCH$ estimators. The results show that among the four estimators squared log returns usually have the largest integration orders and produce hightest ratios of fractional cointegration. The fractional integrated orders are estimated separately and jointly, and the cointegration parameters are estimated by ordinary least squares, a narrow band frequency domain least squares method and a semiparametric estimator of Whittle likelihood. Models are also established when volatility and volume are not fractional cointegrated.

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