The present study has been examined the causal and contemporaneous relations stock returns, trading volume and return volatility using of VAR-GRJGARCH and GRJ-GARCH-DCC multivariate models. To estimate contemporaneous relations stock return and trading volume, rather than a single stage procedure, was used the two-stage procedure, which will prevail to definite numerical problems that often arise in estimating of Multivariate GARCH models. In the first and to respond to the first hypothesis, by using a VAR model (but not standard), positive evidence was apparent of causality of trading volume to the stock returns. Reviews of second and third Hypothesis confirmed that, respectively, there is bi-directional causality between stock returns and trading volume and positive causality of return volatility to the trading volume. The result of fourth hypothesis that using the VAR model's residuals in the conditional variance bivariate model, in 10% level shows the significant positive causality of past trading volume to the return volatility. In the reviews of contemporaneous relationship between returns and trading volume, results of AR (1) -MGRJ-GARCH (1, 1) -DCC model, indicates the positive correlation coefficient and significant at the 1%. Research findings about the sixth hypothesis indicating that, respectively, by increasing or decreases in privatization in the studied periods, that meets data published by the Privatization organization, contemporaneous relationship between stock return strading volume does not increase or decrease; and Even in most periods, contemporaneous relationship between these two variables is not necessary significant. Finally, the findings strongly support the existence of an abnormal distribution in Tehran Stock Exchange.