Abstract
We investigate the predictability of monthly temperature and precipitation by applying automatic univariate time series forecasting methods to a sample of 985 40-year-long monthly temperature and 1552 40-year-long monthly precipitation time series. The methods include a naïve one based on the monthly values of the last year, as well as the random walk (with drift), AutoRegressive Fractionally Integrated Moving Average (ARFIMA), exponential smoothing state-space model with Box–Cox transformation, ARMA errors, Trend and Seasonal components (BATS), simple exponential smoothing, Theta and Prophet methods. Prophet is a recently introduced model inspired by the nature of time series forecasted at Facebook and has not been applied to hydrometeorological time series before, while the use of random walk, BATS, simple exponential smoothing and Theta is rare in hydrology. The methods are tested in performing multi-step ahead forecasts for the last 48 months of the data. We further investigate how different choices of handling the seasonality and non-normality affect the performance of the models. The results indicate that: (a) all the examined methods apart from the naïve and random walk ones are accurate enough to be used in long-term applications; (b) monthly temperature and precipitation can be forecasted to a level of accuracy which can barely be improved using other methods; (c) the externally applied classical seasonal decomposition results mostly in better forecasts compared to the automatic seasonal decomposition used by the BATS and Prophet methods; and (d) Prophet is competitive, especially when it is combined with externally applied classical seasonal decomposition.
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Acknowledgements
We thank Prof. Krzysztof Kochanek for the invitation to submit a manuscript to the special issue of the Acta Geophysica “New Insights in Statistical Hydrology”. We also thank two anonymous reviewers, whose comments have led to the improvement of this paper.
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Appendix A: statistical software
Appendix A: statistical software
The analyses and visualizations have been performed in R Programming Language (R Core Team 2017). We have used the following contributed R packages: ‘devtools’ (Wickham and Chang 2017), ‘forecast’ (Hyndman et al. 2017), ‘fracdiff’ (Fraley et al. 2012), ‘gdata’ (Warnes et al. 2017), ‘ggplot2’ (Wickham 2016), ‘HKprocess’ (Tyralis 2016), ‘knitr’ (Xie 2014, 2015, 2017), ‘maps’ (Brownrigg et al. 2017), ‘prophet’ (Taylor and Letham 2017b) and ‘readr’ (Wickham et al. 2017).
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Papacharalampous, G., Tyralis, H. & Koutsoyiannis, D. Predictability of monthly temperature and precipitation using automatic time series forecasting methods. Acta Geophys. 66, 807–831 (2018). https://doi.org/10.1007/s11600-018-0120-7
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DOI: https://doi.org/10.1007/s11600-018-0120-7