Unbalanced or Unexpected Paranthesis or Bracket Error

İs there any problem with that cod; [theta,se,t]=qreg(tb_26wk,(ones(2585(tb_26wk));_13wk); q(0.1));

Because ı have unbalanced or... error in that command.

Thanks.

[Nathan Jessurun]

What is the goal of that code? It has a few problems:

1. Arguments should be separated by commas, not semicolons (;).
2. What are you trying to do with the expression 2585(tb_26wk)? Variables and functions can't start with a letter, so this expression makes no sense.

If you can answer these questions or provide other clarifications you may get some more helpful answers.

[Anil Cekic]

First, thanks your feedback.

Second, that cod for the Quantile Cointegration which is the one of analysis in time series. So, that expression we could imagine as a mathematical function which is F(x(a)). Actually, i am writing all the cod under the line;

% Empirical Study: Term structure of interest rates.
% Data: US daily rates (missing obs deleted).
% CUSUM test of quantile cointegration.

clear;

% Load the matlab data files

load d_tb.mat  % T_data=2585
load d_tb_date.mat  % 1/2/2002 to 4/30/2012

load d_fcp.mat  % T_data=3748
load d_fcp_date.mat  % 1997-01-02 to 2012-04-30

load d_tcmnom.mat  % T_data=7584*
load d_tcmnom_date.mat  % 1982-01-04* to 2012-04-30

% Compute the size of data for the number of observations, if needed
% [T_data N_data]=size(tb); 

% Rename the variables from the data set

% Treasury bill rates (yields: 4, 13, 26 weeks)
tb_4wk=tb(:,1);  % bank discount
tb_13wk=tb(:,3);
tb_26wk=tb(:,5);
tb_4wk_ce=tb(:,2);  % coupon equivalent
tb_13wk_ce=tb(:,4);
tb_26wk_ce=tb(:,6);

% Financial commercial paper rates (yields: 30, 60, 90 days)
fcp_30d=fcp(:,1);
fcp_60d=fcp(:,2);
fcp_90d=fcp(:,3);

% Treasury constant maturity rates (yields: 3, 6, 12 months)
% One month rate is not used due to large number of missing observations. 
% tcmnom=tcmnom(4896:7584,:);  % 2001-07-31 to 2012-04-30, T=2689 for one month rate
% tcmnom_1=tcmnom(:,1);  % obs 4896:7584, 2001-07-31 to 2012-04-30 for one month rate
tcmnom_3=tcmnom(:,2);  % obs 1:7584, 1982-01-04 to 2012-04-30
tcmnom_6=tcmnom(:,3);  % obs 1:7584, 1982-01-04 to 2012-04-30
tcmnom_12=tcmnom(:,4);  % obs 1:7584, 1982-01-04 to 2012-04-30

% For regression results using different pairs of interest rates, 
% replace y and x variables. 
% e.g. To compute for the results in the last two rows of Table 3,
% consier y=tcmnom_12 and x=tcmnom_6;

% y=tb_26wk;
% x=tb_13wk;
% y=tb_26wk_ce;
% x=tb_13wk_ce;

% y=fcp_90d;
% x=fcp_60d;

y=tcmnom_12;
x=tcmnom_6;

% Compute the quantile regression coefficients and residuals

q =[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9];  % nine quantiles
Lq=length(q);

[T N]=size(x);
xlag=[zeros(1,N);x(1:T-1,:)];

v=x-xlag;
vlag=[zeros(1,N); v(1:T-1,:)];

for n=1:N
    [rho_2,se_v,t_v]=ols(v(:,n), [ones(T,1) vlag(:,n)]);  % for calculation of the kernel estimator later
    rho_v(n,1)=rho_2(2,1);  % rho_v is N-by-1
    res_v=v(:,n)-[ones(T,1) vlag(:,n)]*rho_2;  % ols residuals
    ss_v(n,1)=res_v'*res_v/(T-1);  % s^2=SSR/(n-k), ss_v is N-by-1
end

beta0=zeros(N,1);

D_T_tail=[1 zeros(1,N); zeros(N,1) eye(N)*sqrt(T)];

[theta_ols,se_ols,t_ols]=ols(y,[ones(size(y)) x]);
u_hat=y-[ones(size(y)) x]*theta_ols;

for k=1:Lq

    [theta,se,t]=qreg(tb_26wk,(ones(2585(tb_26wk));tb_13wk); q(0.1));
    alpha = theta(1,1);
    beta = theta(2:(N+1),1);
    se_beta=se(2:(N+1),1);
    u_tau=y-[ones(size(y)) x]*theta;
    psi=q(k)-(u_tau<0);
    
    % Compute the density funtion
    F_inv_tau=quantile(u_hat,q(k));
    M_f=1.364*((2*sqrt(pi))^(-1/5))*sqrt(var(u_hat))*(T^(-1/5));  % bandwidth (Silverman's rule of thumb)
    f_hat=sum(normpdf((F_inv_tau-u_hat)/M_f))/(T*M_f);  % using Gaussian kernel to calculate the density function

    % Choose kernel function and bandwidth to compute the fully-modified estimator
    psilag=[0; psi(1:T-1)];
    [rho_1,se_psi,t_psi]=ols(psi, [ones(size(psilag)) psilag]);  % for kernel estimator
    rho_psi=rho_1(2,1);
    res_psi=psi-[ones(size(psilag)) psilag]*rho_1;	% residuals
    ss_psi=res_psi'*res_psi/(T-1); 	% scalar s^2=SSR/(n-k)
    
   %% Using the Bartlett kernel function:
    a1=4*(rho_psi^2*ss_psi/(((1-rho_psi)^6)*((1+rho_psi)^2))+sum(((rho_v.^2).*ss_v)./(((1-rho_v).^6).*((1+rho_v).^2))))/(ss_psi/((1-rho_psi)^4)+sum(ss_v./((1-rho_v).^4)));  % for Bartlett kernel
    M=2*T^(1/3);  % bandwidth
    M=ceil(M);
    h_set=0:M;
    K=bartlett(h_set/M);  % Bartlett kernel function, row vector

    psi_th_1=zeros(T,M);
    v_th_1=zeros(T,M,N);
    v_th=zeros(T,M+1,N);
    for h=1:M
        psi_th_1(:,h)=[psi((h+1):T);zeros(h,1)];  % column vector
        for n=1:N
            v_th_1(:,h,n)=[v((h+1):T,n);zeros(h,1)];
        end
    end

    K_1=K(1,2:M+1);

    psi_th=[psi psi_th_1];
    Delta_psipsi=K*(psi'*psi_th)'/T;  % for (omega_psi.v)^2
    Lambda_psipsi_prim=K_1*(psi'*psi_th_1)'/T;  % for (omega_psi.v)^2

    Delta_vpsi=(K*(v'*psi_th)')'/T;  % N-by-1

    for n=1:N
        v_th(:,:,n)=[v(:,n) v_th_1(:,:,n)]; 
        Delta_vv(:,n)=(K*(v'*v_th(:,:,n))')'/T;  % N-by-N  
        Lambda_vpsi_prim(n,1)=K_1*(psi'*v_th_1(:,:,n))'/T;  % Lambda_vpsi_prim is N-by-1
        Lambda_vv_prim(n,:)=K_1*(v'*v_th_1(:,:,n))'/T;  % Lambda_vv_prim is N-by-N
    end

    Omega_vpsi=Delta_vpsi+Lambda_vpsi_prim;
    Omega_vv=Delta_vv+Lambda_vv_prim;

    omega2_psi=Delta_psipsi+Lambda_psipsi_prim;  % for (omega_psi.v)^2
    Omega_psiv=Omega_vpsi';  % for (omega_psi.v)^2, which is 1-by-N

    Delta_vpsi_plus=Delta_vpsi-Delta_vv*inv(Omega_vv)*Omega_vpsi;

    omega2_psiv=omega2_psi-Omega_psiv*inv(Omega_vv)*Omega_vpsi;  % for (omega_psi.v)^2

    beta_fm=beta-inv((x-ones(size(y))*mean(x))'*(x-ones(size(y))*mean(x))*f_hat)*((x-ones(size(y))*mean(x))'*v*inv(Omega_vv)*Omega_vpsi+T*Delta_vpsi_plus);  % beta_fm is N-by-1

    beta_set_fm(:,k)=beta_fm;

    se_beta_fm=diag(inv(sqrt((x-ones(size(y))*mean(x))'*(x-ones(size(y))*mean(x)))*f_hat)*sqrt(omega2_psiv));
    t_beta_fm=(beta_fm-beta0)./se_beta_fm;
    t_beta_set_fm(:,k)=t_beta_fm;

    theta_fm=[alpha;beta_fm];

    % CUSUM cointegration test:
 
    y_plus=y-(Omega_psiv*inv(Omega_vv)*v')';  % fm residual
    u_tau_plus=y_plus-[ones(size(y_plus)) x]*theta_fm;  % fm residual
    psi_plus=q(k)-(u_tau_plus<0);  % psi of fm residual
    
    cs=max(abs(cumsum(psi_plus))/sqrt(T*omega2_psiv));  % CS test statistic of the CUSUM test
    cs_set(1,k)=cs;

end

% The critical values are from Hao+Inder (1996) Table 1 (# of regressors=1, excl. constant):
% cv[10% 5% 1%]= [1.0477 1.1684 1.4255]

rej_cointeg_hi1_05=abs(cs_set)>1.1684;  % 1-by-9, 5% level
rej_cointeg_hi1_01=abs(cs_set)>1.4255;  % 1-by-9, 1% level

% Display the result: fully modified slope coefficient estimator, test statistic, and inference 
% where 1 denotes significance at the level considered and 0 denotes insignificance. 

table=[beta_set_fm; cs_set; rej_cointeg_hi1_05; rej_cointeg_hi1_01]  

Answer 1

[Geoff Hayes]

Anil - look carefully at this line of code

 [theta,se,t]=qreg(tb_26wk,(ones(2585(tb_26wk));tb_13wk); q(0.1));

As Nathan has already pointed out, there are problems with the above line of code. Why are some parameters (?) separated by semi-colons? What is the signature for the qreg function? Break this down - presumably

• tb_26wk is the first input parameter to this function - is this correct?
• ones(2585(tb_26wk)) are you trying to create an array of ones that is 2585xtb_26wk? Is tb_26wk an integer or something else?
• (ones(2585(tb_26wk));tb_13wk) or are you trying to concatenate some numbers into an array. If that is the case, then use [] instead of ()
• q(0.1) since q is an array, what are you attempting with q(0.1)? This will fail since 0.1 is not an integer (or logical) index into the array...what do you really want to do here?

If you post the function signature for qreg then we can help you further...

[Anil Cekic]

Thanks for the answer. I solved the problem. I appreciate your helping me.