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Statistica Sinica 26 (2016), 1611-1630

TESTING ADDITIVE ASSUMPTIONS ON MEANS OF
REGULAR MONITORING DATA: A MULTIVARIATE
NONSTATIONARY TIME SERIES APPROACH
Ting Zhang
Boston University

Abstract: In the analysis of surface meteorological data, observations are usually recorded regularly and frequently in time at multiple but fixed locations in space. The data can thus be viewed as multivariate time series in which a small number of lengthy time series is observed. Motivated by a temperature data, the current paper considers the problem of testing the additive assumption of location and time effects via a multivariate time series approach. Test statistics based on both maximum absolute and integrated squared deviations are proposed and their asymptotic properties are studied for a general class of multivariate nonstationary processes. The results are illustrated in a simulation study and applied to temperature data.

Key words and phrases: Local linear estimation, multivariate nonlinear time series, nonparametric hypothesis testing, nonstationary processes, regular monitoring data.

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