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We propose a time series forecasting method for the future prices of agricultural products and present the criteria by which forecasted future time series are evaluated in the context of statistical characteristics. Time series forecasting of agricultural products has the basic importance in maintaining the sustainability of agricultural production. The prices of agricultural products show seasonality in their time series, and conventional methods such as the auto-regressive integrated moving average (ARIMA or the Box Jenkins method) have tried to exploit this feature for forecasting. We expect that recurrent neural networks, representing the latest machine learning technology, can forecast future time series better than conventional methods. The measures used in evaluating the forecasted results are also of importance. In literature, the accuracy determined by the error rate at a specific time point in the future, is widely used for evaluation. We predict that, in addition to the error rate, the criterion for conservation of the statistical characteristics of the probability distribution function from the original past time series to the future time series in the forecasted future is also important. This is because some time series have a non-Gaussian probability distribution (such as the Lévy stable distribution) as a characteristic of the target system; for example, market prices on typical days change slightly, however on certain occasions, change dramatically. We implemented two methods for time series forecasting based on recurrent neutral network (RNN), one of which is called time-alignment of time point forecast (TATP), and another one is called direct future time series forecast (DFTS). They were evaluated using the two aforementioned criteria consisting of the accuracy and the conservation of the statistical characteristics of the probability distribution function. We found that after intensive training, TATP of LTSM shows superior performance in not only accuracy, but also the conservation compared to TATP of other RNNs. In DFTS, DFTS of LSTM cannot show the best performance in accuracy in RMS sense, but it shows superior performance in other criteria. The results suggest that the selection of forecasting methods depends on the evaluation criteria and that combinations of forecasting methods is useful based on the application. The advantage of our method is that the required length of time series for training is enough short, namely, we can forecast the whole cycle of future time series after training with even less than the half of the cycle, and it can be applied to the field where enough numbers of continuous data are not available.

Time series forecasting of agricultural product prices based on recurrent neural networks and its evaluation method