Sequential Estimation and Control of Time-Varying Unit Root Processes with an Application to S&P Stock Price

摘要

Stock price series typically behave like random walks; that is, first-order auto-regressive models whose coefficients (roots) are on the unit circle. This article investigates time-varying unit roots (TVUR; that is, roots that wander about unity), and shows that their pattern is related to troughs and peaks of the observed series. Under the assumption of smooth evolution, exponentially weighted least squares (EWLS) can track roots that wander on the unit circle and so can detect turning points sequentially. This allows implementation of effective strategies of investment, which also provide optimization criteria for selecting the tuning coefficients. Extensive application to Standard & Poor's index and comparison with other methods shows the validity of the method.