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

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).

Error in log_lk_GARCHVIX (line 4)

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.

Answer 1

[Matt J]

Make theta0 a column vector:

>> theta0 = [2,0.2,0.1,0.4].'

theta0 =

    2.0000
    0.2000
    0.1000
    0.4000