Quickest Detection of Changes in the Generating Mechanism of a Time Series via the E-Complexity of Continuous Functions

• Published in: Sequential analysis 2014-04, Vol.33 (2), p.231
• Main Authors: Darkhovsky, Boris, Piryatinska, Alexandra
• Format: Article
• Language: English
• Subjects: Algorithms; Simulation; Time series
• ISSN: 0747-4946; 1532-4176

A novel methodology for the quickest detection of abrupt changes in the generating mechanisms (stochastic, deterministic, or mixed) of a time series, without any prior knowledge about them, is developed. This methodology has two components: the first is a novel concept of the ...-complexity and the second is a method for the quickest change point detection (Darkhovsky, 2013). The ...-complexity of a continuous function given on a compact segment is defined. The expression for the ...-complexity of functions with the same modulus of continuity is derived. It is found that, for the Holder class of functions, there exists an effective characterization of the ...-complexity. The conjecture that the ...-complexity of an individual function from the Holder class has a similar characterization is formulated. The algorithm for the estimation of the ...-complexity coefficients via finite samples of function values is described. The second conjecture that a change of the generating mechanism of a time series leads to a change in the mean of the complexity coefficients, is formulated. Simulations to support our conjectures and verify the efficiency of our quickest change point detection algorithm are performed. (ProQuest: ... denotes formulae/symbols omitted.)