What is MSE (Mean Squared Error) and RMSE (Root Mean Squared Error)?

MSE (Mean Squared Error):

• Simple Explanation: Imagine you’re trying to hit a target with darts. MSE is like averaging the square of the distances from where your darts hit to the bullseye. If every dart you throw hits the bullseye, then the MSE would be zero because there’s no difference between where you aimed and where you hit. But the farther away your darts land from the bullseye, the higher the MSE.
• In Trading: If you have a model predicting next week’s stock prices, MSE will measure how off these predictions are from the actual prices.
• Good or Bad?: Lower MSE is better because it means your predictions (or darts) are closer to the actual values (or bullseye). A high MSE indicates that your model might be making some pretty bad predictions.

RMSE (Root Mean Squared Error):

• Simple Explanation: Building on the dart analogy, while MSE squares the distances, RMSE is like finding the average distance itself. It’s the square root of MSE. So if MSE was like calculating the area of squares with sides of each error (distance from the bullseye), RMSE would be akin to the average side length of those squares.
• In Trading: If your model predicts a stock to be $100 and it’s actually $102, an RMSE of $2 means on average, your model’s predictions are about $2 off.
• Good or Bad?: Just like MSE, a lower RMSE is better. It gives a more interpretable measure of how far off your predictions are, on average. A high RMSE means your model is frequently off by that amount in its predictions.

Which One to Use? 

For a retail trader:

• If you just want to know how “off” your predictions are on average, RMSE is more intuitive.
• However, both MSE and RMSE can be useful. MSE tends to penalize large errors more (because they’re squared), so if occasional big mistakes are a concern, keeping an eye on MSE might be a good idea.

In all cases, context is crucial. An RMSE of $2 might be acceptable if you’re predicting stock prices in the $100s, but it would be terrible if you’re looking at stocks priced around $5.