It is some time ago, that I was fighting with that model and how
to estimate the 3 parameters (until recognizing that one may want
restrictions for them).
Essentially one uses the statistics of the underlying data to get
a reasonable starting guess. 
For an estimation then one can use the Optimization package.
The gradients involved are best coded as a floating point library,
which here is done through a DLL (it should work on all Windows OS),
code in C is included for that.
Meanwhile all can be done using 'Compiler:-compile' or the Watcom
compiler delivered with Maple.
I left that older sheet as it is - in Maple 9 (may be one should
brush it up for concurrent Maple versions, they are grumbling a bit
about the code) and hope it is of interest despite of that.

Maple sheet: www.mapleprimes.com/files/102_Garch.mws
DLL + code:  www.mapleprimes.com/files/102_Garch.dll.zip
as a pdf:    www.mapleprimes.com/files/102_Garch.mws.pdf

How do I plot a elliptical cross section with equation (((x-x[0])^2/1.75^2)+(y-y[0])^2/1.35^2))=1? The ellipse is centred at x[0], y[0].

Hi,

I would like to find the optimal values of the parameters  [ w,  a ,  b ]  in a GARCH(1,1)

I however have some problems specifying the Maximize function in the Optimization package

due to all the individual loops.....Any suggestions?

I have attached the workshet and the data

Download 8342_GARCH-Yen Data Hull.xls
View file details

Hi There,

Here's the problem: I'm trying to tiple-integrate rst e with the limits...
t=r-s...r+s
s=r...∞
r=0...∞

This is a straighforward integral with the use of the gamma function

∫₀ xe dr = Γ(n+1)/a

and my copy of Maple v11 crashes before it yields the answer.

I have been looking at integrals of various summations of cos(m*pi) for m = 1, 2, 3, .....a specific n with limits -1 and 1.  Currently, when maple provides an answer it contains numerous terms of the form sin (m*pi) for some m.  Clearly all these terms should = 0 which would simplify the answer greatly, but maple does not seem to recognise this.  Is there a way of forcing maple to recognise that all these terms should be 0.  I have tried the eval, evalf and value functions but none of these seemed to help.

I want a continous anti-derivate (cos(2*u*m)-alpha*u*sin(2*u*m))/(4*u^2+1)
w.r.t. u, for alpha and m Reals, 0 < u.

What I get with Maple in terms of Ci and Si jumps in m=0 (and for m=0 it
is not defined, due to Ci).

The best I got was

  Si(-conjugate(v))-Si(v); eval(%, v=m*(2*u+I));
  psi:= unapply(%, u,m);
  chi:= (u,m) -> piecewise(0 <= m, -Ci((2*u-I)*m)+Ci(m*(2*u+I)), 

I'm working with a PDE system, I want to bring it from the conservative(or divergent) to not-conservative form. So I have to do some derivatives. I'm working in vectorial form.

I have this expression:

(a*x^2+b*x*sin(y)+c*sin(y))^2+(a*sin(x)^2+b*x)^3

I have to rewrite this as a multipolynomial in the variables x and sin(y).

I'm trying this:

expand((a*x^2+b*x*sin(y)+c*sin(y))^2+(a*sin(x)^2+b*x)^3, x,sin(y));

but i get the same result as expand without the 2 variables at the end.

am i doing it right?

Thanks in advance!

When I integrate the partial derivative of v(x,y) with respect to y from y = 0 to y = Y using

int(diff(v(x,y),y), y=0..Y)

Maple simple echos the integral in typeset format. I expected to get

v(x,Y) - v(x,0)

What am I missing here? This integral comes from integrating the 2D continuity equation in boundary layer. Any help would be greatly appreciated.

Thanks,

Neill Smith

I need help solving the following integral with Maple

int(erfc((R+3*t)/(6*t^1/2)),t=0..1)