×

zbMATH — the first resource for mathematics

Statistical methods for regular monitoring data. (English) Zbl 1101.62115
Summary: Meteorological and environmental data that are collected at regular time intervals on a fixed monitoring network can be usefully studied combining ideas from multiple time series and spatial statistics, particularly when there are little or no missing data. This work investigates methods for modelling such data and ways of approximating the associated likelihood functions. Models for processes on the sphere crossed with time are emphasized, especially models that are not fully symmetric in space-time.
Two approaches to obtaining such models are described. The first is to consider a rotated version of fully symmetric models for which we have explicit expressions for the covariance function. The second is based on a representation of space-time covariance functions that is spectral in just the time domain and is shown to lead to natural partially nonparametric asymmetric models on the sphere crossed with time. Various models are applied to a data set of daily winds at 11 sites in Ireland over 18 years. Spectral and space-time domain diagnostic procedures are used to assess the quality of the fits. The spectral-in-time modelling approach is shown to yield a good fit to many properties of the data and can be applied in a routine fashion relative to finding elaborate parametric models that describe the space-time dependences of the data about as well.

MSC:
62P12 Applications of statistics to environmental and related topics
62M15 Inference from stochastic processes and spectral analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H11 Directional data; spatial statistics
62M30 Inference from spatial processes
PDF BibTeX Cite
Full Text: DOI
References:
[1] Bennett R. J., Spatial Time Series: Analysis-Forecasting-Control (1979) · Zbl 0543.62069
[2] Bras R. L., Random Functions and Hydrology (1985)
[3] Brillinger D. R., Time Series: Data Analysis and Theory (1981) · Zbl 0486.62095
[4] DOI: 10.1111/1467-9868.00269 · Zbl 0957.62081
[5] Caines P. E., Linear Stochastic Systems (1988) · Zbl 0658.93003
[6] DOI: 10.1007/BF02149764 · Zbl 0793.65020
[7] Christakos G., Random Field Models in Earth Sciences (1992) · Zbl 0759.60055
[8] Christakos G., Modern Spatiotemporal Geostatistics (2000)
[9] Cressie N., J. Am. Statist. Ass. 94 pp 1330– (1999)
[10] DOI: 10.1256/smsqj.55416
[11] DOI: 10.1256/smsqj.55905
[12] DOI: 10.1198/016214502760047113 · Zbl 1073.62593
[13] T. Gneiting, K. Larson, K. Westrick, M. G. Genton, and E. Aldrich (2004 ) Calibrated forecasting at the Stateline wind energy center: the regime-switching space-time (RST) method . Manuscript. (Available fromhttp://www.stat.washington.edu/www/research/reports/tr464.pdf.) · Zbl 1120.62341
[14] DOI: 10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2
[15] DOI: 10.1198/1085711031175
[16] Haslett J., Appl. Statist. 38 pp 1– (1989)
[17] DOI: 10.1175/1520-0493(2001)129<0123:ASEKFF>2.0.CO;2
[18] DOI: 10.1016/S0167-7152(00)00200-5 · Zbl 1129.62413
[19] DOI: 10.1023/A:1014075310344 · Zbl 1033.86003
[20] DOI: 10.1023/A:1022425111459 · Zbl 1302.86022
[21] Jones R. H., Modelling Longi-tudinal and Spatially Correlated Data pp 289– (1997)
[22] M. Jun, and M. L. Stein (2004 ) An approach to producing space-time covariance functions on spheres .Manuscript. University of Chicago, Chicago. (Available fromhttp://www.stat.uchicago.edu/ cises/research/cises-tr18.pdf.)
[23] DOI: 10.1016/j.advwatres.2004.04.002
[24] DOI: 10.1023/A:1007528426688 · Zbl 0970.86013
[25] Luna X., Statist. Sin. 15 pp 547– (2005)
[26] DOI: 10.1016/S0378-3758(02)00353-1 · Zbl 1043.62051
[27] Priestley M. B., Spectral Analysis and Time Series (1981) · Zbl 0537.62075
[28] DOI: 10.1016/S0169-2070(02)00095-X
[29] Reinsel G. C., Elements of Multivariate Time Series Analysis (1997) · Zbl 0873.62086
[30] DOI: 10.1111/j.1467-9876.2005.00480.x · Zbl 05188682
[31] Smith R. L., J. Geophys Res. 108 (2003)
[32] Stein M. L., Interpolation of Spatial Data: Some Theory for Kriging (1999) · Zbl 0924.62100
[33] DOI: 10.1198/016214504000000854 · Zbl 1117.62431
[34] DOI: 10.1046/j.1369-7412.2003.05512.x · Zbl 1062.62094
[35] Vecchia A. V., J. R. Statist. Soc. 50 pp 297– (1988)
[36] DOI: 10.1175/1520-0493(1993)121<2611:SROSCF>2.0.CO;2
[37] Yadrenko M. I., Spectral Theory of Random Fields (1983) · Zbl 0539.60048
[38] Yaglom A. M., Correlation Theory of Stationary and Related Random Functions (1987) · Zbl 0685.62078
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.