Have you ever tried to identify ARIMA for your data? The old school Box-Jenkins methodology implies analysing ACF/PACF plots and selecting the orders iteratively. This approach has a fundamental flaw I discussed in one of my earlier posts. Brute force does not help either: even p ≤ 3, d ≤ 2, q ≤ 3 gives … Read more
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
ARIMA has been a workhorse for decades. But the standard implementations quietly hard-code assumptions: one seasonal cycle, Gaussian errors, regressors handled separately etc. This is fine for textbook well-behaved data. But what do you do when you face real data? The conventional implementations (statsmodels or pmdarima in Python, stats in R) do their job well: … Read more
Why train a forecasting model on one-step-ahead errors when you care about 10-step-ahead accuracy? This is the core motivation behind multistep losses in dynamic models. This has connection with the so-called “direct forecasting strategy”. And here what it is and how to work with it in Python. Conventional maximum likelihood estimation minimises one-step-ahead errors. It … Read more
This time, at ISF2026, I presented the paper that I have worked on together with Juan Ramon Trapero and Diego Pedregal. The idea of the paper is to introduce a taxonomy of the models in the Multiple Sources of Error (MSOE) framework. In the Single Source of Errors one, there is ETS, in the MSOE, … Read more
You have probably seen my post about the STI classification of Hans Levenbach (this one). Well, I’ve decided to implement it, and it has landed in the greybox package for R/Python. What’s greybox? It is a package for statistical modelling focusing on forecasting and time series analysis. I created it back in 2018 to split … 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