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Modeling Hydrological Process by ARIMA–GARCH Time Series
Published in Saeid Eslamian, Faezeh Eslamian, Handbook of Drought and Water Scarcity, 2017
Reza Hadizadeh, Saeid Eslamian
MAPE is used to compare the results of several time series with different scales. For forecasting problems, more than MAPE, two other criteria, that is, root mean squared error and mean absolute scaled error, are used: RMSE=1n∑i=1n(yi−y^i)2MASE=1n∑i=1n(|yi−y^i|(1/(n−1))∑i=2n|yi−yi−1|)
Integrated demand forecasting and planning model for repairable spare part: an empirical investigation
Published in International Journal of Production Research, 2023
Vahid Babaveisi, Ebrahim Teimoury, Mohammad Reza Gholamian, Bahman Rostami-Tabar
This method has its cons, e.g. it is time-consuming, and its robustness is not sufficiently investigated. Jiang, Huang, and Liu (2021) present a new version of SVM considering outliers and errors that outperform the basic model considering computation time and non-smooth demand forecasting accuracy; however, the validation period is constant. is defined as the dot product where w, x, and b are the coefficient, attribute vector, and intercept. It is allowed that data fluctuates in the interval , the outlier distance is defined as the penalty where counts the data samples used in the training process. The nonlinear form of attribute is generally denoted by . The forecasting error formulated by Mean Absolute Scaled Error (MASE) is used to measure accuracy. An important factor in forecasting accuracy is the number of intervals utilised in estimating demand. We determine the number of intervals by the planning model, expressed in section 3.3.1. The indices may be omitted for simplicity while explaining.
Intermittent demand forecasting for spare parts in the heavy-duty vehicle industry: a support vector machine model
Published in International Journal of Production Research, 2021
Peng Jiang, Yibin Huang, Xiao Liu
Many measures were employed to evaluate the forecasting accuracy of intermittent demand (Hyndman and Koehler 2006; Lolli et al. 2017), such as mean errors, square errors, absolute errors, percentage errors, relative absolute errors, scaled errors and some geometric or symmetric variants. Amongst them, since the mean absolute scaled error (MASE) is scale-independent of different time series, it was recommended by Hyndman and Koehler (2006) as the standard measure to compare forecasting accuracy across multiple time series. Another scaled measure, the scaled mean error (SME) introduced by Syntetos and Boylan (2005), can check the scale dependence of a mean error and judge the bias characteristic of a model. SME was widely used for bias analysis (Kourentzes 2013; Petropoulos, Kourentzes, and Nikolopoulos 2016). Apart from these scaled measures, an intuitively scale-free measure—namely, the alternative mean absolute percentage error (AMAPE) (Hoover 2006)—was widely adopted as a measure for accuracy comparison. Division-by-zero problems occur when calculating a mean absolute percentage error. Such problems also hinder the application of the mean arctangent absolute percentage error (Kim and Kim 2016). As an alternative, in AMAPE, division by the average of all actual demands transforms the mean absolute percentage error into the mean absolute error item divided by the mean value.
Forecasting road accidental deaths in India: an explicit comparison between ARIMA and exponential smoothing method
Published in International Journal of Injury Control and Safety Promotion, 2023
Prafulla Kumar Swain, Manas Ranjan Tripathy, Khushi Agrawal
The mean error is a term that usually refers to the average of all the errors in a set. It usually results in a number that isn’t helpful because positives and negatives cancel each other out. Hence MAE is used as it is a measure of overall accuracy that gives an indication of the degree of spread, where all errors are assigned equal weights. If a method fits the past time series data very good, MAE is near zero, whereas if a method fits the past time series data poorly, MAE is large. Thus, when two or more forecasting methods are compared, the one with the minimum MAE can be selected as most accurate. MSE is also a measure of overall accuracy that gives an indication of the degree of spread, but here large errors are given additional weight. It is a generally accepted technique for evaluating exponential smoothing and other methods. Often the square root of MSE, RMSE, is considered, since the seriousness of the forecast error is then denoted in the same dimensions as the actual and forecast values themselves. MAPE is a relative measure that corresponds to MAE. It is one measure of accuracy commonly used in quantitative methods of forecasting. If MAPE calculated value is less than 10%, it is interpreted as excellent accurate forecasting, between 10–20% good forecasting, between 20 and 50% acceptable forecasting and over 50% inaccurate forecasting. Mean Absolute Scaled Error (MASE) is a scale-free error metric that gives each error as a ratio compared to a baseline’s average. The advantages of MASE include that it never gives undefined or infinite values and so is a good choice for intermittent-demand series (which arise when there are periods of zero demand in a forecast). It can be used on a single series, or as a tool to compare multiple series.