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 […]

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. […]

Recursive vs Direct Forecasting Strategy

Have you heard about the recursive vs direct forecasts? There’s literature about them in the areas of both ML and statistics. What’s so special about them? Here is a short post. The term “recursive” forecasting refers to the approach, when we produce one-step-ahead forecast first, then use it to produce two-steps-ahead, three-steps-ahead, and so on. […]

Seasonal or not?

Not every pattern that appears seasonal is genuinely seasonal. This means you don’t always require a seasonal model when you see repetitive patterns with fixed periodicity. How come? First things first, in forecasting, the term “seasonality” refers to any natural pattern repeating with some periodicity. For example, if you work in a hospital with A&E […]

Don’t forget about bias!

So far, we’ve discussed forecasts evaluation, focusing on the precision of point forecasts. However, there are many other dimensions in the evaluation that can provide useful information about your model’s performance. One of them is bias, which we’ll explore today. Introduction But before that, why should we bother with bias? Research suggests that bias is […]

What is “forecasting”?

What is “forecasting”? Many people will have a ready answer to this question, but I would argue that not many have spent enough time thinking about it. Should we spend a couple of minutes of our time today to do that? Straight to the point: my answer to the question comes to the following definition: […]

Avoid using MAPE!

Frankly speaking, I didn’t see the point in discussing MAPE when I wrote recent posts on error measures. However, I’ve received several comments and messages from data scientists and demand planners asking for clarification. So, here it is. TL;DR: Avoid using MAPE! MAPE, or Mean Absolute Percentage Error, is a still-very-popular-in-practice error measure, which is […]

Detecting patterns in white noise

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 […]