Abstract
We examine the relationship between trading volumes, number of transactions, and volatility using daily stock data of the Tokyo Stock Exchange. Following the mixture of distributions hypothesis, we use trading volumes and the number of transactions as proxy for the rate of information arrivals affecting stock volatility. The impact of trading volumes or number of transactions on volatility is measured using the generalized autoregressive conditional heteroscedasticity (GARCH) model. We find that the GARCH effects, that is, persistence of volatility, is not always removed by adding trading volumes or number of transactions, indicating that trading volumes and number of transactions do not adequately represent the rate of information arrivals.
Highlights
The empirical properties of asset returns have been intensively studied, and some universal properties are classified as ”stylized facts” [1]
In order to elaborate the volatility dynamics, we examine the relationship between trading volume and stock volatility by using the daily stock data of the Tokyo Stock Exchange from June 3, 2006, to December 30, 2009
We find that α + β is close to 1, implying that a strong persistence of volatility, in other words, the generalized autoregressive conditional heteroscedasticity (GARCH) effect, exists
Summary
The empirical properties of asset returns have been intensively studied, and some universal properties are classified as ”stylized facts” [1]. Several studies have verified this assumption [2]–[8] by examining whether rt/σt is consistent with the random variable ∼ N (0, 1) Another unresolved issue relates to volatility dynamics. Some other studies, such as [18, 19, 20, 21, 22], report that the inclusion of trading volume in the GARCH model does not completely remove the GARCH effects; the MDH is not supported. We use the number of transactions as a proxy for the rate of information arrivals and examine its effect on GARCH volatility. The effect of trading volume or the number of transactions is examined by adding a term to the GARCH process, as σt2 = ω + αrt2−1 + βσt2−1 + γNt,. We infer the GARCH parameters by the Bayesian inference conducted using the Markov Chain Monte Carlo (MCMC) method [23]–[28]
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