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Re: alternative to cubic splines

Posted: October 31st, 2020, 11:55 am
by JohnLeM
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 ?

Re: alternative to cubic splines

Posted: October 31st, 2020, 1:00 pm
by Cuchulainn
Polynomial extrapolation; what's that?

Re: alternative to cubic splines

Posted: October 31st, 2020, 1:24 pm
by JohnLeM
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 ?

Re: alternative to cubic splines

Posted: October 31st, 2020, 6:34 pm
by Olga1597
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!

Re: alternative to cubic splines

Posted: October 31st, 2020, 7:31 pm
by Cuchulainn
you're welcome!

Re: alternative to cubic splines

Posted: November 1st, 2020, 7:44 pm
by JohnLeM

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 !

Re: alternative to cubic splines

Posted: November 6th, 2020, 2:16 pm
by ExSan
Why is cubic splines so important? 
what is it used for?