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Olga1597
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alternative to cubic splines

October 24th, 2020, 10:02 pm

Could someone suggest interpolation algorithm alternative to cubic splines? Interpolated function has to be continuous, with continuous first differential and perfect fit with input data.
 
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bearish
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Re: alternative to cubic splines

October 24th, 2020, 10:28 pm

Your application may or may not be related to yield curve fitting, but either way this classic from the Great Dane is worth a look: https://papers.ssrn.com/sol3/papers.cfm ... _id=871088
 
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Olga1597
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Re: alternative to cubic splines

October 25th, 2020, 1:22 pm

Your application may or may not be related to yield curve fitting, but either way this classic from the Great Dane is worth a look: https://papers.ssrn.com/sol3/papers.cfm ... _id=871088
Thanks for the paper! It is very interesting.
 
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Cuchulainn
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Re: alternative to cubic splines

October 25th, 2020, 9:49 pm

Could someone suggest interpolation algorithm alternative to cubic splines? Interpolated function has to be continuous, with continuous first differential and perfect fit with input data.
What problem are you trying to solve? Do you want monotonicity and convexity?
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Mars
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Re: alternative to cubic splines

October 26th, 2020, 10:28 am

Could someone suggest interpolation algorithm alternative to cubic splines? Interpolated function has to be continuous, with continuous first differential and perfect fit with input data.
What about Stineman interpolation ( https://pages.uoregon.edu/dgavin/software/stineman.pdf )
 
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Cuchulainn
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Re: alternative to cubic splines

October 26th, 2020, 3:39 pm

Akima
Hyman-Dougherty
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Olga1597
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Re: alternative to cubic splines

October 27th, 2020, 12:27 pm

Akima
Hyman-Dougherty
Thanks! 
 "Akima" has a lot of meanings in google, could you provide more details please?
I found this paper https://www.researchgate.net/publicatio ... erpolation (I haven't looked it yet). 

"Do you want monotonicity and convexity?"

Yes I need monotonicity, convexity as main constraints and some others. Now I solve it as cubic spline + linear constraints and it works for me. But it seems very unnatural make cubic spline behave convex.
 
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Olga1597
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Re: alternative to cubic splines

October 27th, 2020, 12:29 pm

What about Stineman interpolation ( https://pages.uoregon.edu/dgavin/software/stineman.pdf )
Thanks! I'll see it.
 
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Re: alternative to cubic splines

October 27th, 2020, 12:49 pm

Akima
Hyman-Dougherty
Thanks! 
 "Akima" has a lot of meanings in google, could you provide more details please?
I found this paper https://www.researchgate.net/publicatio ... erpolation (I haven't looked it yet). 

"Do you want monotonicity and convexity?"

Yes I need monotonicity, convexity as main constraints and some others. Now I solve it as cubic spline + linear constraints and it works for me. But it seems very unnatural make cubic spline behave convex.
In the book "C# In Financial Markets (Wiley)" I wrote with Andrea Germani we discuss about 7 methods for fixed-income. The most robust for us were Dougherty/Hyman, Akima and Hagan/West (I would avoid cubic splines in this context).

And in Quantlb

https://rkapl123.github.io/QLAnnotatedS ... ation.html

Akima 1970, 1991

https://en.wikipedia.org/wiki/Akima_spline
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Cuchulainn
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Re: alternative to cubic splines

October 28th, 2020, 12:25 am

But it seems very unnatural make cubic spline behave convex.
And kind of impossible, especially for non-equidistant grid point ==> overshoot..

However, it is popular with US COVID gov advisors because of pleasing curves.

https://thecorrespondent.com/465/proble ... 0-ba285389

He described the model as one meant to level the swings of reported cases which vary each day, and he used “just a canned function in Excel, a cubic polynomial,” according to the newspaper.

Image


To better visualize observed data, we also continually update a curve-fitting exercise to summarize COVID-19's observed trajectory. Particularly with irregular data, curve fitting can improve data visualization. As shown, IHME's mortality curves have matched the data fairly well. pic.twitter.com/NtJcOdA98R
— CEA (@WhiteHouseCEA) May 5, 2020
The curve in the cubic model reaches its peak in mid-April and swoops back down through the end of May. 
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JohnLeM
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Re: alternative to cubic splines

October 30th, 2020, 2:12 pm

Could someone suggest interpolation algorithm alternative to cubic splines? Interpolated function has to be continuous, with continuous first differential and perfect fit with input data.
Hello. I can provide that quite easily with support vector machines, whatever the dimension is. Could you describe more precisely the fitting curve ?
 
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Cuchulainn
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Re: alternative to cubic splines

October 30th, 2020, 2:19 pm

Could someone suggest interpolation algorithm alternative to cubic splines? Interpolated function has to be continuous, with continuous first differential and perfect fit with input data.
Hello. I can provide that quite easily with support vector machines, whatever the dimension is. Could you describe more precisely the fitting curve ?
NDA. BTW can you reproduce the wacky output?
Trump Administration. Send your queries to Pennsylvania Avenue.
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JohnLeM
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Re: alternative to cubic splines

October 31st, 2020, 9:42 am

Could someone suggest interpolation algorithm alternative to cubic splines? Interpolated function has to be continuous, with continuous first differential and perfect fit with input data.
Hello. I can provide that quite easily with support vector machines, whatever the dimension is. Could you describe more precisely the fitting curve ?
NDA. BTW can you reproduce the wacky output?
Trump Administration. Send your queries to Pennsylvania Avenue.
? I dont understand your answer cuchullain. Could you precise please ?
 
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Cuchulainn
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Re: alternative to cubic splines

October 31st, 2020, 9:54 am

Please look at those links I posted for the answer.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

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JohnLeM
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Re: alternative to cubic splines

October 31st, 2020, 10:15 am

I did. You talk about yield curve interpolation, covid interpolation, stineman interpolation. We can add monotone convex interpolation with perfect fit as asked by the owner of the post. But without the problem description, aren t we blind ?