Spatio-Temporal Prediction of a Nonstationary and Nonseparable Random Fields with Tucker Decomposition of Covariance Tensor

Document Type : Original Paper

Authors

Department of Statistics, Tarbiat Modares University

Abstract

In spatio-temporal data analysis, the most common way to consider the spatio-temporal correlation structure of data is to use the covariance function, which is usually unknown and estimated based on observations. This method requires constraints such as stationarity, isotropy and separability for the random field. Although the acceptance of these hypotheses facilitates the fitting of valid models to the spatio-temporal covariance function, they are not necessarily realistic in applied problems. In this paper, to expedite the calculation of spatio-temporal prediction for a non-stationary and non-separable random field, a possible model based on spatial-temporal covariance tensor analysis based on Tucker analysis is investigated. Then, we show the proposed method for predicting wind energy based on spatio-temporal wind speed data at 31 weather stations in Iran.

Keywords

Main Subjects


[1] س. زحمتکش و م. محمدزاده، مدل بندی داده های فضایی-زمانی با گمشدگی غیرقابل چشم پوشی. مجله مدل سازی پیشرفته ریاضی، ]
.۶۱–۳۹ (۱۳۹۹) (۱)۱۰
[2]م. محمدزاده،آمار فضایی و کاربردهای آن. چاپ سوم، مرکز نشر آثار علمی دانشگاه تربیت مدرس، تهران، ۱۳۹۸
[3] م. عصمتی و م. محمدزاده، پیش گویی فضایی-زمانی میدان های تصادفی نامانا و تفکیک ناپذیر. دومین سمینار آمار فضایی و کاربردهای آن، دانشگاه صنعتی شاهرود، ۱۳۹۸
[4] D. Ghosh and A. Suryawanshi, Approximation of spatio-temporal random processes using tensor decomposition. Communications in Computational Physics, 16(1) ()20147 5–95.
[5] T. Gneiting, Nonseparable, stationary covariance functions for space–time data. Journal of the American Statistical Association, 97(458) (2002) 590–600.
[6] J. Haslett and A.E. Raftery, Space-time modelling with long-memory dependence: Assessing ireland’s wind power resource. Journal of the Royal Statistical Society: Series C (Applied Statistics), 38(1) (1989) 1–21.
[7] F. L. Hitchcock, The expression of a tensor or a polyadic as a sum of products. Journal of Mathematics and Physics, 6(1-4) (1927) 164–189.
[8] T.G. Kolda and B. W. Bader, Tensor decompositions and applications. SIAM review, 51(3) (2009) 455–500.
[9] J.B. Kruskal, Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear algebra and its applications, 18(2) (1977) 95–138.
[10] P. Lynch, The origins of computer weather prediction and climate modeling. Journal of computational physics, 227(7) (2008) 3431–3444.
[11] E. Serrano, J.J. Gómez-Sanz, J.A. Botía, and J. Pavón, Intelligent data analysis applied to debug complex software systems. Neurocomputing, 72(13-15) (2009) 2785–2795.
[12] S.S. Soman, H. Zareipour, O. Malik, and P. Mandal, A review of wind power and wind speed forecasting methods with different time horizons. In North American Power Symposium 2010, pages 1–8. IEEE, 2010.
[13] L.R. Tucker, Implications of factor analysis of three-way matrices for measurement of change. Problems in measuring change, 15 (1963) 122–137.
[14] S. Zahmatkesh and M. Mohammadzadeh, Bayesian Prediction of spatial data with non-ignorable missingness. Statistical Papers, DOI:10.1007/s00362-020-01186-0, 2020.