Forecasting of geophysical processes using stochastic and machine learning algorithms

We perform an extensive comparison between four stochastic and two machine learning (ML) forecasting algorithms by conducting a multiple-case study. The latter is composed by 50 single-case studies, which use time series of total monthly precipitation and mean monthly temperature observed in Greece. We apply a fixed methodology to each individual case and, subsequently, we perform a cross-case synthesis to facilitate the detection of systematic patterns. The stochastic algorithms include the Autoregressive order one model, an algorithm from the family of Autoregressive Fractionally Integrated Moving Average models, an Exponential Smoothing State Space algorithm and the Theta algorithm, while the ML algorithms are Neural Networks and Support Vector Machines. We also use the last observation as a Naïve benchmark in the comparisons. We apply the forecasting methods to the deseasonalized time series. We compare the one-step ahead as also the multi-step ahead forecasting properties of the algorithms. Regarding the one-step ahead forecasting properties, the assessment is based on the absolute error of the forecast of the last observation. For the comparison of the multi-step ahead forecasting properties we use five metrics applied to the test set (last twelve observations), i.e. the root mean square error, the Nash-Sutcliffe efficiency, the ratio of standard deviations, the index of agreement and the coefficient of correlation. Concerning the ML algorithms, we also perform a sensitivity analysis for time lag selection. Additionally, we compare more sophisticated ML methods as regards to the hyperparameter optimization to simple ones.