There’s no such thing as “deterministic forecast”

Sometimes I see people referring to a “deterministic” forecast, and I have some personal issues with this. Because if you apply a model to data then there is nothing deterministic about your forecasts! In many contexts, “deterministic” has a precise meaning: no randomness, no uncertainty. A deterministic solution to an optimisation problem (e.g. linear programming) … Read more

On randomness and uncertainty

A weather forecaster rolling a dice

Everything is random! Your data, your model, its parameter estimates, the forecasts it produces, and even the minimum of the loss function you used. There is no such thing as a “deterministic” forecast – everything is stochastic! Whenever you work with data, you are working with a sample from a population. In some cases, this … Read more

Model vs Method – why should we care?

Image of a model discussing a method

Image above depicts a fashion model making a presentation about a forecasting method. I like the forecast for the final period in that image… Over the last few years, I’ve seen phrases like “LightGBM model” or “Neural Network model” on LinkedIn many times, and the statistician in me shivers every time. So, I figured it’s … Read more

There is no such thing as an “assumption-free approach”

Spherical unicorn in a vacuum

One thing that bothers me when I read posts on social media or papers in peer-reviewed journals is the claim that a proposed approach is “assumption-free.” In forecasting, this is never true. Such an approach is like a spherical unicorn in a vacuum (see image above). Here’s why. Every model is a simplification of reality, … Read more

Structure vs. Noise: A Fundamental Concept in Forecasting

Structure vs Noise. Cloud in the shape of mushroom

One of the core ideas in statistics, which extends to many other fields including forecasting, is the concept of structure versus noise. You’ve probably heard of it, but it’s often overlooked by those without a strong quantitative background. So, let’s discuss. The core of the idea is that any data consists of two fundamental parts: … Read more

Complex-Valued Econometrics with Examples in R

Back in 2022, my father asked me to help him in amending and editing a monograph he wrote on the topic of “Complex-Valued Econometrics”. The original book focused on dynamic models, but after looking through the material and a thorough discussion, we decided to write something more fundamental. The monograph is based on the research … Read more

Multistep loss functions: Geometric Trace MSE

While there is a lot to say about multistep losses, I’ve decided to write the final post on one of them and leave the topic alone for a while. Here it goes. Last time, we discussed MSEh and TMSE, and I mentioned that both of them impose shrinkage and have some advantages and disadvantages. One … Read more

Multistep loss functions: Trace MSE

As we discussed last time, there are two possible strategies in forecasting: recursive and direct. The latter aligns with the estimation of a model using a so-called multistep loss function, such as Mean Squared Error for h-steps-ahead forecast (MSEh). But this is not the only loss function that can be efficiently used for model estimation. … Read more