Automatic time series forecasting using nonlinear autoregressive neural network model with exogenous input

This study aims to determine an automatic forecasting method of univariate time series, using the nonlinear autoregressive neural network model with exogenous input (NARX). In this automatic setting, users only need to supply the input of time series. Then, an automatic forecasting algorithm sets up the appropriate features, estimate the parameters in the model, and calculate forecasts, without the users’ intervention. The algorithm method used include preprocessing, tests for trends, and the application of first differences. The time series were tested for seasonality, and seasonal differences were obtained from a successful analysis. These series were also linearly scaled to [−1, +1]. The autoregressive lags and hidden neurons were further selected through the stepwise and optimization algorithms, respectively. The 20 NARX models were fitted with different random starting weights, and the forecasts were combined using the ensemble operator, in order to obtain the final product. This proposed method was applied to real data, and its performance was compared with several available automatic models in the literature. The forecasting accuracy was also measured by mean squared error (MSE) and mean absolute percent error (MAPE), and the results showed that the proposed method outperformed the other automatic models.

Fuzzy Prediction Intervals Using Credibility Distributions

We present a new forecasting scheme based on the credibility distribution of fuzzy events. This approach allows us to build prediction intervals using the first differences of the time series data. Additionally, the credibility expected value enables us to estimate the k-step-ahead pointwise forecasts. We analyze the coverage of the prediction intervals and the accuracy of pointwise forecasts using different credibility approaches based on the upper differences. The comparative results were obtained working with yearly time series from the M4 Competition. The performance and computational cost of our proposal, compared with automatic forecasting procedures, are presented.

SUGGESTIONS FOR KILL PERFORMANCE FORECASTING OF VARIOUS OBJECTS AFLOAT AT THE SHORTEST TIME

The paper suggests ways to enhance the operational and tactical calculation complexes forming a part of the decisionmaking support system for naval strength employment. These ways comprise automatic forecasting of kill performance of objects afloat at the shortest time. It gives analytical calculations determining space and time parameters for planning of destroying enemy’s surface combat formations afloat by maneuvering combat formations of surface action groups. The combat formations are supposed to use these parameters to approach to enemy’s forces maneuvering beyond their reach in order to provide an effective engagement range. The paper describes an algorithm of possible optimal allocation of combat formations per objects to be destroyed. It also suggests an algorithm of automatic generation of proposals to the object-destroying schedule including required ammunition calculations employed to destroy an object in order to comply with required level of decision-making effectiveness. The authors give the results of space and time parameters calculations using the module for computer-aided construction of the shortest deployment route.