Forecasts of time series: Definition, functioning and forecasting models
- Data Science, Predictive Analytics
- forecast, time series
- 4 min reading time
Lukas Weixler
A forecast incorporates all available information, such as values from the past or knowledge about future events, in order to predict the future as accurately as possible. Reliable forecasts help to optimize planning and accurately assess risks and are therefore considered indispensable components of successful business management. This article provides an overview of both forecasting in general and the well-known forecasting algorithms.
What are forecasts and how do they work?
An algorithm that takes past values as input and provides a forecast as output can be structured as a process in various ways. Traditionally, models are designed for this purpose that can make computer-based estimates based on assumptions. The best-known representatives of such traditional models are called:
- ARIMA,
- ETS,
- Random Walk with Drift,
- Theta, Seasonal-Naive, or
- Naive.
The example of the Naive Model shows that such a procedure does not have to be complex: Here, only the last known value from the past is constantly continued for the future - here is a graph to illustrate this:
In this example, data through August 2019 is used as information to predict the September 2020-August 2021 period. The last value of the known data is 0, so the Naïve Model predicts a constant 0. Especially for such time series as in the example - i.e. without trends and with rare/low swings, the Naive Algorithm is a popular prediction method precisely because of its trivial model.
For more on forecasting hierarchical time series and different approaches to it, see this wiki article.
Forecasts & dealing with uncertainty
While the graph shown above provides the company with an estimate for the future, it does not provide any guidance regarding uncertainty of the forecast. However, it is precisely the estimation of risks that constitutes the value of a forecast for many companies. Therefore, in addition to the point estimate shown above, a useful forecast should also depict a so-called forecast interval. An example can be found in the following graphic:
This graph shows that we expect a value in the dark blue range for 80% of the cases. 95 % of the cases are expected to be either in the dark blue or light blue range. On this basis, the risks can be estimated much more clearly than in the first case study.
The best-known forecasting models
Even though the Naive Model is an interesting variant in the present case, it is of little use for time series with trend or other structural properties. For this reason, a whole series of other known prediction algorithms exist, whose point estimates for our example time series are listed in the following graph:
Seasonal Naive Forecasts
In Seasonal Naïve forecasts, the most recent seasonal period is retained and updated for the desired forecast horizon. For example, the forecast for next February corresponds to the value of the last observed February. In cases where there is no clear seasonal structure, this can lead to similar error values for naïve and seasonally naïve forecasts.
Random Walk with Drift
Another simple model for forecasting time series is Random Walk with Drift. Here, a future value is assumed to be based on its first lag value, to which a constant and the error are added. In general, over a given period of time, the time series drifts in a negative direction if the constant is negative and in a positive direction if the constant is positive.
Theta method
As a frequently used algorithm in forecasting competitions, the theta method is also included in this introduction. Essentially, after a seasonal adjustment, several time series - so-called theta lines - are generated from the local curvature of the time series by means of exponential smoothing. Each of these lines is extrapolated separately and the corresponding forecasts are then combined.
Exponential Smoothing - ETS
The basis for forecasts with Exponential Smoothing - ETS are weighted averages of past observations. There are a number of different ETS forecasting algorithms that can be used depending on the available time series. Characteristic of the usability of a method are the two components trend (none, additive, additive damped) and seasonality (none, additive and multiplicative). A third component (error) is added to distinguish between additive and additive damped. Therefore, three parameters are used for ETS: Error, Trend and Seasonality.
ARIMA models
The combination of autoregression, differencing, and moving average that characterizes ARIMA models can be determined using three parameters (p, d, q): Where p represents the number of autoregressive terms, d represents the degree of non-seasonal first differences needed for stationarity, and q represents the number of lagged forecast errors in the moving average component. Based on weighted observations from the past, an appropriate forecast can thus be determined by means of an equation.
Neural networks
In addition, a whole range of other prediction methods are available, especially in the field of neural networks, but these would exceed the scope of this article.
Conclusion: That's why forecasts are important for your business success
Good forecasts are crucial in the context of successful planning and business management. A whole range of algorithms are available for this purpose, which examine data from the past for recurring patterns. Based on this knowledge, predictions for the future are made, which, however, are always associated with a certain degree of uncertainty. Being able to clearly limit and name this uncertainty is also part of a good forecast.
A central challenge for users remains the question under which type of time series which of the presented forecasting methods is most likely to prove successful. My master's thesis at s-peers AG deals with this question. The main finding is as follows: The combined use of several forecasting algorithms can provide significantly more reliable results under certain conditions than a single one of the methods presented here.
Know more?
Would you like to delve deeper into this topic and use forecasts to plan your company's success? My team and I look forward to hearing from you!
