Multivariate GARCH Models On The Relationship Between Price And Trading Volume

In Wall Street, there is a famous say 'volume move before the price', which describes the importance of trading volume in the investment theory. And the relationship between stock trading volume and price defined in this sentence improved the situation of technology analysis theory.Mixed Distribution Hypothesis ( MDH) gave a theory support for the relationship between trading volume and stock price. MDH point out that the underlying invisible information flux pushes the price and trading volume to fluctuate at the same time, and if there is an impulse for the information flux, it is going to bring a change to the price and trading volume. This is agreed on the essential hypothesis of technologic analysis theory. Just this hypothesis enlightened economists to imply the time series methods into the forward price and volume estimation. In these researches, GARCH models worked very well, and attracted great attention form all over the world.After tested there actually was a linear and nonlinear Granger causation relationship between trading volume and price, we set a binary GARCH model with the profit of investment and exchange rate as the two variables, in which the mean equation was a VAR expression. These two variables are the adjusted replacements of price and trading volume series separately. To improve the estimate definition, we adjusted this model, added two exogenous variables, which can show what a trend the price or volume are in. All of we did, we try to give better estimation for the price and trading volume in the going future, and give useful investment advice.In this paper, we did several relative statistics tests, such as basic statistics character test, auto-correlation test, ARCH LM test and Granger causation test. In order to test the model's ability of estimation, used the data including price and volume series of 12 stocks form China's stock markets for one year, we estimated the price and volume 5 days and one month later. After we compared the parameters and estimation results of two models, we got result as following:1. There is a bidirectional nonlinear affection between the price fluctuation andvolume change.2. The effect of trend variables could not be ignored. So in the investment process, we should give enough attention to them.3. Financial time series has the auto-correlation character to some extent. Our models proved the past information flux can give useful advice for price and volume estimation.4. The Multi-GARCH model do a better estimation in a medium period than a short period.5. Trading volume series is stable than price series, and can be estimated easily.