[其他] [MATLAB/R]Simulation of a GARCH(p,q) with Gaussian innovations [推广有奖]

匿名网友

楼主

匿名网友 发表于 2015-8-28 09:55:28 |AI写论文

是否 +2 论坛币

k人参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

Simulation of a GARCH(p,q) with Gaussian innovations

Matlab：

function [Returns, Vol, varlimit, Prices] = SimGARCHGaussian( mu, omega, garchcoeff, archcoeff, x0, h0, n, graph )
% Simulation of a GARCH(p,q) with Gaussian innovations:
%
% x_i = mu + sqrt(h_i) epsilon_i,
%
% h_i = omega + sum_{k=1}^q archcoef(k)(x_{i-k}-mu)^2
% + sum_{k=1}^p garchcoef(k) h_{i-k}, i=max(p,q)+1,...,n,
% with starting points x_0 and h_1.
%
% Caution: The condition alpha+beta <1 is required for stationarity. In
% that case, the asymptotic variance (varlimit) is :
% varlimit = omega/(1-alpha-beta).
%
% [Returns,Vol,varlimit,Prices] = SimGarchGed(-0.004,0.005, 0.6, 0.3,5.4,0,0.1,250,1)
%
% If graph=1, returns and volatilies will be plotted.
if nargin < 8
graph=0;
end
Prices = [];
eps = randn(n,1);
% memory allocation
v = zeros(n,1);
x = zeros(n,1);
h = zeros(n,1);
varlimit = Inf;
persistence = sum(archcoeff) + sum(garchcoeff);
if persistence < 1
varlimit = omega / ( 1 - persistence );
end
% generate time series
p = length(garchcoeff);
q = length(archcoeff)
r = max(p,q);
h(1:r) = h0;
x(1:r) = x0;
tp = (1:p)';
tq = (1:q)';
for t = (r+1):n
h( t ) = omega + garchcoeff'* h( t- tp ) + archcoeff'* ( x( t- tq ) - mu ).^2;
x( t ) = mu + sqrt( h( t ) ) * eps( t );
end
t = (1:1:n)';
Vol = sqrt( h );
Returns = x;
if graph
Prices = 100*[1; exp(cumsum(x))];
subplot(3,1,1); plot( [0;t], Prices );
title({' Prices S starting from 100';['Parameters: \mu = ' num2str(mu) ' , \omega = ' num2str(omega) ]});
subplot(3,1,2); plot( t, x );
title([' Returns x starting from x_0 = ' num2str(x(1))]);
subplot(3,1,3); plot( t, Vol );
title([' Conditional volatilities v^{1/2} starting from h_1 = ' num2str(h(1))] );
end

复制代码

R：

sim.garch.gaussian <- function(mu, omega, garchcoef, archcoef, x0, h0, n, graph = FALSE){
# Simulation of a GARCH(p,q) with Gaussian innovations:
#
# x_i = mu + sqrt(h_i) epsilon_i,
#
# h_i = omega + sum_{k=1}^q archcoef(k)(x_{i-k}-mu)^2
# + sum_{k=1}^p garchcoef(k) h_{i-k}, i=max(p,q)+1,...,n,
# with starting points x_0 and h_1.
#
# Caution: The condition alpha+beta <1 is required for stationarity. In
# that case, the asymptotic variance (varlimit) is :
# varlimit = omega/(1-alpha-beta).
#
# [Returns,Vol,varlimit,Prices] = SimGarchGed(-0.004,0.005, 0.6, 0.3,5.4,0,0.1,250,1)
#
# If graph=1, returns and volatilies will be plotted.
#Prices <- []
eps <- rnorm(n)
# memory allocation
v <- mat.or.vec(n,1)
x <- mat.or.vec(n,1)
h <- mat.or.vec(n,1)
varlimit <- Inf
persistence <- sum(archcoef) + sum(garchcoef)
if(persistence < 1){
varlimit <- omega / ( 1 - persistence )
}
# generate time series
p <- length(garchcoef)
q <- length(archcoef)
r <- max(p,q)
h[1:r] <- h0
x[1:r] <- x0
tp <- (1:p)
tq <- (1:q)
for(t in (r+1):n){
h[t] <- omega + garchcoef* h[ t- tp ] + archcoef* ( x[t- tq ] - mu )^2
x[t] <- mu + sqrt( h[ t] ) * eps[ t ]
}
t <- (0:n)
Vol <- sqrt( h )
Returns <- x
if(graph){
library('ggplot2')
Prices <- 100*c(1,exp(cumsum(x)))
values.graph <- ggplot(data.frame(x=t, y=Prices),
aes(x=x, y=y))
values.graph <- values.graph + geom_line() +
ggtitle(sprintf(' Prices S starting from 100 Parameters: mu <- %2.2f , omega <- %2.2f',mu,omega))
print(values.graph)
values.graph <- ggplot(data.frame(x=t[-1], y=x),
aes(x=x, y=y))
values.graph <- values.graph + geom_line() +
ggtitle(sprintf(' Returns x starting from x_0 <- %2.2f', x[1]))
print(values.graph)
values.graph <- ggplot(data.frame(x=t[-1], y=Vol),
aes(x=x, y=y))
values.graph <- values.graph + geom_line() +
ggtitle(sprintf(' Conditional volatilities v^{1/2} starting from h_1 <- %2.2f', h[1]))
print(values.graph)
}
return(list(Returns=Returns, Vol=Vol, varlimit=varlimit, Prices=Prices))
}
##
GEDRnd <- function(nu,n,m=1){
V <- runif(n,m)-0.5
eps <- sign(V)
a<- 1/nu
theta0 <- sqrt(gamma(a)/gamma(3*a))
z <- replicate(m,rgamma(n,a,1))
X <- theta0*eps*(z^a)
return(x)
}