Abstract
We extend our earlier work on predicting a univariate time series in real time with confidence intervals (Hirata, et al., Renew. Energy 67, 35 (2014)) to a multivariate time series. We realize this extension by using the “p-norm” where p is smaller than 1. We compare the performance when p is 0.5 with that when p is 2 using solar irradiation data and wind data measured all over Japan.
References
Y. Hirata, T. Yamada, J. Takahashi, H. Suzuki, Phys. Lett. A 376, 3092 (2012)
Y. Hirata, T. Yamada, J. Takahashi, K. Aihara, H. Suzuki, Renew. Energy 67, 35 (2014)
F. Kwasniok, L.A. Smith, Phys. Rev. Lett. 92, 164101 (2004)
T. Yamada, J. Takahashi, K. Aihara, Reliability Eng. Ass. Jpn. 28, 489 (2006) (in Japanese)
H. Kantz, T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, 2004)
D. Françios, High-dimensional Data Analysis (VDM Verlag, 2008)
E. Lorenz, Proc. Seminar Predictability, ECMWF 1 (1996)
J.A. Hansen, L.A. Smith, J. Atmos. Sci. 57, 2859 (2000)
L. Cao, A. Mees, K. Judd, Physica D 121, 75 (1998)
S. Boccaletti, D.L. Valadares, L.M. Pecora, H.P. Geffert, T. Carroll, Phys. Rev. E 65, 035204(R) (2002)
S.P. Garcia, J.S. Almeida, Phys. Rev. E 72, 027205 (2005)
Y. Hirata, H. Suzuki, K. Aihara, Phys. Rev. E 74, 026202 (2006)
I. Vlachos, D. Kugiumtzis, Phys. Rev. E 82, 016207 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hirata, Y., Aihara, K. & Suzuki, H. Predicting multivariate time series in real time with confidence intervals: Applications to renewable energy. Eur. Phys. J. Spec. Top. 223, 2451–2460 (2014). https://doi.org/10.1140/epjst/e2014-02210-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2014-02210-3