Stage 1: Statement of a theory or hypothesis

The beginning of the demand forecasting process involves the determination of a set of objectives or essential information to derive various business strategies. These objectives are based on a set of hypotheses that are generally derived from a combination of economic theory and previous empirical studies. For example, a manager might be interested in identifying the optimal price and production quantity for a new product, based on how the elasticity of demand has impacted the company's past sales.

Stage 2: Model Specification

There are numerous econometric models to choose from, and the selection of the specific model to forecast demand is subject to several factors. These include the type of data collected, the number of observations and other aspects pertinent to the analysis that managers wish to perform.[9] At this stage it is important to define the type of variables that will be used for forecast demand. Regression analysis is the main statistical method for forecasting. There are several types of regression analysis, but in essence, they all provide an analysis of how one or more variables influence the dependent variable being measured. An example of a model for forecasting demand is M. Roodman's (1986) demand forecasting regression model to measure the effects of seasonality on a data point being measured.[10] The model was based on linear regression, used to quantify linear trends arising from seasonal cycles and their influences on demand. That is, it was used to understand the seasonal demand for a product in relation to sales during the summer and winter.

The linear regression model is described as:.

Being the dependent variable (the value to be predicted), the intercept, the slope coefficient, the independent variable (the explanatory value) and the error term.

M. Roodman's model for demand forecasting is based on linear regression and is described as follows:

is the set of all - indices of the quarter. The calculation for all periods that fall in the quarter is given by:.

Stage 3: data collection

Once the type of model has been defined in stage 2, it is crucial to detail the data and the corresponding collection method. In the first instance, the model is specified to identify the variables that need to be collected. On the other hand, when selecting the desired forecast model, it is necessary to consider both the existing data and the available methods for collecting information, making sure to formulate the model accurately and adapted to the specific conditions of the analysis. Time series data collection and cross-sectional data are the different collection methods that can be used. Time series data are based on historical observations collected sequentially over time. These observations form the basis for extracting statistics, identifying key characteristics and obtaining relevant knowledge that facilitates the understanding of the behavior of the variable in question throughout the temporal evolution.[11]​ The types of data that can be collected using time series data can be sales, prices, manufacturing costs and their corresponding time intervals, that is, weekly, monthly, quarterly, annually or any other regular interval. Cross-sectional data refers to data collected on a single entity over different time periods. Cross-sectional data used in demand forecasting typically represents a data point collected from an individual, company, industry, or area. For example, Company A's sales during Quarter 1. This type of data encapsulates a variety of data points that resulted in the final data point. The subset of data points may not be observable or feasible to determine, but it can be a practical method to add precision to the demand forecasting model.[12]​ The source of the data can be found through company records, commercial or private agencies, or official sources.

Stage 4: Parameter estimation

Once the model and data have been determined, the values ​​are calculated to evaluate the effects that the independent variables have on the dependent variable in question. Taking as an example a linear regression model for parameter estimation, the following steps are followed:

Linear regression formula:

The beginning of the process involves finding the line that minimizes the sum of the differences between the observed values ​​and the fitted values ​​of the line, squared.[8]​ Which is expressed by , so that and , the fitted value of the regression line, is minimized.

and represent the intercept and slope of the line, respectively. The method to determine these coefficients involves the use of partial derivatives with respect to both variables, setting both expressions equal to zero and solving them simultaneously:.

Evaluating the accuracy of forecasts in the supply chain is commonly performed using the mean absolute percentage error") or MAPE. Statistically, MAPE") is defined as the average percentage errors, obtained as the difference in absolute value between the forecast values ​​and the actual data.

This volume-weighted MAPE approach, or MAD/Mean ratio, offers a more accurate perspective by considering the magnitude of deviations relative to average sales. By dividing the sum of the mean absolute deviations by the total sales, a more equitable and representative evaluation of the accuracy of the forecasts is achieved, considering the relative importance of each product in the total set of sales. This weighted approach more accurately reflects the true impact of errors on demand, providing a more robust metric for evaluating the effectiveness of forecasts in the supply chain context.

This calculation, where is the actual value and the forecast, is also known as WAPE or weighted absolute percentage error.

Another interesting option is weighted MAPE:

The advantage of this measure is its ability to weight errors. However, the only drawback is that an undefined result will be obtained when = 0, which is not symmetric. This implies that it can be considerably more inaccurate when sales exceed forecasts compared to when they are lower. To address this problem, symmetric mean absolute percentage error (sMAPE) is often used.

Finally, in the case of intermittent demand patterns, the previously mentioned error measures may have limitations. In this context, companies may choose to use MASE (mean absolute scaling error) as a key performance indicator. However, it is important to note that the calculation of the MASE presents a challenge, as it is not as intuitive as the methods mentioned above.[13] Another metric worthy of consideration, especially in the presence of intermittent or irregular demand patterns, is the SPEC (stock-oriented forecast error costs).[14] The logic underlying this metric lies in the comparison between the forecasted demand and the actual demand, by calculating the theoretical costs incurred during the forecast horizon. It is assumed that a predicted demand greater than actual demand generates costs associated with maintaining stocks, while a predicted demand lower than actual demand results in opportunity costs. SPEC takes into account temporal changes (prediction before or after actual demand) or cost-related aspects and also allows comparisons between demand forecasts based on commercial aspects.

Stage 6: Hypothesis testing

Once the model has been determined, it is used to test the theory or hypothesis formulated in the first stage. The results must clearly describe the objectives sought and determine whether the theory or hypothesis is valid or not. In the context of the example provided in Stage 1, the model should demonstrate the relationship between the elasticity of market demand and its correlation with the company's past sales. This, in turn, will enable managers to make informed decisions about the optimal price and production levels for the new product.

Stage 7: Forecast

The last step involves forecasting demand based on the data set and model created. To carry out this projection, estimates of a selected variable are used in order to determine its effects on demand. Regarding the estimation of the selected variable, it is possible to use a regression model or implement both qualitative and quantitative assessments. Examples of qualitative and quantitative evaluations include:.

Contenido

Existen diversos análisis estadísticos y econométricos que se emplean para prever la demanda.[8]​ La previsión de la demanda puede desglosarse en un proceso de siete etapas:.

Stage 1: Statement of a theory or hypothesis

The beginning of the demand forecasting process involves the determination of a set of objectives or essential information to derive various business strategies. These objectives are based on a set of hypotheses that are generally derived from a combination of economic theory and previous empirical studies. For example, a manager might be interested in identifying the optimal price and production quantity for a new product, based on how the elasticity of demand has impacted the company's past sales.

Stage 2: Model Specification

There are numerous econometric models to choose from, and the selection of the specific model to forecast demand is subject to several factors. These include the type of data collected, the number of observations and other aspects pertinent to the analysis that managers wish to perform.[9] At this stage it is important to define the type of variables that will be used for forecast demand. Regression analysis is the main statistical method for forecasting. There are several types of regression analysis, but in essence, they all provide an analysis of how one or more variables influence the dependent variable being measured. An example of a model for forecasting demand is M. Roodman's (1986) demand forecasting regression model to measure the effects of seasonality on a data point being measured.[10] The model was based on linear regression, used to quantify linear trends arising from seasonal cycles and their influences on demand. That is, it was used to understand the seasonal demand for a product in relation to sales during the summer and winter.

The linear regression model is described as:.

Being the dependent variable (the value to be predicted), the intercept, the slope coefficient, the independent variable (the explanatory value) and the error term.

M. Roodman's model for demand forecasting is based on linear regression and is described as follows:

is the set of all - indices of the quarter. The calculation for all periods that fall in the quarter is given by:.

Stage 3: data collection

Once the type of model has been defined in stage 2, it is crucial to detail the data and the corresponding collection method. In the first instance, the model is specified to identify the variables that need to be collected. On the other hand, when selecting the desired forecast model, it is necessary to consider both the existing data and the available methods for collecting information, making sure to formulate the model accurately and adapted to the specific conditions of the analysis. Time series data collection and cross-sectional data are the different collection methods that can be used. Time series data are based on historical observations collected sequentially over time. These observations form the basis for extracting statistics, identifying key characteristics and obtaining relevant knowledge that facilitates the understanding of the behavior of the variable in question throughout the temporal evolution.[11]​ The types of data that can be collected using time series data can be sales, prices, manufacturing costs and their corresponding time intervals, that is, weekly, monthly, quarterly, annually or any other regular interval. Cross-sectional data refers to data collected on a single entity over different time periods. Cross-sectional data used in demand forecasting typically represents a data point collected from an individual, company, industry, or area. For example, Company A's sales during Quarter 1. This type of data encapsulates a variety of data points that resulted in the final data point. The subset of data points may not be observable or feasible to determine, but it can be a practical method to add precision to the demand forecasting model.[12]​ The source of the data can be found through company records, commercial or private agencies, or official sources.

Stage 4: Parameter estimation

Once the model and data have been determined, the values ​​are calculated to evaluate the effects that the independent variables have on the dependent variable in question. Taking as an example a linear regression model for parameter estimation, the following steps are followed:

Linear regression formula:

The beginning of the process involves finding the line that minimizes the sum of the differences between the observed values ​​and the fitted values ​​of the line, squared.[8]​ Which is expressed by , so that and , the fitted value of the regression line, is minimized.

and represent the intercept and slope of the line, respectively. The method to determine these coefficients involves the use of partial derivatives with respect to both variables, setting both expressions equal to zero and solving them simultaneously:.

Evaluating the accuracy of forecasts in the supply chain is commonly performed using the mean absolute percentage error") or MAPE. Statistically, MAPE") is defined as the average percentage errors, obtained as the difference in absolute value between the forecast values ​​and the actual data.

This volume-weighted MAPE approach, or MAD/Mean ratio, offers a more accurate perspective by considering the magnitude of deviations relative to average sales. By dividing the sum of the mean absolute deviations by the total sales, a more equitable and representative evaluation of the accuracy of the forecasts is achieved, considering the relative importance of each product in the total set of sales. This weighted approach more accurately reflects the true impact of errors on demand, providing a more robust metric for evaluating the effectiveness of forecasts in the supply chain context.

This calculation, where is the actual value and the forecast, is also known as WAPE or weighted absolute percentage error.

Another interesting option is weighted MAPE:

The advantage of this measure is its ability to weight errors. However, the only drawback is that an undefined result will be obtained when = 0, which is not symmetric. This implies that it can be considerably more inaccurate when sales exceed forecasts compared to when they are lower. To address this problem, symmetric mean absolute percentage error (sMAPE) is often used.

Finally, in the case of intermittent demand patterns, the previously mentioned error measures may have limitations. In this context, companies may choose to use MASE (mean absolute scaling error) as a key performance indicator. However, it is important to note that the calculation of the MASE presents a challenge, as it is not as intuitive as the methods mentioned above.[13] Another metric worthy of consideration, especially in the presence of intermittent or irregular demand patterns, is the SPEC (stock-oriented forecast error costs).[14] The logic underlying this metric lies in the comparison between the forecasted demand and the actual demand, by calculating the theoretical costs incurred during the forecast horizon. It is assumed that a predicted demand greater than actual demand generates costs associated with maintaining stocks, while a predicted demand lower than actual demand results in opportunity costs. SPEC takes into account temporal changes (prediction before or after actual demand) or cost-related aspects and also allows comparisons between demand forecasts based on commercial aspects.

Stage 6: Hypothesis testing

Once the model has been determined, it is used to test the theory or hypothesis formulated in the first stage. The results must clearly describe the objectives sought and determine whether the theory or hypothesis is valid or not. In the context of the example provided in Stage 1, the model should demonstrate the relationship between the elasticity of market demand and its correlation with the company's past sales. This, in turn, will enable managers to make informed decisions about the optimal price and production levels for the new product.

Stage 7: Forecast

The last step involves forecasting demand based on the data set and model created. To carry out this projection, estimates of a selected variable are used in order to determine its effects on demand. Regarding the estimation of the selected variable, it is possible to use a regression model or implement both qualitative and quantitative assessments. Examples of qualitative and quantitative evaluations include:.