{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,14]],"date-time":"2026-11-14T17:08:38Z","timestamp":1794676118002,"version":"4.9.1"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2005,11,1]],"date-time":"2005-11-01T00:00:00Z","timestamp":1130803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001589","name":"Environmental Protection Agency","doi-asserted-by":"publisher","award":["R-82940201-0"],"award-info":[{"award-number":["R-82940201-0"]}],"id":[{"id":"10.13039\/501100001589","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005,11,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>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\u2013time. 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\u2013time 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\u2013time 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\u2013time dependences of the data about as well.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2005.00520.x","type":"journal-article","created":{"date-parts":[[2005,11,10]],"date-time":"2005-11-10T15:10:14Z","timestamp":1131635414000},"page":"667-687","source":"Crossref","is-referenced-by-count":58,"title":["Statistical Methods for Regular Monitoring Data"],"prefix":"10.1093","volume":"67","author":[{"given":"Michael L.","family":"Stein","sequence":"first","affiliation":[{"name":"University of Chicago , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2005,11,10]]},"reference":[{"key":"2023040705114167900_","volume-title":"Spatial Time Series: Analysis\u2013Forecasting\u2013Control","author":"Bennett","year":"1979"},{"key":"2023040705114167900_","volume-title":"Random Functions and Hydrology","author":"Bras","year":"1985"},{"key":"2023040705114167900_","volume-title":"Time Series: Data Analysis and Theory","author":"Brillinger","year":"1981"},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1111\/1467-9868.00269","article-title":"Blur-generated non-separable space\u2013time models","volume":"62","author":"Brown","year":"2000","journal-title":"J. R. Statist. Soc."},{"key":"2023040705114167900_","volume-title":"Linear Stochastic Systems","author":"Caines","year":"1988"},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BF02149764","article-title":"Circulant preconditioners for Toeplitz-block matrices","volume":"6","author":"Chan","year":"1994","journal-title":"Numer. Alg."},{"key":"2023040705114167900_","volume-title":"Random Field Models in Earth Sciences","author":"Christakos","year":"1992"},{"key":"2023040705114167900_","volume-title":"Modern Spatiotemporal Geostatistics","author":"Christakos","year":"2000"},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1080\/01621459.1999.10473885","article-title":"Classes of nonseparable, spatiotemporal stationary covariance functions","volume":"94","author":"Cressie","year":"1999","journal-title":"J. Am. Statist. Ass."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1002\/qj.49712555417","article-title":"Construction of correlation functions in two and three dimensions","volume":"125","author":"Gaspari","year":"1999","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"2449","DOI":"10.1002\/qj.49712555906","article-title":"Correlation functions for atmospheric data analysis","volume":"125","author":"Gneiting","year":"1999","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1198\/016214502760047113","article-title":"Nonseparable, stationary covariance functions for space-time data","volume":"97","author":"Gneiting","year":"2002","journal-title":"J. Am. Statist. Ass."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","DOI":"10.21236\/ADA459831","volume-title":"Calibrated forecasting at the Stateline wind energy center: the regime-switching space-time (RST) method","author":"Gneiting","year":"2004"},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"2776","DOI":"10.1175\/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2","article-title":"Distance-dependent filtering of background error covariance estimates in and ensemble Kalman filter","volume":"129","author":"Hamill","year":"2001","journal-title":"Mnthly Weath. Rev."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1198\/1085711031175","article-title":"Identification of model components for a class of continuous spatiotemporal models","volume":"8","author":"Hartfield","year":"2003","journal-title":"J. Agric. Biol. Environ. Statist."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2347679","article-title":"Space\u2013time modelling with long-memory dependence: assessing Ireland's wind power resource (with discussion)","volume":"38","author":"Haslett","year":"1989","journal-title":"Appl. Statist."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1175\/1520-0493(2001)129<0123:ASEKFF>2.0.CO;2","article-title":"A sequential ensemble Kalman filter for atmospheric data assimilation","volume":"129","author":"Houtekamer","year":"2001","journal-title":"Mnthly Weath. Rev."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0167-7152(00)00200-5","article-title":"Space-time analysis using a general product-sum model","volume":"52","author":"de Iaco","year":"2001","journal-title":"Statist. Probab. Lett."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1023\/A:1014075310344","article-title":"Nonseparable space-time covariance models: some parametric families","volume":"34","author":"de Iaco","year":"2002","journal-title":"Math. Geol."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1023\/A:1022425111459","article-title":"The linear coregionalization model and the product-sum space-time variogram","volume":"35","author":"de Iaco","year":"2003","journal-title":"Math. Geol."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/978-1-4612-0699-6_25","volume-title":"Modelling Longi-tudinal and Spatially Correlated Data","author":"Jones","year":"1997"},{"key":"2023040705114167900_","volume-title":"An approach to producing space-time covariance functions on spheres. Manuscript","author":"Jun","year":"2004"},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1016\/j.advwatres.2004.04.002","article-title":"Methods for generating non-separable spatiotemproal covariance models with potential environmental applications","volume":"27","author":"Kolovos","year":"2004","journal-title":"Adv. Wat. Resour."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1023\/A:1007528426688","article-title":"Geostatistical space-time models: a review","volume":"31","author":"Kyriakidis","year":"1999","journal-title":"Math. Geol."},{"key":"2023040705114167900_","first-page":"547","article-title":"Predictive spatio-temporal models for spatially sparse environmental data","volume":"15","author":"de Luna","year":"2005","journal-title":"Statist. Sin."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/S0378-3758(02)00353-1","article-title":"Families of spatio-temporal stationary covariance models","volume":"116","author":"Ma","year":"2003","journal-title":"J. Statist. Planng Inf."},{"key":"2023040705114167900_","volume-title":"Spectral Analysis and Time Series","author":"Priestley","year":"1981"},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1016\/S0169-2070(01)00153-4","article-title":"Bayesian prediction for vector ARFIMA processes","volume":"18","author":"Ravishanker","year":"2002","journal-title":"Int. J. Forecast."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0679-8","volume-title":"Elements of Multivariate Time Series Analysis","author":"Reinsel","year":"1997","edition":"2nd edn"},{"key":"2023040705114167900_","first-page":"223","article-title":"A Bayesian kriged Kalman model for short-term forecasting of air pollution levels","volume":"54","author":"Sahu","year":"2005","journal-title":"Appl. Statist."},{"key":"2023040705114167900_","doi-asserted-by":"publisher","DOI":"10.1029\/2002JD002914","article-title":"Spatiotemporal modeling of PM2.5 data with missing values","volume":"108","author":"Smith","year":"2003","journal-title":"J. Geophys Res."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1494-6","volume-title":"Interpolation of Spatial Data: Some Theory for Kriging","author":"Stein","year":"1999"},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1198\/016214504000000854","article-title":"Space-time covariance functions","volume":"100","author":"Stein","year":"2005","journal-title":"J. Am. Statist. Ass."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1046\/j.1369-7412.2003.05512.x","article-title":"Approximating likelihoods for large spatial data sets","volume":"66","author":"Stein","year":"2004","journal-title":"J. R. Statist. Soc."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1111\/j.2517-6161.1988.tb01729.x","article-title":"Estimation and identification for continuous spatial processes","volume":"50","author":"Vecchia","year":"1988","journal-title":"J. R. Statist. Soc."},{"key":"2023040705114167900_","doi-asserted-by":"crossref","first-page":"2611","DOI":"10.1175\/1520-0493(1993)121<2611:SROSCF>2.0.CO;2","article-title":"Some remarks on spatial correlation function models","volume":"121","author":"Weber","year":"1993","journal-title":"Mnthly Weath. Rev."},{"key":"2023040705114167900_","volume-title":"Spectral Theory of Random Fields","author":"Yadrenko","year":"1983"},{"key":"2023040705114167900_","volume-title":"Correlation Theory of Stationary and Related Random Functions","author":"Yaglom","year":"1987"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.1467-9868.2005.00520.x","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/67\/5\/667\/49795209\/jrsssb_67_5_667.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/67\/5\/667\/49795209\/jrsssb_67_5_667.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,5]],"date-time":"2025-01-05T12:17:33Z","timestamp":1736079453000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/67\/5\/667\/7109673"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,11,1]]},"references-count":38,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2005,11,10]]},"published-print":{"date-parts":[[2005,11,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.1467-9868.2005.00520.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2005,11]]},"published":{"date-parts":[[2005,11,1]]}}}