Handling Regression Splines Beyond the Training Range

Summary

The document raises the problem of using regression splines when new predictor values fall outside the range covered by calibration data. Its example is electricity load forecasting: a model trained on winter temperatures may be used as spring temperatures emerge, while recalibration is only possible every other month. It notes that the same extrapolation issue can arise in quantitative finance.

One candidate approach mentioned is a natural spline, which extrapolates linearly beyond the fitted range. The document asks whether this or other techniques can make spline estimates robust when extrapolation is unavoidable, and seeks practical experience or references. It provides no comparative evidence, chosen method, or performance results. Its central limitation is that predictions outside the training range depend on assumptions the observed data cannot validate; the question frames linear extrapolation as a possibility rather than an established solution.

Key ideas

• Spline models may be used on predictor values outside the range observed during calibration.
• Infrequent model recalibration can make extrapolation necessary as conditions change.
• Natural splines are cited as an option that extrapolates linearly beyond the fitted range.
• The document offers no evidence comparing extrapolation methods or establishing their reliability.

Tags

# What to do with linear regression or regression splines outside of the training range?


# What to do with linear regression or regression splines outside of the training range?












This is a cross-post from here

In my question on a load forecast model using temperature data as covariates I was advised to use regression splines. This really seems to be a/the solution.

Now I face the following problem: if I calibrate my model on winter data (for technical reasons calibration can not be done on a daily basis, rather every second month) and slowly spring arises I will have temperature data outside of the calibration set.

Although load forecasting is not a financial topic per se the same issues arise in quantitative finance at certain points.

Are there good techniques to make the regression spline fit robust for values outside of the calibration range? The members of cross-validated already proposed natural splines where extrapolation is done linear. What do you do if you have to do something? And please don't hate me for this question - I am aware that anything outside of the training set is bad but what is a good solution if I have to do something ... ? Any experiences or references? Thanks!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.