###### Building seasonal inventory ahead of holiday sales spike

15 October 2020###### Use of neural networks for time series forecasting

22 December 2021###### Building seasonal inventory ahead of holiday sales spike

15 October 2020###### Use of neural networks for time series forecasting

22 December 2021# Classical treatment of forecast errors as determinants of the effectiveness of the demand forecasting process and their use when neural networks are applied

With the increasing ability to process large volumes of data involving both endogenous (from within the organization) and exogenous (from the environment in which the organization operates) information, the application of neural networks in demand forecasting and supply chain optimization is gaining interest.

Is the transition from demand forecasting based on the classical approach to a model using neural networks a simple process ? Let’s start with the issue related to counting forecast error.

When using the classical approach to calculating forecast errors, the forecast error is understood as the deviation of the actual values of the forecast variable that will be realized during the forecasting period from the set forecasts. There are two types of forecast errors:

- forecast error
*ex post*, which is used to assess its relevance, - forecast error
*ex ante*, informing about the admissibility of the forecast.

The first is determined after the expiration of the time for which the forecast was set (when the realization of the forecast variable is already known), and the second is determined before the expiration of that time.

The quality of a predictive model determines its compatibility with empirical data, i.e. the degree to which the model fits the empirical data. To assess the quality of a forecasting model, among other things, one can use. coefficient of determination (coefficient of fit), which takes values in the range [0,1] and is described by the formula:

The forecast’s accuracy can be determined by ex post errors belonging to one of two groups.

The first group are the errors that are determined for a single period (absolute and relative ex post forecast error). The absolute error of the ex post forecast (Error) informs about the deviation of the forecast from the actual value in a given unit of time and is calculated according to the formula:

The relative ex-post forecast error (Percentage Error – PE) conveys the same information as the absolute one with the difference that its magnitude is determined as a percentage of the actual value. This error is calculated according to the formula:

The second group is the average errors, which characterize the entire range of empirical verification. These include. Root Mean Square Error (RMSE), we calculate according to the formula:and Mean Absolute Percentage Error (MAPE), the value of which is determined in % according to the following formula:Unfortunately, however, the above formulas do not directly translate into the determination of forecast errors using a neural network. In this case, it is necessary to separate the learning set, testing and non-deterministic approach to the process of determining prediction intervals of forecasts, but about this in a separate article.

This article was written thanks to the funds from the European Union’s co-financing of the Operational Program Intelligent Development 2014-2020, a project implemented under the competition of the National Center for Research and Development: under the “Fast Track” competition for micro, small and medium-sized entrepreneurs – competition for projects from less developed regions under Measure 1.1: R&D projects of enterprises Sub-measure 1.1.1 Industrial research and development work carried out by enterprises. Project title: “Developing software to improve forecast accuracy and inventory optimization from the perspective of customer and supplier collaborating in the supply chain using fuzzy deep neural networks.”

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