Abstract
The problem of sequential testing of simple hypotheses for time series with a trend is considered. Analytic expressions and asymptotic expansions for error probabilities and expected numbers of observations are obtained. Robustness analysis is performed. Numerical results are given.
Highlights
The sequential approach to test parametric hypotheses proposed by Wald (see Wald (1947)) has been applied in many practical problems of computer data analysis
The problem of sequential test performance characteristics evaluation is well studied for the case of identical distribution of observations (see Govindarajulu (2004), Kharin (2013), Kharin (2016))
The model of non-identical distribution is considered for the problem of two simple hypotheses testing (see Kharin and Ton (2016))
Summary
The sequential approach to test parametric hypotheses proposed by Wald (see Wald (1947)) has been applied in many practical problems of computer data analysis. The problem of sequential test performance characteristics (error probabilities and expected number of observations) evaluation is well studied for the case of identical distribution of observations (see Govindarajulu (2004), Kharin (2013), Kharin (2016)). The model of non-identical distribution is considered for the problem of two simple hypotheses testing (see Kharin and Ton (2016)). Data does not often follow the hypothetical model exactly (see Huber (1981), Kharin (2005)), and the problem of robustness under distortions (see Kharin (1997), Maevskii and Kharin (2002)) is important for sequential testing (see Kharin (2011), Kharin and Kishylau (2015)). We consider the problem of robustness of sequential tests for time series with trend
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