Serving the Quantitative Finance Community

 
User avatar
Olga1597
Topic Author
Posts: 8
Joined: February 19th, 2016, 12:40 pm

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.
 
User avatar
bearish
Posts: 5188
Joined: February 3rd, 2011, 2:19 pm

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
 
User avatar
Olga1597
Topic Author
Posts: 8
Joined: February 19th, 2016, 12:40 pm

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.
 
User avatar
Cuchulainn
Posts: 20254
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

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?
 
User avatar
Mars
Posts: 14
Joined: November 13th, 2002, 5:10 pm

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 )
 
User avatar
Cuchulainn
Posts: 20254
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

Re: alternative to cubic splines

October 26th, 2020, 3:39 pm

Akima
Hyman-Dougherty
 
User avatar
Olga1597
Topic Author
Posts: 8
Joined: February 19th, 2016, 12:40 pm

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.
 
User avatar
Olga1597
Topic Author
Posts: 8
Joined: February 19th, 2016, 12:40 pm

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.
 
User avatar
Cuchulainn
Posts: 20254
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

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
 
User avatar
Cuchulainn
Posts: 20254
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

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. 
 
User avatar
JohnLeM
Posts: 379
Joined: September 16th, 2008, 7:15 pm

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 ?
 
User avatar
Cuchulainn
Posts: 20254
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

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.
 
User avatar
JohnLeM
Posts: 379
Joined: September 16th, 2008, 7:15 pm

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 ?
 
User avatar
Cuchulainn
Posts: 20254
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

Re: alternative to cubic splines

October 31st, 2020, 9:54 am

Please look at those links I posted for the answer.
 
User avatar
JohnLeM
Posts: 379
Joined: September 16th, 2008, 7:15 pm

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 ?