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JohnLeM
Posts: 469
Joined: September 16th, 2008, 7:15 pm

Re: alternative to cubic splines

October 31st, 2020, 11:55 am

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
This is not the post topic, but for such kind of curves, would n t it worth trying to mix periodical / polynomial extrapolation ?
 
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Cuchulainn
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Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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Re: alternative to cubic splines

October 31st, 2020, 1:00 pm

Polynomial extrapolation; what's that?
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
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JohnLeM
Posts: 469
Joined: September 16th, 2008, 7:15 pm

Re: alternative to cubic splines

October 31st, 2020, 1:24 pm

Polynomial extrapolation; what's that?
I meant : mixing any classical interpolation, as one of those quoted above or other ones (as predictor / corrector methods - I implemented them with fortran as I served French army 30 years ago, they were quite good at predicting planes trajectories), together with periodic interpolation (the covid curve seems to incorporate weekly effects in any countries). I could try it, producing error estimates on extrapolation points. Might it be useful ?
 
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Olga1597
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Joined: February 19th, 2016, 12:40 pm

Re: alternative to cubic splines

October 31st, 2020, 6:34 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
Thanks!
 
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Cuchulainn
Posts: 63379
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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Re: alternative to cubic splines

October 31st, 2020, 7:31 pm

you're welcome!
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
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JohnLeM
Posts: 469
Joined: September 16th, 2008, 7:15 pm

Re: alternative to cubic splines

November 1st, 2020, 7:44 pm


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
Thanks!
You re welcome !
 
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ExSan
Posts: 4597
Joined: April 12th, 2003, 10:40 am

Re: alternative to cubic splines

November 6th, 2020, 2:16 pm

Why is cubic splines so important? 
what is it used for? 
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