Temperature prediction based on a space–time regression-kriging model

JOURNAL OF APPLIED STATISTICS(2020)

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Abstract
Many phenomena exist in the space-time domain, often with a low data sampling rate and sparsely distributed network of observed points. Therefore, spatio-temporal interpolation with high accuracy is necessary. In this paper, a space-time regression-kriging model was introduced and applied to monthly average temperature data. First, a time series decomposition was applied for each station, and a multiple linear regression model was used to fit space-time trends. Second, a valid nonseparable spatio-temporal variogram function was utilized to describe similarities of the residuals in space-time. Finally, space-time kriging was applied to predict monthly air temperature. Jackknife techniques were used to predict the monthly temperature at all stations, with correlation coefficients between predictions and observed data very close to 1. Moreover, to evaluate the advantages of space-time kriging, pure time forecasting also was executed employing an autoregressive integrated moving average (ARIMA) model. The results of these two methods show that both mean absolute error (MAE) and root-mean-square error (RMSE) of space-time prediction are much lower than those of the pure time forecasting. The estimated temperature curves for stations also show that the former present a conspicuous improvement in interpolation accuracy when compared with the latter.
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Key words
Monthly temperature prediction,space-time kriging,multiple linear regression,spatio-temporal variogram,geostatistics
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