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Anthony S. Tay . Christopher T<strong>in</strong>g<br />

Intraday stock prices, volume, and duration:<br />

a nonparametric conditional density analysis<br />

Abstract We <strong>in</strong>vestigate the distribution <strong>of</strong> <strong>high</strong>-<strong>frequency</strong> price changes, conditional<br />

on trad<strong>in</strong>g volume and duration between trades, on four stocks traded on<br />

the New York Stock Exchange. The conditional probabilities are estimated nonparametrically<br />

us<strong>in</strong>g local polynomial regression methods. We f<strong>in</strong>d substantial<br />

skewness <strong>in</strong> the distribution <strong>of</strong> price changes, with the direction <strong>of</strong> skewness<br />

dependent on the sign <strong>of</strong> trade. We also f<strong>in</strong>d that the probability <strong>of</strong> larger price<br />

changes <strong>in</strong>creases with volume, but only for trades that occur with longer durations.<br />

The distribution <strong>of</strong> price changes vary with duration primarily when volume<br />

is <strong>high</strong>.<br />

1 Introduction<br />

Time—<strong>in</strong> the form <strong>of</strong> the duration between trades—matters <strong>in</strong> the formation <strong>of</strong><br />

stock prices. This has been demonstrated from both theoretical and empirical<br />

perspectives. Durations may be negatively related to prices because short-sell<strong>in</strong>g<br />

constra<strong>in</strong>ts prevent trad<strong>in</strong>g on private bad news whereas there are no similar<br />

constra<strong>in</strong>ts to prevent trad<strong>in</strong>g on private good news (Diamond and Verrecchia<br />

1987). Durations may also be negatively related to volatility <strong>of</strong> price changes<br />

(Easley and O’Hara 1992). The connection between price change and duration has<br />

been verified empirically (Engle 2000; Grammig and Wellner 2002). Further<br />

<strong>in</strong>vestigations <strong>in</strong>to the relationship between durations and prices have yielded<br />

<strong>in</strong>terest<strong>in</strong>g <strong>in</strong>sights. For <strong>in</strong>stance, the size and speed <strong>of</strong> price movements <strong>in</strong>crease<br />

with decreas<strong>in</strong>g duration (Dufour and Engle 2000), reflect<strong>in</strong>g a l<strong>in</strong>k between<br />

duration and market liquidity. There is also an <strong>in</strong>terest<strong>in</strong>g dynamic relationship<br />

A. S. Tay (*)<br />

School <strong>of</strong> Economics and Social Sciences, S<strong>in</strong>gapore Management University,<br />

90 Stamford Road, S<strong>in</strong>gapore, 178903, S<strong>in</strong>gapore<br />

E-mail: anthonytay@smu.edu.sg<br />

C. T<strong>in</strong>g<br />

Lee Kong Chian School <strong>of</strong> Bus<strong>in</strong>ess, S<strong>in</strong>gapore Management University, S<strong>in</strong>gapore, S<strong>in</strong>gapore

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