The Influence of Correlation between Observations on the Probabilistic Characteristics of the MA-Algorithm for Detecting a Gaussian Time Series Disorder from Mathematical Expectation

Abstract

The problem of detecting a spontaneous abrupt change in the mathematical expectation (disorder) of a Gaussian time series using the Moving Average or MA-algorithm is considered. It is noted that the probabilistic characteristics of this algorithm necessary for its practical use have been obtained with the necessary completeness relatively recently and concerned only the case when the time series elements (its observations) are uncorrelated. The purpose of this work is a full-scale study of the MA-algorithm characteristics under the conditions of correlated observations, with a view to ultimately obtain the reference material necessary for synthesizing the optimal procedure for detecting a disorder. Simulation was carried out, which made it possible to reveal the features of choosing a decision threshold for a given value of the average time between false alarms depending on the smoothing window width of the controlling MA-algorithm and the maximum correlation interval of its observations. In a similar way, the values of the average delay time in producing an alarm signal when a disorder of a given fixed level occurs have been determined, as well as the dependences of the control procedure efficiency indicator on the procedure parameters. A comparison of the effectiveness of MA-algorithms for uncorrelated and correlated observations is carried out.