Fractional-Frequency-Fourier-Part2-OxGauss/4. OxGuass code for Fourier ARDL analysis(1).src at OxGauss-codes · nonlinear-lab/Fractional-Frequency-Fourier-Part2-OxGauss · GitHub

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@===============================================================================@
@ OxGauss code for Fourier ARDL analysis			                	@
@ Input: 			y: Tx1 vector of time series (LGDP)		@
@ 	: 			x: Tx1 vector of time series (LPOP)		@
@ Output: 			bounds test (BT) statistics			@
@ Subprgram: 			none                                            @
@ Max Lag length: 		4                                        	@
@===============================================================================@

closeall;

output file=bt_out(1).txt reset;

@=====Data input===============================================@
load data[26,5]=data1.txt;
rr=rows(data);
cc=cols(data);

y0=data[1:rr,1];
x1=data[1:rr,2];
x2=data[1:rr,3];
x3=data[1:rr,4];
x4=data[1:rr,5];

@=====ARDL model===============================================@
akaike0=-73737373;
k=1;
"++ARDL method (long-run) ++";
kk=0.1;
Do while kk<=4;

n=rows(y0);
const=ones(n,1);
tt=seqa(1,1,n);
sinf=sin((2*3.141592*tt*kk)/n);
cosf=cos((2*3.141592*tt*kk)/n);
x=y0[k:n-1]~x1[k+1:n]~x1[k:n-1]~x2[k+1:n]~x2[k:n-1]~x3[k+1:n]~x3[k:n-1]~x4[k+1:n]~x4[k:n-1]~const[k+1:n]~sinf[k:n-1]~cosf[k:n-1];
y=y0[k+1:n];
invx=inv(x'x);
beta=invx*x'y;
e=y-x*beta;
ssr=e'e;
var=(e'e/(rows(y)-cols(x)))*invx;
sd=sqrt(diag(var));
t=beta./sd;
LK=-(rows(y)/2)*(1+ln(3.141593*2)+ln(e'e/rows(y)));
akaike=-2*(LK/rows(y))+2*(cols(x)/rows(y));
if akaike>akaike0;
kk0=kk;
akaike0=akaike;
endif;

kk=kk+0.1;
endo;

tt=seqa(1,1,n);
sinf=sin((2*3.141592*tt*kk0)/n);
cosf=cos((2*3.141592*tt*kk0)/n);
x=y0[k:n-1]~x1[k+1:n]~x1[k:n-1]~x2[k+1:n]~x2[k:n-1]~x3[k+1:n]~x3[k:n-1]~x4[k+1:n]~x4[k:n-1]~const[k+1:n]~sinf[k:n-1]~cosf[k:n-1];
y=y0[k+1:n];
invx=inv(x'x);
beta=invx*x'y;
e=y-x*beta;
ssr=e'e;
var=(e'e/(rows(y)-cols(x)))*invx;
sd=sqrt(diag(var));

"beta=" beta;
"sd=" sd;

@=====ECM model===============================================@
"++ECM method++";

/* lr is long-run coefficient */

lr11=(beta[2]+beta[3])/(1-beta[1]);
lr12=(beta[4]+beta[5])/(1-beta[1]);
lr13=(beta[6]+beta[7])/(1-beta[1]);
lr14=(beta[8]+beta[9])/(1-beta[1]);
lr2=(beta[11]+beta[12])/(1-beta[1]);

"lr11=" lr11;
"lr12=" lr12;
"lr13=" lr13;
"lr14=" lr14;
"lr2=" lr2;

sinf0=sin((2*3.141592*tt*kk0)/n);
cosf0=cos((2*3.141592*tt*kk0)/n);
coin=y0-lr11*x1-lr12*x2-lr13*x3-lr14*x4-lr2*(sinf0+cosf0);

n=rows(y0);
const=ones(n,1);
trend=seqa(1,1,n);
dy1=y0[2:n]-y0[1:n-1];
dx1=x1[2:n]-x1[1:n-1];
dx2=x2[2:n]-x2[1:n-1];
dx3=x3[2:n]-x3[1:n-1];
dx4=x4[2:n]-x4[1:n-1];
tt=seqa(1,1,n);
sinf=sin((2*3.141592*tt*kk0)/n);
cosf=cos((2*3.141592*tt*kk0)/n);
@x=const[k+1:n]~sinf0[k:n-1]~cosf0[k:n-1]~dx1[k:n-1]~dx2[k:n-1]~dx3[k:n-1]~dx4[k:n-1]~coin[k:n-1];@
@x=const[k+1:n]~sinf0[k+1:n]~cosf0[k+1:n]~dx1[k:n-1]~dx2[k:n-1]~dx3[k:n-1]~dx4[k:n-1]~coin[k:n-1];@
x=const[k+1:n]~dx1[k:n-1]~dx2[k:n-1]~dx3[k:n-1]~dx4[k:n-1]~coin[k:n-1];

y=dy1[k:n-1];
invx=inv(x'x);
beta=invx*x'y;
e=y-x*beta;
ssr=e'e;
var=(e'e/(rows(y)-cols(x)))*invx;
sd=sqrt(diag(var));
t=beta./sd;

"beta=" beta;
"sd=" sd;

@=====UECM model===============================================@
"++UECM method++";
n=rows(y0);
const=ones(n,1);
trend=seqa(1,1,n);
tt=seqa(1,1,n);
sinf=sin((2*3.141592*tt*kk0)/n);
cosf=cos((2*3.141592*tt*kk0)/n);
x=dx1[k:n-1]~dx2[k:n-1]~dx3[k:n-1]~dx4[k:n-1]~const[k+1:n]~trend[k:n-1]~sinf0[k:n-1]~cosf0[k:n-1]~y0[k:n-1]~x1[k:n-1]~x2[k:n-1]~x3[k:n-1]~x4[k:n-1];
x1=dx1[k:n-1]~dx2[k:n-1]~dx3[k:n-1]~dx4[k:n-1]~const[k+1:n]~sinf0[k:n-1]~cosf0[k:n-1];
y=dy1[k:n-1];
invx=inv(x'x);
beta=invx*x'y;
e=y-x*beta;
ee=e'e;
    invx1=inv(x1'x1);
    beta1=invx1*x1'y;
    "beta1=" beta1;
    e1=y-x1*beta1;
    ee1=e1'e1;
    f_num=(ee1-ee)/(cols(x)-cols(x1));
    f_den=ee/(rows(y)-cols(x));
    ff=f_num/f_den;
ssr=e'e;
var=(e'e/(rows(y)-cols(x)))*invx;
sd=sqrt(diag(var));
t=beta./sd;
LK=-(rows(y)/2)*(1+ln(3.141592*2)+ln(e'e/rows(y)));
akaike=-2*(LK/rows(y))+2*(cols(x)/rows(y));

"beta=" beta;
"sd=" sd;
"optimal frequency=" kk0;
"Akaike Information Criterion =" akaike0;
"Bounds test (BT) statistics=" ff;