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Modelling spatio-temporal variability of temperature

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Abstract

Forecasting temperature in time and space is an important precondition for both, the design of weather derivatives and the assessment of the hedging effectiveness of index based weather insurance. In this article, we show how this task can be accomplished by means of Kriging techniques. Moreover, we compare Kriging with a dynamic semiparametric factor model (DSFM) that has been recently developed for the analysis of high dimensional financial data. We apply both methods to comprehensive temperature data covering a large area of China and assess their performance in terms of predicting a temperature index at an unobserved location. The results show that the DSFM performs worse than standard Kriging techniques. Moreover, we show how geographic basis risk inherent to weather derivatives can be mitigated by regional diversification.

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Notes

  1. The procedure could also be conducted in the opposite way: first, daily temperature models are fitted to the historical data at all locations to forecast the temporal scale. Then, Kriging is used to interpolate the forecasted data for the left-out location on the spatial scale. Although the RMSE results show no significant difference between the two sub-models, the computational effort is much higher.

  2. Note that the temperature model and all coefficients depend on the specific location. To simplify notation, however, we omit the location index \(i\) in this section.

  3. Unfortunately, there is no automatic selection procedure so far to select \(K\) and \(L\). According to Song et al. (2013), either the classic “90 %” rule in principal component analysis could be used to select \(K\) and \(L\) or the “explained variance” method. Alternatively, one could also sequentially test the size of the eigenvalues. These procedures, however, are becoming very costly and time-consuming and a theory for those in the context of DSFM has not yet been developed.

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Acknowledgments

Financial support from the German Research Foundation via CRC 649 “Economic Risk” is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Agricultural Economics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Xiaofeng Cao, Martin Odening & Matthias Ritter

  2. Chair of Statistics and Econometrics, Transportation Faculty, Technische Universität Dresden, Würzburger Str. 35, 01187, Dresden, Germany

    Ostap Okhrin

  3. SFB 649, School of Business and Economics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Ostap Okhrin

Authors
  1. Xiaofeng Cao
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  2. Ostap Okhrin
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  3. Martin Odening
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  4. Matthias Ritter
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Corresponding author

Correspondence to Matthias Ritter.

Appendix

Appendix

See Figs. 9, 10 and 11.

Fig. 9
figure 9

Ten years of temperature data (black) with the fitted conditional mean function (red) in station Quzhou (color figure online)

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Fig. 10
figure 10

Estimated model residuals in station Quzhou after removing the trend, seasonality, and the AR components

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Fig. 11
figure 11

Empirical and fitted volatility function in station Quzhou

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Cao, X., Okhrin, O., Odening, M. et al. Modelling spatio-temporal variability of temperature. Comput Stat 30, 745–766 (2015). https://doi.org/10.1007/s00180-015-0561-2

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