Aspects on the controi of false alarms in statistical surveillance and the impact on the return of financial decision systems

Abstract

Systems for on-line detection of regime shifts are important, e.g. for making timely financial transactions. For daily data, it means that we make a new decision each day, based on the data available, and when there is enough evidence of a regime shift, an alarm is called. There is always the risk of a false alarm and here two principally different ways of controlling the false alarms are compared: systems with a fixed average run length until the first false alarm, and systems with a fixed probability «1) of any false alarm (fixed size). The effects of the two approaches are evaluated in terms of the timeliness of alarms. A system with a fixed size is found to have a drawback: the ability to detect a change deteriorates rapidly with the time of the change. Consequently, the probability of successful detection will tend to zero and the expected delay of a motivated alarm tends to infinity. This drawback is present even when the size is set to be very large (close to 1). Utility measures are used in the investigation, expressing the different costs for the gain of a motivated alarm and the loss of a false alarm. Drawbacks and advantages of the two approaches are investigated. How the choice of the best approach can be guided by the parameters of the process and the relation between the cost of a too earlyor too late alarm is demonstrated. The technique is illustrated by application to transactions of the Hang Seng Index.