Comparison of Stochastic and Machine Learning Methods for Multi-Step Ahead Forecasting of Hydrological Processes

Abstract

Abstract:We perform an extensive comparison between 11 stochastic to 9 machine learning methods regarding their multi-step ahead forecasting properties by conducting 12 large-scale computational experiments. Each of these experiments uses 2 000 time series generated by linear stationary stochastic processes. We conduct each simulation experiment twice; the first time using time series of 110 values and the second time using time series of 310 values. Additionally, we conduct 92 real-world case studies using mean monthly time series of streamflow and particularly focus on one of them to reinforce the findings and highlight important facts. We quantify the performance of the methods using 18 metrics. The results indicate that the machine learning methods do not differ dramatically from the stochastic, while none of the methods under comparison is uniformly better or worse than the rest. However, there are methods that are regularly better or worse than others according to specific metrics.

One-step ahead forecasting of geophysical processes within a purely statistical framework

“…(4) On the contrary, the relative performance of the forecasting methods is slightly affected by the length of the time series for the experiments of the present study. The same has been found to mostly apply to the multi-step ahead forecasting performance of the same methods in Papacharalampous et al (2017a) for two other time series lengths. (5) Some forecasting methods are more accurate than others.…”

“…These two methods, as well as the simple, auto_ARIMA_f, auto_ARIMA_s and auto_ ARFIMA methods serve as reference points within our approach. In particular, ARIMA_f, auto_ARIMA_f and auto_ARFIMA are theoretically expected to be the most accurate within our simulation experiments [for an explanation see Papacharalampous et al (2017a), chapter 2], while BATS is also expected to perform well in these experiments, since it comprises an ARMA model. In summary, the experiments are controlled to some extent, while their components (datasets, methods and metrics)…”

“…We implement the forecasting methods described in Tables 4, 5 and 6. The latter constitute an adapted reproduction from Papacharalampous et al (2017a). Naïve is the last observation benchmark, while random walk (RW) is a commonly used variation of Naïve (Hyndman and Athanasopoulos 2013).…”

“…In geoscience, on the other hand, there are only four recent studies, all companions of the present, to be subsequently discussed. Papacharalampous et al (2017a) compare 11 stochastic and nine machine learning univariate time series forecasting methods in multi-step ahead forecasting of geophysical processes and (empirically) prove that stochastic and machine learning methods can perform equally well. The comparisons are conducted using 24,000 simulated time series of 110 values, 24,000 simulated time series of 310 values and 92 mean monthly time series of streamflow with varying lengths, as well as 18 metrics.…”

“…Alongside with this study, Papacharalampous et al (2017b) investigate the error evolution in multistep ahead forecasting when adopting this specific set of methods. The tests are performed on 6000 simulated time series of 150 values, 6000 simulated time series of 350 values and the streamflow dataset used in Papacharalampous et al (2017a). Some different behaviours are revealed within these experiments, also suggesting the fact that one-and multi-step ahead forecasting are different problems to be examined for the same methods.…”