Spatial correlation in weather forecast accuracy: a functional time series approach

Phillip A. Jang () and David S. Matteson
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Phillip A. Jang: Cornell University
David S. Matteson: Cornell University

Computational Statistics, 2023, vol. 38, issue 3, No 7, 1215-1229

Abstract: Abstract A functional time series approach is proposed for investigating spatial correlation in daily maximum temperature forecast errors for 111 cities spread across the U.S. The modelling of spatial correlation is most fruitful for longer forecast horizons, and becomes less relevant as the forecast horizon shrinks towards zero. For 6-day-ahead forecasts, the functional approach uncovers interpretable regional spatial effects, and captures the higher variance observed in inland cities versus coastal cities, as well as the higher variance observed in mountain and midwest states. The functional approach also naturally handles missing data through modelling a continuum, and can be implemented efficiently by exploiting the sparsity induced by a B-spline basis. The temporal dependence in the data is modeled through temporal dependence in functional basis coefficients. Independent first order autoregressions with generalized autoregressive conditional heteroskedasticity [AR(1)+GARCH(1,1)] and Student-t innovations work well to capture the persistence of basis coefficients over time and the seasonal heteroskedasticity reflecting higher variance in winter. Through exploiting autocorrelation in the basis coefficients, the functional time series approach also yields a method for improving weather forecasts and uncertainty quantification. The resulting method corrects for bias in the weather forecasts, while reducing the error variance.

Keywords: Functional data analysis; Spatiotemporal; Random effects; GARCH; Weather forecast data; Data Expo 2018 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00180-023-01338-4

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