ETS is powerful. ARIMA is powerful. But when you need both, you are typically left with fitting ARMA to the residuals of ETS, which biases the parameters. There is a much neater solution: combine them in one state space model to estimate everything jointly… The standard practice when ETS is not enough to capture the … Read more
So, you know quite well that the normal distribution is one of the most popular distributions in statistics. The reasons are manifold, including convenience for the academic community and the fact that it is taught in every single statistics course in the world. But what if we don’t want to be normal? There are situations … Read more
Another interesting case in demand forecasting is the high frequency data. For example, if you work with demand on daily level, you might notice that demand increases every Monday but also exhibits proper seasonal fluctuations (e.g. decline every Winter). What do you do in this case? One of the solutions (old but gold) is the … Read more
We continue our series of posts on the functions from the smooth package for Python/R. Today we will see how to enhance your exponential smoothing with explanatory variables. What? Yes, you heard me! Let’s dive in! We all know that in real life sales don’t just evolve over time on their own. Any univariate model, … Read more
Last time we saw how to do automated model selection using the ES function from the smooth package. Now I want to show how to produce combined forecasts from ETS. Why bother? There is a vast body of literature on forecast combinations (read this great review). The main idea is that you should not put … Read more
As some of you have heard, the smooth package is now on PyPI. So, I’ve decided to write a series of posts showcasing how some of its functions work. We start with the basics, ETS. ETS stands for the “Error-Trend-Seasonal” model or ExponenTial Smoothing. It is a statistical model that relies on time series decomposition … Read more
Here is another piece of news I have been hoping to deliver for quite some time now (since January 2026 actually). We have finally created the first release of the smooth package for Python and it is available on PyPI! Anyone interested? Read more! On this page: Why does “smooth” exist? A bit of history … Read more
Back in 2015, when I was working on my paper on Complex Exponential Smoothing, I conducted a simple simulation experiment to check how ARIMA and ETS select components/orders in time series. And I found something interesting… One of the important steps in forecasting with statistical models is identifying the existing structure. In the case of … Read more
Whenever I see results of an experiment that include Holt-Winters method, I shrug. You should not use it, and here is why. Holt-Winters was developed in 1960 by a student of Charles Holt, Peter Winters (Winters, 1960). He extended Holt’s exponential smoothing method (the method that introduced a trend component) to include a seasonal component. … Read more
Authors: Ivan Svetunkov, John E. Boylan Journal: IMA Journal of Management Mathematics Abstract: Exponential smoothing in state space form (ETS) is a popular forecasting technique, widely used in research and practice. While the additive error ETS models have been well studied, the multiplicative error ones have received much less attention in forecasting literature. Still, these … Read more