The Analytic Relationship between Intervaling and Nontrading Effects in Continuous Time
从理论上分析连续时间下，使用短间隔数据估计贝塔系数时，非交易效应如何导致贝塔随区间长度增加而上升，并解释这一现象与Scholes-Williams和Dimson估计量的关系。
Empirical studies in finance generally use data defined over the shortest re? turn period available. Originally, data bases such as CRSP, tended to have data collected over monthly periods and most analyses tended to use monthly data rather than data compounded over periods greater than a month with the implicit argument that the more data the better. Since the development of data bases with data collected over shorter differencing intervals, there has been a growing tendency in finance to use returns data defined over increasingly shorter differ? encing intervals.1 This development is desirable, but is not without problems. The problem with using data defined over shorter differencing intervals is that, although greater estimating efficiency will be achieved,2 nontrading effects could be introduced into the analysis. These will lead to biased beta estimators and biases in tests of capital market efficiency. The purpose of this paper is to investi? gate, analytically, the interrelation of the and nontrading effects both in estimating beta factors and in testing capital market efficiency. Levhari and Levy [9] demonstrated theoretically (and empirically) that beta will be dependent upon the return interval length when returns are measured in discrete time. In continuous time, this dependency will be removed due to the additivity of the return variables in this domain. However, several studies carried out on U.S. [15], French [1], and U.K. data [7], [16] have demonstrated that beta factors estimated in continuous time increase with the differencing interval, seemingly contradicting this invariance property. This paper will demonstrate, analytically, how this phenomenon can arise in the presence of nontrading ef? fects, and how this intervaling effect relates to the estimators developed by Scholes and Williams [14] and Dimson [7] for handling the nontrading problems. * Manchester University, England. The author is grateful to two anonymous referees for their