Extrapolation using a spline is insane. Period. You get what you deserve, i.e., a virtually random result. In fact, any extrapolation tends to be dangerous, unless you use a viable model that makes physical sense. So polynomials are also useless.
You can use my own gridfit tool (found on the File Exchange) to extrapolate, as at least it tends to extrapolate as smoothly and linearly as possible. Even so, extrapolate too far and you will get what Mark Twain said...
"In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. This is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upward of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact."
Mark Twain, Life on the Mississippi (1883)
So, what happens when you try to extrapolate using splines which are essentially polynomials, carved into segments? Think of what a cubic polynomial does as it goes to infinity. It swoops up (or down) with great alacrity. (Hmm, I think I'm starting to sound like Mark Twain himself.) And the shape of that swoop will depend on subtle variations of the data along the edges. It will also depend on subtle variations in the code, on exactly how the spline was implemented. So trusting a spline extrapolant is, as I said, simply insane.
In fact, trusting any extrapolant is a dangerous thing to do. You can put more faith in models used for extrapolation that are based on intelligently chosen physical principles. But even then, extrapolation too far is a dangerous thing to do. Sorry, but it just is. Just remember what Mark said.
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