台灣股市非線性價量關係之研究

行政院國家科學委員會補助專題研究計畫成果報告

台灣股市非線性價量關係之研究　

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計畫類別：√個別型計畫　　□整合型計畫

計畫編號：NSC 89－2416－H－004－024

執行期間：八十八年八月一日至八十九年七月三十一日

計畫主持人：郭維裕

共同主持人：

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執行單位：國立政治大學國際貿易學系

中　華　民　國 九十 年 一 月 三十　日

Nonlinear Pr ice-Volume Dynamics in the Taiwanese Stock Mar ket

中文摘要

本文應用 Granger(1969)的線性因果關係檢定以及 Hiemstra and Jones(1994)的非線性因果關係檢定來 檢測台灣股市的量價關係。本文所使用的資料是五分鐘台灣股價指數和交易量的高頻資料，此有別 於以往的研究。資料期間涵蓋民國八十七年四月至民國八十九年三月，整整兩年的時間。由於交易 量指標有許多種，我們決定採用較具代表性的三種指標來進行檢測。它們分別為交易次數、交易金 額以及週轉率。結果發現：就線性量價因果關係而言，在民國八十七年四月至民國八十八年三月期 間，交易次數與週轉率和股價指數報酬之間存在單向因果關係，亦即股價指數報酬導致交易次數與 週轉率的變動，反之則不成立；然而交易金額和股價指數報酬之間卻有顯著的雙向因果關係。在民 國八十八年四月至民國八十九年三月期間，上述的交易量指標與股價指數報酬皆存在著顯著的雙向 線性因果關係。由此可知，高頻線性量價關係會因資料期間與所使用的交易量指標的不同而改變。 相對地，非線性量價因果關係則呈現較具一致性的結果。在兩個期間內，三種交易量指標和股價指 數報酬間存在著顯著的單向非線性量價因果關係；亦即股價指數報酬會導致交易量指標的非線性變 動，反之則不成立。此結果即使在應用 GARCH 模型過濾三種交易量指標和股價指數報酬之後，依然 顯著。本文的結果與 Hiemstra and Jones(1994)所發現的雙向非線性量價因果關係不同。此外，本文也 發現顯著的季節性現象存在於高頻的交易量和股價指數報酬資料中，只是交易量的季節性遠較股價 指數報酬的季節性來得強烈。

關鍵詞：高頻資料、季節性、線性量價因果關係、非線性量價因果關係

Abstr act

This study provides evidence on the linear and nonlinear Granger causality relations between stock returns and trading volume in the Taiwanese stock market. These causal relations are investigated based on high-frequency 5-minute data of stock index and three different measures of trading volume. These measures are share volume, dollar volume, and turnover rate. The sample period is from April, 1998 to March, 2000. The causality tests are performed in two subperiods, April, 1998-March, 1999 and April, 1999-March, 2000. We find that there exists significant unidirectional linear Granger causality from stock index return to share volume and turnover rate and significant bidirectional linear Granger causality between dollar volume and stock return during the first subperiod. During the second subperiod, there are significant bidirectional causal relations between stock index return and these three volume measures. In contrast, we discover significant unidirectional nonlinear Granger causal relations from stock return to both share volume, dollar volume and turnover rate even after filtering the stock return and volume measures with GARCH-type models. In addition, we also present evidence on the intraday and intraweek seasonality of stock return and three different volume measures. Average volume traded shows significant differences across trading 5-minute intervals of the day and across days of the week while average stock index return differs significantly across trading 5-minute intervals of the day but not that significantly across days of the week.

JEL Classification: C50, G10, G12

Recently the role of volume in predicting stock prices has attracted enormous attention from both the academics and practitioners. Several studies attempt to provide theoretical background for the price-volume dynamics. Clark(1973), Copland(1976), Epps and Epps(1976), and Jennings, Starks, and Fellingham(1981) show that the price-volume relation is contemporaneous. In contrast, Blume, Easley, and O’Hara(1992) prove that there exists a lead-lag relation between stock price and trading volume. However, these studies have not indicated whether these relations are linear or not. Campbell, Lo, and Wang(1993), Gallant, Touchen, and Pitts(1993), and Llorente, Michaely, Saar, and Wang(1999) document that there exist certain specific forms of nonlinear relationship between stock return and trading volume. In view of these theoretical backgrounds of both linear and nonlinear price-volume dynamics, it would be interesting to distinguish them based on empirical data.

Using a direct test of independence/causality developed by Haugh(1976), Rogalski(1977) presents empirical evidence on the positive interrelation at lag zero between monthly stock price change per se and trading volume for individual securities but fails to establish any lead-lag relationship. His study supports the model of Epps and Epps(1976). Jain

and Joh(1988) apply the causality test of Haugh(1976) to hourly common stock trading volume and returns on the NYSE finding that there is a strong contemporaneous relation between stock returns and trading volume as well as a significant unidirectional Granger causality from returns to volume lagged up to four hours. Smirlock and Starks(1988) investigate the Granger causal relation between stock returns and trading volume with transactional data of 49 consecutive trading days from 15 June through 21 August 1981 documenting that there exists a significant causal relation between absolute price changes and volume at the firm level. A seemingly irrelevant evidence on the causality between trading volume and stock price changes is provided by Stickel and Verrecchia(1994). They find that large price increases with strong volume support tend to be followed by another price increase the next day whereas the large price changes on days with weak volume support tend to reverse, at least partially, the next day. This finding suggests that there may exist an asymmetric unidirectional causality from trading volume to stock returns.

LeBaron(1992) documents a quite complex relation between volume and return correlations in which persistence in the Dow Jones Index increases more significantly on rising volume than on declining volume. He also uses some nonlinear models trying to explain these

results but is not able to acquire satisfactory results. However, using different data, Campbell, Grossman, and Wang(1993) discover different results from those of LeBaron. They shows that a stock price decline on a high-volume day is actually more likely than a stock price decline on a low-volume day to be associated with an increase in the expected stock return. The aforementioned studies of nonlinear causal relation between stock returns and trading volume are based on specific nonlinear models. In contrast, Hiemstra and Jones(1994) empirically test nonlinear Granger causality in the stock price-volume relation through the use of a general nonlinear Granger causality test extended by them from a nonlinear causality test of Baek and Brock(1988). They find significant bidirectional nonlinear causal relationship between monthly stock returns and trading volume. Ghysels, Gourieroux, and Jasiak(1998) also find a significant nonlinear causality from volume to returns in calendar time of the Alcatel stock traded in the Paris Bourse. Note that the test of Ghysels, Gourieroux, and Jasiak(1998) is different from that of Hiemstra and Jones(1994). The former is developed in a Markovian framework and tested on qualitative data rather than commonly used quantitative data. As a holdout sample test of the nonlinear causal relation between stock returns and volume documented by Hiemstra and

Jones, Silvapulle and Choi(1999) apply the test of Hiemstra and Jones to the Korean stock market showing that there exists strong bidirectional causality between stock returns and trading volume. They push their argument further and claim that the finding of strong bidirectional price-volume causal relationships implies that knowledge of current trading volume improves the ability to forecast stock prices and that this evidence is not consistent with the efficient market hypothesis.

The main purpose of this paper is to investigate the linear and nonlinear price-volume relations in the Taiwanese stock market. The methodologies we use are Granger’s(1969) causality test and the generalized Baek-Brock nonlinear causality test of Hiemstra and Jones(1994). Our paper differs to the previous studies in two ways. First, we use 5-minute high frequency stock return and trading volume data. Although transactional data has been used by Smirlock and Starks(1988), our sample period is much longer than theirs. Our sample period spans from April, 1998 to March, 2000. The reason for us to use high frequency data is that as Granger(1969) points out, the causal relation may depend on the frequency of data. In other words, if we cannot find significant causality between monthly stock return and trading volume, it does not mean that we cannot discover significant causal relation between them at higher frequencies. Second, the

nonlinear causality test is performed based on three different measures of trading volume. The ultimate proxy of volume has been an issue of hot debate and still remains an open question. Two popular measures frequently used by previous studies are share volume and dollar volume. We include turnover rate in addition to share volume and dollar volume in our study. Turnover rate has been suggested by Lo and Wang(2000) as an appropriate proxy of volume because it can be derived in an equilibrium framework of portfolio allocation. Furthermore, we also study intraday and intraweek seasonality patterns of both stock returns and trading volumes.

We conduct the causality tests in two subperiods: April, 1998-March, 1999 and April, 1999-March, 2000. We find that during the first subperiod, there exist certain seasonality patterns in both stock index return and trading volumes. On average, stock return is obviously negative on Mondays while it is significantly positive at 0.03% on Saturdays. In particular, the latter is significantly different from the average return from Monday to Friday. Average index return also varies significantly in 36 5-minute intervals from 9:05 to 12:00 every trading day. The return is a positive 0.2% in first 5 minutes after the opening. It is also positive in the 5-minute interval before the closing. The stock index returns in these two intervals are both statistically

significantly different from the average return in the other 34 intervals. The results during the second subperiod are qualitatively identical but more significant. In sum, stock index return varies substantially across 5-minute trading intervals of the day and across trading days of the week. The former is much more significant than the latter. The results of the seasonality patterns for three different measures of volume are quite similar to those of stock index returns but more significantly.

We find that there exists significant unidirectional linear Granger causality from stock index return to share volume and turnover rate and significant bidirectional linear Granger causality between dollar volume and stock return during the first subperiod. During the second subperiod, there are significant bidirectional causal relations between stock index return and these three volume measures. In contrast, we discover significant unidirectional nonlinear Granger causal relations from stock return to both share volume, dollar volume and turnover rate. Since trading volume is often used to be the proxy of information flow in the stock market, the nonlinear causal relation may be an artifact resulting from the failure of optimal linear models to capture the inherent heteroskedasticity of volume measures. In order to reduce the effect of this heteroskedasticity on the nonlinear causality test, we adopt GARCH and

EGARCH models to filter the time series of stock index return and trading volume before applying the causality test to them. Similar results are found with the filtered data. Generally speaking, these results are supportive of the efficient market hypothesis. The result that there only exists a unidirectional nonlinear causality from return to volume implies that at least the three volume measures in this paper are not useful for investors to predict future stock price movements.

In future work we plan to apply the qualitative causality test of Ghysels, Gourieroux, and Jasiak(1998) to the price-volume dynamics in the Taiwanese stock market. We will also attempt to fit several potential nonlinear parametric models to our high-frequency data in order to further confirm the results about nonlinear price-volume dynamics in this paper.

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