Index in position 1 exceeds array bounds (must not exceed 1). FMINCON

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A Garch model with a Vix as a esogenous variable
Yt = dev.std * Epsilon
Epsilon = Normal or student (0,1)
dev.std^2_t = omega + alpha*r_t-1^2 + Beta*dev.std^2_t-1 + lambda*VIX^2_t-1
i coefficienti omega alpha beta e delta si trovano con la maximum likelihood.
il resto è dato.
global y
filename = 'Dati_daily.xlsx';
xlRange = 'A1:L7420';
[num] = xlsread(filename,xlRange);
Dati
CAC40 =num(:,1);
FTSE100 =num(:,2);
DAX =num(:,3);
FTSEMIB =num(:,4);
SP500 =num(:,5);
NASDAQ =num(:,6);
FTSECHINA =num(:,7);
HANGSENG =num(:,8);
TOPIX =num(:,9);
ASX200 =num(:,10);
VIX =num(:,11);
%
returns_CAC40 = diff(log(CAC40));
returns_FTSE100 = diff(log(FTSE100));
returns_DAX = diff(log(DAX));
returns_FTSEMIB = diff(log(FTSEMIB));
returns_SP500 = diff(log(SP500));
returns_NASDAQ = diff(log(NASDAQ));
returns_FTSECHINA = diff(log(FTSECHINA));
returns_HANGSENG = diff(log(HANGSENG));
returns_TOPIX = diff(log(TOPIX));
returns_ASX200 = diff(log(ASX200));
returns_VIX =diff(log(VIX));
y1=returns_CAC40;
y2=returns_FTSE100;
y3=returns_DAX;
y4=returns_FTSEMIB;
y5=returns_SP500;
y6=returns_NASDAQ;
y7=returns_FTSECHINA;
y8=returns_HANGSENG;
y9=returns_TOPIX;
y10=returns_ASX200;
y11=returns_VIX;
% selezione dati singoli
y = y1;
y(isnan(y))=0;
y11(isnan(y11))=0;
% Creazione modello
[T] = size(y,1);
sigma2 = zeros(T,1);
log_likelihood_i = zeros(T,1);
%% function [log_lik] =log_lk_GARCHVIX(theta)
omega = theta(1,1);
alpha = theta(2,1);
beta = theta(3,1);
delta = theta(4,1);
sigma2(1,1) = omega;
log_likelihood_i(1,1) = -0.5 * log(2*pi) - 0.5* log(sigma2(1,1)) - 0.5/sigma2(1,1)*(y(1,1))^2;
for t = 2 : 1 : T
sigma2(t,1) = omega + alpha * y(t-1,1)^2 + beta * sigma2(t-1,1)^2 + delta * y11(t-1,1)^2;
log_likelihood_i(t,1) = -0.5 * log(2*pi) - 0.5* log(sigma2(t,1)) - 0.5/sigma2(t,1)*(y(t,1))^2;
end
log_lik = -sum(log_likelihood_i);
end
%%
theta0 = [2,0.2,0.1,0.4];
lb = [0.000000001;
0
0
0];
ub = [1000000;
0.999999
0.999999
0.999999];
[x,fval,exitflag,output,lambda,grad,hessian] = fmincon('log_lk_GARCHVIX',theta0,[],[],[],[],lb,ub)
THE ERRORS ARE:
Index in position 1 exceeds array bounds (must not exceed 1).
alpha = theta(2,1);
Error in fmincon (line 562)
initVals.f = feval(funfcn{3},X,varargin{:});
Caused by:
Failure in initial objective function evaluation. FMINCON cannot continue.

Accepted Answer

Matt J
Matt J on 2 Aug 2020
Make theta0 a column vector:
>> theta0 = [2,0.2,0.1,0.4].'
theta0 =
2.0000
0.2000
0.1000
0.4000

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