R-vine models for spatial time series with an application to daily mean temperature. (English) Zbl 1390.62326

Summary: We introduce an extension of R-vine copula models to allow for spatial dependencies and model based prediction at unobserved locations. The proposed spatial R-vine model combines the flexibility of vine copulas with the classical geostatistical idea of modeling spatial dependencies using the distances between the variable locations. In particular, the model is able to capture non-Gaussian spatial dependencies. To develop and illustrate our approach, we consider daily mean temperature data observed at 54 monitoring stations in Germany. We identify relationships between the vine copula parameters and the station distances and exploit these in order to reduce the huge number of parameters needed to parametrize a 54-dimensional R-vine model fitted to the data. The new distance based model parametrization results in a distinct reduction in the number of parameters and makes parameter estimation and prediction at unobserved locations feasible. The prediction capabilities are validated using adequate scoring techniques, showing a better performance of the spatial R-vine copula model compared to a Gaussian spatial model.


62P12 Applications of statistics to environmental and related topics
62F10 Point estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M30 Inference from spatial processes


VineCopula; CDVine
Full Text: DOI arXiv


[1] Aas, Pair-copula constructions of multiple dependence, Insurance: Mathematics and Economics 44 pp 182– (2009) · Zbl 1165.60009
[2] Azzalini, Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution, Journal of the Royal Statistical Society, Series B, Statistical Methodology 65 pp 367– (2003) · Zbl 1065.62094
[3] Bedford, Probability density decomposition for conditionally dependent random variables modeled by vines, Annals of Mathematics and Artificial Intelligence 32 pp 245– (2001) · Zbl 1314.62040
[4] Bedford, Vines ’ a new graphical model for dependent random variables, The Annals of Statistics 30 pp 1031– (2002) · Zbl 1101.62339
[5] Brechmann, Truncated regular vines in high dimensions with applications to financial data, Canadian Journal of Statistics 40 pp 68– (2012) · Zbl 1274.62381
[6] Brechmann, Modeling dependence with C- and D-Vine Copulas: The R package CDVine, Journal of Statistical Software 52 pp 1– (2013)
[7] Cressie, Statistics for Spatio-Temporal Data. Wiley Series in Probability and Statistics (2011) · Zbl 1273.62017
[8] Czado, Pair-copula constructions of multivariate copulas, Copula Theory and Its Applications. Lecture Notes in Statistics pp 93– (2010)
[9] Czado , C. Brechmann , E. C. Gruber , L. 2013 Selection of vine copulas Copulae in Mathematical and Quantitative Finance P. Jaworski F. Durante W. K. Härdle · Zbl 1273.62110
[10] Dißmann, Selecting and estimating regular vine copulae and application to financial returns, Computational Statistics & Data Analysis 59 pp 52– (2013) · Zbl 1400.62114
[11] Erhardt , T. M. 2013 http://mediatum.ub.tum.de/node?id=1173363
[12] Fisher, Frequency distribution of the values of the correlation coefficients in samples from an indefinitely large population, Biometrika 10 pp 507– (1915)
[13] Gelfand, Handbook of Spatial Statistics (2010) · Zbl 1188.62284
[14] Genest, Everything you always wanted to know about copula modeling but were afraid to ask, Journal of Hydrologic Engineering 12 pp 347– (2007)
[15] Genest, A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika 82 pp 543– (1995) · Zbl 0831.62030
[16] Gneiting, Strictly proper scoring rules, prediction, and estimation, Journal of the American Statistical Association 102 pp 359– (2007) · Zbl 1284.62093
[17] Gräler, The pair-copula construction for spatial data: A new approach to model spatial dependency, Procedia Environmental Sciences 7 pp 206– (2011)
[18] Joe, Distributions with Fixed Marginals and Related Topics, Volume 28 of Lecture Notes-Monograph Series pp 120– (1996)
[19] Joe , H. Xu , J. J. 1996
[20] Kim, Comparison of semiparametric and parametric methods for estimating copulas, Computational Statistics & Data Analysis 51 pp 2836– (2007) · Zbl 1161.62364
[21] Kurowicka, Uncertainty Analysis with High Dimensional Dependence Modelling. Wiley Series in Probability and Statistics (2006) · Zbl 1096.62073
[22] Kurowicka, Dependence Modeling: Vine Copula Handbook (2011)
[23] Schepsmeier, VineCopula: Statistical Inference of Vine Copulas (2014)
[24] Simmons, Time-series decomposition using the sinusoidal model, International Journal of Forecasting 6 pp 485– (1990)
[25] Sklar, Publications de l’Institut de Statistique de L’Université de Paris pp 229– (1959)
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.