The Menace of ML: Simple Moving Average

Simple Moving Average of order 8

And here is another forecasting method that is hard to beat in practice. In a recent competition, it gave data scientists huge headaches and even outperformed some powerful ML methods. What’s the name of this beast?! Simple Moving Average! The idea behind the Simple Moving Average (SMA) is to take the average of the last … Read more

Five assumptions behind “forecastability”

Example of two time series with exactly the same coefficient of variation

Here is a confession. I don’t like the idea of “forecastability”. I think it does not bring value and can be harmful in some cases. Let me explain. One of the definitions I see on the internet: “A measure of the degree to which something may be forecast with accuracy”. This definition is so disturbing … Read more

On differencing of ARIMA in state space

The model fit of MSARIMA

A reader left a comment under the MSARIMA post on LinkedIn saying that in order to compare ARIMAs via information criteria, we need to make sure that the candidate models have the same order of differencing. They are right — for the conventional ARIMA. BUT! In the state space formulation, the problem disappears. Here is … Read more

smooth in python: Multiple Seasonal ARIMA

MSARIMA model fit and point forecast

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

Another important Naïve method

Seasonal Naive depiction

There is another forecasting method that is extremely popular, hard to beat, and has no parameters to estimate. It also has “Naïve” in its name. Do you know what I’m talking about? It is called “Seasonal Naïve”. While the simple Naïve copies the last observed actual into the future as a forecast, the seasonal one … Read more

smooth in python: Multistep losses

Example of fits of ETS with several multistep losses

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

Why Naïve is popular and important

How Naive works

There is one forecasting method that appears more often than any other in competitions and evaluations. An experienced forecaster will always use it as a benchmark. This method is called “Naïve”, and here is why it is popular and important. Naïve is a very simple forecasting method: the forecast equals to the last observed value. … Read more

Demand Forecasting Principles course, October 2026

A photo of the participants of Demand Forecasting Principles open course

Our demand forecasting course is back! This time under the OpenForecast umbrella. Since 2024, Kandrika Pritularga and I have run a demand forecasting principles course at the Centre for Marketing Analytics and Forecasting. We ran it three times, and it has received good reviews from the participants. They liked that the material was motivated by … Read more