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

We propose a security price data cleaning technique based on Reynold’s decomposition that uses T0 (the time period of integration) to determine the de-noise level of the price data. The goal of this study is to find the optimal T0 that reveals 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. Preliminary results suggest that the graphs of ↵ (a key percentage measure) versus T0 of the thirty companies and the DJIA Index exhibit at least two properties: (1) ↵ drops exponentially as T0 increases when T0 / order of magnitude of 100 days, and (2) ↵ drops linearly as T0 increases when T0 ' order of magnitude of 100 days. For the DJIA Index itself, T0 is less than order of magnitude of 100 days. The result of applying our technique to each component stock of the DJIA parallels the result of the technique applied to the DJIA Index itself.