# Accuracy of Demand Forecasting

Joannes Vermorel, June 2013

In statistics, the accuracy of forecast is the degree of closeness of the statement of quantity to that quantity’s actual (true) value. The actual value usually cannot be measured at the time the forecast is made because the statement concerns the future. For most businesses, more accurate forecasts increase their effectiveness to serve the demand while lowering overall operational costs.

In this article, we adopt a statistical viewpoint primarily relevant to commerce and manufacturing, especially for inventory optimization and demand planning areas.

## Use of the accuracy estimates

The accuracy, when computed, provides a quantitative estimate of the expected quality of the forecasts. For inventory optimization, the estimation of the forecasts accuracy can serve several purposes:

• to choose among several forecasting models that serve to estimate the lead demand which model should be favored.
• to compute the safety stock typically assuming that the forecast errors follow a normal distribution.
• to prioritize the items that need the most dedicated attention because raw statistical forecasts are not reliable enough.

In other contexts, such as strategic planning, the accuracy estimates are used to support the what-if analysis, considering distinct scenarios and their respective likelihood.

## Impact of aggregation on the accuracy

It is a frequent misconception to interpret the quality of the forecasting model as the primary factor driving the accuracy of the forecasts: this is not the case.

The most important factor driving the value of the accuracy is the intrinsic volatility of the phenomenon being forecasted. In practice, in commerce or manufacturing, this volatility highly correlated to the aggregation level:

• larger areas, such as national forecasts vs local forecasts, yield more accuracy.
• idem for longer periods, such as monthly forecasts vs daily forecasts.

Anecdotal evidence: At Lokad, we routinely observe that there is no such thing as a good accuracy; it’s specific of the context. When forecasting the next-day nationwide electricity consumption for a large European country, 0.5% of error was considered as relatively inaccurate; while achieving less than 80% of error for the store-level forecasts of the first day of sales of newly introduced fresh products was considered a significant achievement.

Then, once a level of aggregation is given, the quality of the forecasting model plays indeed to primary role in the accuracy that can be achieved. Finally, the accuracy decreases when looking further ahead in the future.

## Empirical accuracy vs real accuracy

The term accuracy is most frequently used referring to quality of a physical measurement of some kind. Unfortunately, this vision is somewhat misleading when it comes to statistical forecasting. Indeed, unlike the physical setup where the measurement could be compared to alternative methods, the real accuracy of forecast should be strictly measured against data you don’t have.

Indeed, once the data is available, it is always possible to produce perfectly accurate forecasts, as it only requires mimicking the data. This single question has kept statisticians puzzled for more than a century, as a deeply satisfying viewpoint has only been found at the end of the 20th century with the advent of Vapnik-Chervonenkis theory (1).

The accuracy of the forecasts can only be practically measured against available data; however, when the data is available, those forecasts aren’t true forecasts anymore, being statements about the past rather than being statements about the future. Thus, those measurements are referred as the empirical accuracy, as opposed to the real accuracy.

Overfitting problems can lead to large discrepancies between the empirical accuracy and the real accuracy. In practice, a careful use of backtesting can mitigate most overfitting problems when forecasting time-series.

## Popular accuracy metrics

There are many metrics to measure accuracy of forecasts. The most widely used metrics are:

In practice, a metric should be favored over another based on its capacity to reflect the costs incurred by the company because of the inaccuracies of the forecasts.