One of the pitfalls of fitting high-order polynomial trends is that such models can yield hghly inaccurate forecasts, particularly at long horizons.

Sure, I can explain this concept.

Fitting high-order polynomial trends is a method used in statistical modeling to capture more complex relationships in the data. However, this approach has some potential pitfalls.

1. Overfitting: High-order polynomial models can fit the training data very well, even capturing the noise in the data. This is known as overfitting. Overfit models perform well on the training data but poorly on new, unseen data.

2. Extrapolation: High-order polynomial models can yield highly inaccurate forecasts, particularly at long horizons. This is because these models are very sensitive to the range of the data. If you try to make a prediction outside of this range (extrapolation), the model can produce unrealistic results.

3. Complexity: High-order polynomial models are more complex than lower-order models. This can make them more difficult to interpret and understand.

4. Instability: High-order polynomial models can be unstable. Small changes in the data can lead to large changes in the model, making the model unreliable.

In summary, while high-order polynomial models can capture complex patterns in the data, they can also overfit the data, produce inaccurate forecasts, be difficult to interpret, and be unstable. Therefore, it's important to use these models with caution.