Specific Forecasting Methods

This overview presents the most common forecasting methods, ranging from classical statistical procedures and machine learning approaches to modern foundation models. It serves as a guide to better understand the fundamental logic and mechanics of the various forecasting models. The methods listed here represent a selection of the most practice-relevant approaches.

Naive Forecast

The naive forecast is a simple, intuitive forecasting method. For the forecast, the most recent value of the given time series is projected forward into the future as a constant.

Moving Average

The moving average is a simple, intuitive forecasting method. To create a forecast, the arithmetic mean of current data points from the given time series (e.g., from all data points of the last quarter) is calculated and projected forward into the future as a constant. The number of current data points to be included in the averaging is referred to as the order of the moving average, and it must be defined a priori. A special case of the moving average is the naive forecast (moving average of order 1).

Autoregressive Integrated Moving Average (ARIMA)

An ARIMA model (ARIMA = Autoregressive Integrated Moving Average) is a model for the analysis and forecasting of time series, which includes past values of the time series itself as well as past error terms. The analysis can be performed on raw data or (multiple) differentiated data. Seasonality and exogenous factors can also be included in ARIMA models.

Exponential Smoothing with Covariates (ESCov)

Exponential smoothing is a well-established method for the analysis and forecasting of time series, which can take into account level, trend, and multiple seasonal components. In this method, earlier time series values are usually weighted less than the recent history. The extension "Exponential Smoothing with Covariates" (ESCov) can additionally handle exogenous influences.

TBATS

TBATS is an extension of exponential smoothing developed by De Livera, Hyndman & Snyder (2011), which is particularly advantageous for complex seasonal patterns. Seasonality modeling is carried out using Fourier analysis and trigonometric functions. The name TBATS is an acronym that summarizes the capabilities of the method: trigonometric functions for modeling multiple seasonality (T), Box-Cox transformation (B), ARMA error modeling (A), trend (T), and seasonality (S).

Croston Method (Croston)

The Croston method is a forecasting technique for intermittent time series. The method was proposed by Croston in 1972 for forecasting sporadic demand for items. The method separately models the size of demand events (= non-zero values of the time series) and the duration between two consecutive events (= zero intervals), usually using exponential smoothing, and then derives a forecast from this.

In addition to the classic version of Croston, there are now several extensions and variations of the method, such as the Teunter-Syntetos-Babai method (TSB).

Teunter-Syntetos-Babai Method (TSB)

TSB is an extension of Croston developed by Teunter, Syntetos, and Babai (2011), which addresses and overcomes two disadvantageous aspects of the original version:

1. Positive bias in the forecasts
2. Inertia in demand events that are ending (Obsolescence)

Essentially, this is achieved by TSB shifting from modeling the duration between two events (zero intervals) to modeling the probabilities of their occurrence.

Machine Learning for Forecasting

Machine learning methods can also be used for forecasting and offer an advantage over classical approaches such as ARIMA and Exponential Smoothing for hidden or multifaceted patterns and a multitude of influencing factors. To model the structures of the data history and temporal effects, a selected set of various lagged actual values as well as specifically engineered features is generally used. These various input variables include trend components and seasonal indicators to map cyclically recurring patterns within the data structure.

Foundation Models for Time Series

Foundation models, which are based on the advancements of Deep Learning and especially the Transformer architecture, have also gained importance in forecasting applications. A significant advantage of foundation models lies in their ability to generalize and adapt to new time series. Different approaches can be distinguished in how these models can be used for forecasting:

1. Zero-Shot-Prediction: Due to their extensive pre-training on diverse datasets, foundation models can generate forecasts for completely new time series without being explicitly trained on them. This allows for accurate predictions to be obtained in just a few seconds, even for long time series. Zero-shot-prediction represents the main application of foundation models in time series forecasting.
2. Few-Shot-Prediction: With only a few example time series, foundation models can be trained to more quickly adjust to the specific characteristics of those time series. This enables better adaption of the model and potentially more accurate forecasts compared to zero-shot-prediction, without requiring extensive finetuning.
3. Full-Shot-Prediction: Similar to traditional machine learning techniques, foundation models can also be trained on complete datasets that include different types of time series. This comprehensive training aims to optimise performance through thorough finetuning on historical data. However, full-shot-application is rarely used in practice because the effort for training such large models is enormous and often not in proportion to the potential performance gain.

Architecturally, various approaches exist for foundation models in time series forecasting. Initially, pre-trained language models were often used, however, it has been shown that models that are trained exclusively on time series data tend to achieve better results. Moreover, there are different models that also enable multivariate predictions and the integration of covariates. More details on foundation models in time series forecasting can be found in the survey by Liang et al. (2024), available here. Generally, foundation models can also be utilized in other areas.