Estimating artificial level shifts in the presence of smooth trends
2008 (English)In: Environmental Monitoring and Assessment, ISSN 0167-6369Article in journal (Other academic) Submitted
Changes in observational data over time can be severely distorted by errors in measurements, sampling, or reporting. Here, we show how smooth trends in vector time series can be separated from one or two abrupt level shifts that occur simultaneously in all coordinates. Trends are modelled nonparametrically, whereas abrupt changes and the impact of covariates are modelled parametrically. The model is estimated using a backfitting algorithm in which estimation of smooth trends is alternated with estimation of regression coefficients for covariates and assessment of sudden level shifts. The proposed method is adaptive in the sense that the degree of smoothing over time and across coordinates is controlled by a roughness penalty and cross-validation procedure that automatically identifies the interdependence of the analysed data. Furthermore, it uses a resampling technique that can accommodate correlated error terms in the assessment of the uncertainty of both smooth trends and discontinuities. The method is applied to water quality data from Swedish national monitoring programmes to illustrate how known discontinuities can be quantified and how previously unrecognized discontinuities can be detected.
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IdentifiersURN: urn:nbn:se:liu:diva-52245OAI: oai:DiVA.org:liu-52245DiVA: diva2:280807