Abstract
This paper proposes a locally stationary spatio-temporal process to analyze the motivating example of US precipitation data, which is a huge data set composed of monthly observations of precipitation on thousands of monitoring points scattered irregularly all over US continent. Allowing the parameters of continuous autoregressive and moving average (CARMA) random fields by Brockwell and Matsuda (J R Stat Soc Ser B 79(3):833–857, 2017) to be dependent spatially, we generalize locally stationary time series by Dahlhaus (Ann Stat 25:1–37, 1997) to spatio-temporal processes that are locally stationary in space. We develop Whittle likelihood estimation for the spatially dependent parameters and derive the asymptotic properties rigorously. We demonstrate that the spatio-temporal models actually work to account for nonstationary spatial covariance structures in US precipitation data.
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Acknowledgements
The research was supported by the Grants-in-Aid for Scientific Research, 17H01701, 17H02508.
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Matsuda, Y., Yajima, Y. Locally stationary spatio-temporal processes. Jpn J Stat Data Sci 1, 41–57 (2018). https://doi.org/10.1007/s42081-018-0003-9
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DOI: https://doi.org/10.1007/s42081-018-0003-9