A Security Price Data Cleaning Technique: Reynold’s Decomposition Approach

Abstract

We propose a security price data cleaning technique based on Reynold’s decomposition that uses \(T_I\), the time period of integration, to determine the de-noise level of the price data. As price is a function of time, \(T_0\), the optimal time period of integration, may reveal an underlying price trend, possibly indicating the intrinsic value of the security. The DJIA (Dow Jones Industrial Average) Index and the thirty companies comprising the index are our fundamental interest under the initial investigation period from 1990 to 2016. Also, intra-day security price data from February 8th to August 19th, 2016 are obtained to further study \(T_0\) on a minute-by-minute basis. Preliminary results include the following: (1) It was discovered that \(\alpha \), a key percentage measure, drops exponentially for low \(T_I\) and then drops linearly at a fairly shallow slope for high \(T_I\). (2) In the linear region, the \(\alpha \) hardly varies as \(T_I\) increases. Thus, we propose that the optimal time period of integration, \(T_0\), is when \(\alpha \) transitions from an exponential behavior to a linear behavior. We calculated that the average of the \(T_0\)’s for the thirty DJIA component companies is 64 business days and that for the DJIA itself is 63 business days. For intra-day study of \(T_0\), \(\alpha \) seems to drop proportionally with the length of \(T_I\), exhibiting an almost linear relationship. The change in slope for the intra-day study is not as noticeable as the total time period study. The average of the intra-day \(T_0\)’s for the thirty DJIA component companies is 52 min and for the DJIA Index is 69 min.