Sequential procedures for detecting deviations in the parameters of the autoregressive model from specified targets

Abstract

Sequential procedures are developed for detecting deviations in the parameters of a time-dependent autoregressive model from specified targets. This model can be formulated so that its parameters represent typically relevant aspects, e.g. the mean or variance, of a time series, and hence is useful for monitoring these aspects of autoregressive series. The procedures are based on scores-type statistics aimed at detecting arbitrary shifts in the parameters, and are capable of addressing any subset of the model parameters, so that any combination of these aspects may be monitored. The procedures' false signal rates are controlled, and their reaction quickness under local shift alternatives studied, via invariance principles obtained by exploiting the martingale structure of the scores vector. Non-local shifts in the mean and variance are studied via simulation

Keywords:

• autoregressive model
• sequential detec- tion procedure;
• false sipaZ rate; reaction time
• martingale central limit theorem
• Bessel process
• first crossing time