The Core Forecasting Parameters with Alfa Beta Gamma

Executive Summary

  • We cover the core forecasting parameters of alpha, beta and gamma.
  • Alpha, beta and gamma have specific definitions that are assisted by renaming the parameters.

Introduction

Forecast parameters control the methods within statistical forecasting systems. A specific combination of parameters converts a forecast method (say Holt Winters or a constant) into a specific model. In this article, you will learn about the core parameters.

What Are the Different Statistical Forecasting Parameters?

Every statistical forecasting application ships with a series of standard forecasting methods. As an example, here is the list of methods that ship with SAP DP.

  • First Order Exponential Smoothing
  • Constant Model with Auto Alpha Adaptation
  • Moving Average
  • Weighed Moving Average
  • Forecast with Trend Model
  • Holt’s Method
  • Second Order Exponential Smoothing
  • Trend Model with Automatic Alpha
  • Forecast with Seasonal Model
  • Seasonal Model Based on Winter’s Model
  • Seasonal Linear Regression
  • Median Method
  • Forecast with Seasonal and Trend Model
  • Holt and Winters’ Exponential Smoothing
  • Forecast with Automatic Model Selection
  • Test for Trend
  • Test for Season
  • Test for Trend and Season
  • Seasonal Model and Test for Trend
  • Trend Model and Test for Seasonal Pattern
  • Model Selection Procedure 2
  • Historical Data Adopted
  • Manual Forecast
  • Croston’s Model
  • Linear Regression
  • No Forecast
  • External Forecast

The forecast methods can be considered the starting point for creating a statistical forecast.

Forecast Methods Require Parameters

These forecast methods require parameters in order to provide the desired forecasting output. The definition of a parameter as follows: A numerical or other measurable factor forming one of a set that defines a system or sets the conditions of its operation.

There are different categories of forecast parameters. Some are common to every forecasting tool, and others are less commonly used or are only used in specific types of forecasts. To organize the discussion, I have broken the possible parameters into three categories that will be explained in this chapter.

These categories are:

  1. Core Forecast Parameters: Alfa Beta Gamma
  2. Secondary (to the Core) Forecast Parameters: Alfa 2, Alfa End, Alfa Increment, Sigma, Trend Dampening
  3. Time Based Forecast Parameters: Seasonal Periods, Period Indicator, Forecast Horizon, Historical Periods

For this article, we will only focus on the core forecast parameters.

The Core Forecast Parameters

We are fortunate that, in the information age, the most common statistical parameters have been well defined online. This includes Alfa Beta Gamma. Despite this, many people who have worked in statistical forecasting can list of these parameters. However, a much smaller subset can actually tell you what they mean. It doesn’t help that these parameters were named nonsensically with jargon labels. This, in our view, was done for academic reasons rather than being given a more descriptive appellation.

If we take the example of the gamma, it is difficult to see why it was chosen to represent the seasonal factor. This is because Gamma’s definitions are historically in nuclear science or stellar cartography. Adding to the confusion, dictionaries generally do not bring up the forecasting definitions of any of these terms, as they are niche.

What the Outcome of the Misnaming Has Caused

All of which leads to widespread confusion that would be resolved if they had been called something meaningful like “Base Factor”, “Trend Factor”, and “Seasonality Factor”.

Alas, we’re stuck with the first names given, and forecasting tools continue to use them with two notable exceptions. JDA Demand Management, which is JDA’s forecasting application, uses the latter and more straightforward terminology of Base, Trend, and Seasonality in lieu of Alfa Beta Gamma. DemandWorks Smoothie also dispenses with the common terms and replaces them with something more descriptive.

Now that we have described the history of the alpha, beta and gamma, lets us define each one.

Alfa Beta Gamma Definitions and Examples

Alfa

This is also known as the base value. This value determines the weighting of past data values in setting the baseline (magnitude) for the forecast, with higher values of alfa leading to increased weight being given to the most recent observations. Lower values of alfa implying a more uniform weighting.

Therefore if a time series were 90, 100, 110, 150, 250, 300, 375, and a higher alfa value were used, then the forecast generated would be higher. This is because the more recent data points would be emphasized. The more recent data points are higher than the less recent data points.

Beta

This is also known as the trend value. Beta determines the degree to which recent data trends should be valued compared to older trends when making the forecast.

Going back to the previous time series of 90,100, 110, 150, 250, 300, 375, if a higher beta were applied, the forecast would be higher than if a lower beta were applied because the trend is increasing more rapidly in the more recent data points.

Gamma

This is the seasonal component of the forecast. The higher the parameter the more the recent seasonal component is weighed. The seasonal component is the repeating pattern of the forecast. A seasonal pattern is often thought of as a seasonal pattern per year.

If the year is broken into four periods then a standard seasonal pattern would break down along the seasons of spring, summer, autumn, and winter. However, a seasonal pattern can also apply within a month or even within a week. For instance, when shipment patterns are analyzed, there is often a seasonal pattern within a week, or a month, as shipments are created only once per week, or multiple times per month. The duration over which the seasonal component repeats is not what defines the seasonal component, only that there is a pattern of repetition.

If a higher gamma value is used, then the more recent seasonal pattern is emphasized over the less recent. The first time series cannot be used to illustrate the effect of using a higher or lower gamma value as the time series does not have a seasonal component.

However, if we were instead to use the following time series of 100, 105, 120, 100, 100, 115, 125, 100, and if we were to use a higher gamma value then the forecast will be higher. This is because the seasonal increase of the second four data points is higher than the seasonal increase in the first four data points.

Conclusion

The core statistical forecast parameters control how much the more recent demand history should be weighted versus the demand history further back in time. These core forecast parameters are applied for the Alpha (the base), the Beta (the trend) and the Gamma (the seasonality) components of the demand history.

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Reference

The topic of alfa beta gamma is covered in the following book.

Forecasting Parameters Book

Forecast Parameters

Uses of Forecast Parameters

Statistical forecasting is one of the major approaches to creating forecasts across many different fields. Statistical forecasting has proven unmatched in the ability to cost effectively create enormous numbers of items, and the statistical forecast is often the first forecast which is created – although manual adjustments may follow.

The Need to Understand Forecast Parameters

However, in many statistical forecasting systems, it is necessary to understand the parameters, which control the forecasting model and to tune it for the specific items to which it applied. This book not only explains the statistical forecast parameters (dividing them into three parameter categories) but also shows many examples of parameters and how the parameters affect the different forecasting examples.
 By reading this book you will:
  • Understand the different categories of forecast parameters.
  • How different statistical forecasting applications work with forecast parameters (learn the difference between manually set and internally set forecast parameters and so-called best-fit forecasting)
  • Learn how changes in forecast parameters create changes to the forecast produced.
  • How to compare and contrast forecast parameters to understand better the forecast profiles which a company uses.

Chapters

  • Chapter 1: Introduction
  • Chapter 2: Where Forecasting Fits within the Supply Chain Forecasting Footprint
  • Chapter 3: The Common Problems with Statistical Forecasting
  • Chapter 4: Forecast Parameters
  • Chapter 5: Introduction to Best-Fit Forecasting
  • Chapter 6: Conclusion

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