Time Series Behaviour of Stock Trading Volume:An Evidence from Indian Stock Market
In this paper, we attempt to study the time series dynamics of the stock trading volume, or equivalently stock turnover using recently available data for individual stocks traded on the Bombay Stock Exchange (BSE) and the National Stock Exchange (NSE). Stock turnover has been studied intensively in finance literature because of its use as an incomplete measure of liquidity, its use as a proxy for information arrival and its use as a proxy for heterogeneous belief among investors. Return on stock prices and trading volume are the two prime indicators of trading activity in a stock market. These factors are jointly determined by the same market dynamics and may contain valuable information about a security (Lo and Wang 2001). Yet the finance literature has centered more on prices and much less on quantities. In recent years the potential presence of stochastic long memory in financial variables has also been an important topic of research. Though the long memory behavior of stock return has been studied extensively, very few researchers have analyzed the long memory hypothesis for stock trading volume. A large body of literature has documented the behavior of trading volumes in the US stock markets. By contrast, relatively little attention has been devoted to trading volume in the Indian stock markets. Our effort is to fill this gap by analyzing the time series dynamics of the trading volume in two distinct markets: the BSE and the NSE. Over the last two decades, Indian stock markets have witnessed significant changes in terms of trading environment that have made the price discovery process more efficient. Various reforms such as dematerialization of shares, setting of clearing houses, introduction of derivative products have eliminated the risks involved thereby widening the investor base and increasing the turnover and market capitalization of the stock exchanges. The data used in the study are based on time series of daily trading data for individual stocks listed in the Bombay Stock Exchange (BSE) during the period 1995-2003 and the National Stock Exchange (NSE) during the period 1996-2003. The data for the individual stocks listed in BSE and NSE are collected from PROWESS database provided by the 'Center for Monitoring Indian Economy' (CMIE). For our analysis we have taken only those stocks which have traded at least 75% of the total trading days. We have taken turnover as a measure of trading activity throughout this paper, which is given as the ratio of number of shares traded by the number of shares outstanding. Since the numbers of shares outstanding and the number of shares traded have both grown steadily over the period of our study, the use of turnover helps to reduce the low-frequency variation in the series. Instead of focusing on the behavior of the time series of individual stockâ€™s turnover and return data, we have constructed value weighted and equal weighted turnover and return series. As documented in Lo and Wang (2000) and in many other studies, aggregate turnover series seems to be non-stationary, exhibiting a significant time trend and time-varying volatilities. We computed autocorrelations of turnover and return series and the corresponding Ljung-Box Q-statistics. Unlike return, turnover is highly persistent, with autocorrelations decaying very slowly. This slow decay suggests some kind of nonstationarity in turnover series. As in the case of many empirical studies involving volume, we have also used some kind of detrending methods to adjust for the shifts in the turnover series. We have used six different kind of detrending methods like linear, logarithmic, first differencing, moving average, seasonal deseasonalization (in the spirit of GRT,1987) and kernel regression to induce stationarity and examined the behavior of these series after detrending them by each of the above stated procedures. Linear, log-linear, GRT detrending and kernel regression seem to do little to eliminate the persistence in autocorrelations and first differencing and moving average method seem to eliminate the persistence of the autocorrelations. However the conventional unit root tests have no power to distinguish a long memory process with a unit root process because of their inability to capture an order of integration that may not be an integer (Baillie, 1996). Hence as our next step we tried to examine the consistent estimation of the long-memory parameterâ€˜dâ€™ of the turnover series. Using robust Sowellâ€™s exact maximum likelihood ARFIMA procedures, we found strong evidence that turnover series for the stocks listed in the BSE and the NSE exhibits long memory. The main advantages of this method are that it avoids the small sample bias and arbitrariness of the cut-off parameters of Robinsonâ€™s method and also allows us to control for short memory effects. We have implemented ARFIMA model using the software of Doornik and Oooms(1996). We have used Akaike Information Criteria (AIC) to choose the order of the ARFIMA model and set the maximum number of orders for both AR and MA as 3. We have estimated ARFIMA models using trend as well as without using trend. The ARFIMA estimators for different orders of the ARMA parameters vary greatly and also vary for BSE and NSE turnover series. The conclusion that turnover process is a long memory process provides a consistent and satisfactory description of the dynamics of Indian stock turnover
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