Source codes
R code to produce Bootstrap AR(5) results using matrix notations:
# ---- GENERATING AR COEFFICIENTS ---#
generateAR<-function (n=1) {
repeat
{
minroots =0
ar=runif(n,-1,1)
minroots <- min(Mod(polyroot(z=c(1,-ar))))
if(minroots > 1) break
}
return(ar)
}
# ---- start bootstrap ----#
par(mfrow=c(1,2),las=2,cex=.5);
n=100
nv=5
m=matrix(ncol=n,nrow=nv)
v=generateAR(nv)
for (t in 1:n){
ars<-arima.sim(model=list(ar=v),n=2000);
ars=scale(ars)
#acf(ars);pacf(ars)
x=makematrix(ars,nv,mean(ars))
y=ars
l=lm(y~x+0)
for (i in 1:nv){
m[i,t]=l$coeff[i]
}
}
matplot(m,pch=c('+'))
abline(h=v,lty=1:length(y))
axis(side=2,at=v)
boxplot(t(m),notch=TRUE,axes=FALSE,outline=FALSE)
axis(side=2,at=round(v,3))
abline(h=v,lty=1:length(y))
The code below produces numerical results for H'pHq matrix. Note that this code simulates REGARMA ten times and compute H'pHq.
require(Mparcor)
ar=12;ma=11
p=15;m=10000;
H=matrix(0,ncol=ma,nrow=ar)
for ( i in 1:10){
x=matrix(runif(m*p),ncol=p)
y=rnorm(m)
n=1
x2=x[-(1:n),];x2=scale(x2)
y2=y[-(1:n)];y2=scale(y2)
Hp=makematrix(y2,ar,rname='Hp')
adl=lm(y2~cbind(Hp,x2)+0)
yy=cbind(Hp,x2) %*% adl$coefficients
ey=y2-yy
colMeans(t(ey) %*% cbind(Hp,x2))
Hq=makematrix(ey,ma,rname='Hq')
H=H+(t(Hp) %*% Hq/length(y2))
#print(round(colSums(H/i),3))
}
H=H/10
plot(diag(H),type='b')
Auto backup script for TexStudio.
Auto backup script for TexStudio.
Auto backup script for TexStudio.
To use this script create a folder named 'backup' within the same directory as your project directory. If you have multiple files, don't forget to create a backup folder within each project file.
%SCRIPT
var Debug = false; //default = false
var DoSave = true; //default = true
var Interval = 60000*15;// set the time in milliseconds. 60000=1mins
registerAsBackgroundScript("auto_save");
setTimeout(TimedFunction,Interval);
function TimedFunction() {
if (Debug) { alert('timer expired') };
SaveAllDocuments();
setTimeout(TimedFunction,Interval); //rearm the timed function
}
function SaveAllDocuments(){
if (Debug) { alert('SaveAllDocuments called') };
var NumOfDocs = documents.length;
if (Debug) { alert('NumOfDocs='+NumOfDocs) };
for (var i = 0; i < NumOfDocs; i++) {
SaveDocument(i, documents[i]);
};
};
function SaveDocument(i, Document) {
var t = new Date();
var tt='_'+t.getSeconds()+'_'+t.getMinutes()+'_'+t.getHours()+'_'+t.getDate()+'_'+(t.getMonth() +1)+'_'+t.getFullYear()+'_';
var CurEditor = Document.editorView.editor;
var CurFileName = CurEditor.fileName();
if (Debug) { alert('i='+i+' FileName='+CurFileName) };
var fname=(CurFileName.replace(/^.*[\\\/]/, ''));
var newName =CurFileName.replace(fname,'backup/'+fname+ tt+'_bak.tex');
if (Debug) { alert('i='+i+' newName='+newName) };
if (DoSave) { CurEditor.saveCopy(newName); };
};
Generate REGARMA(1,1) results
library(REGARMA)
#rm(list=ls(all=TRUE))
iterate=100
n=1000
beta=c(-.712,.123,-.093);nbeta=length(beta)
phi=-.612; nphi=length(phi)
theta=.361; ntheta=length(theta)
THETA=c(phi,theta)
bmatrix=matrix(ncol=(nphi+ntheta+nbeta),nrow=iterate)
LMbmatrix=matrix(ncol=nbeta,nrow=iterate)
for(i in 1:iterate){
y=REGARMA:::sim.regARMA(n=n,beta=beta,phi=phi,theta=theta,var.error=.5,x.independent = FALSE)
Hp=REGARMA:::makematrix(y$y,p=nphi,beforestart.mean = 0)
epsilon=y$y-predict(lm(y$y~y$x+Hp+0))
Hq=REGARMA:::makematrix(epsilon,p=ntheta)
lmm=lm(y$y~Hp+Hq+y$x+0)
bmatrix[i,]=as.vector(lmm$coefficients)
LMbmatrix[i,]=as.vector(lm(y$y~y$x+0)$coefficients)
}
boxplot(bmatrix,outline=FALSE,ylab='Parameter space',ylim=c(min(bmatrix)-.2,max(bmatrix)+.4),add=FALSE)
legend('topright',lty=1:(nbeta+1), legend=paste('beta',1:nbeta,'=',round(beta,3),sep=' '), bty='n',cex=.85)
legend('topleft',lty=4:5, legend=paste(c('phi','theta'),'=',round(c(phi,theta),3),sep='.'), bty='n',cex=.85)
abline(h=beta,pch=1,lty=1:nbeta)
abline(h=theta,pch=2,lty=5)
abline(h=phi,pch=3,lty=6)
abline(v=2.5)
Below is a sample output of this code!
Download a file
Reliability 2012 (persian)
Forecasting methods(persian)
Brunel University, thesis template (Latex file) : download
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Moore-Penrose Pseudoinverse - R code
pinv<-function(H){ x=t(H) %*% H s=svd(x) xp=s$d for (i in 1:length(xp)){ if (xp[i] != 0){ xp[i]=1/xp[i] } else{ xp[i]=0 } } return(s$u %*% diag(xp) %*% t(s$v) %*% t(H))}
Simulating multiple regression - R
sim.regression<-function(n.obs=10,coefficients=runif(10,-5,5),s.deviation=.1){ zero.coefficients=.1 n.var=length(coefficients) M=matrix(0,ncol=n.var,nrow=n.obs) if(zero.coefficients>1){stop(print('zero-coefficients percent must be between zero and one!'))} beta=as.matrix(coefficients) for (i in 1:n.var){ M[,i]=rnorm(n.obs,0,1) } y=M %*% beta +rnorm(n.obs,0,s.deviation) return (list(x=M,y=y,coeff=coefficients)) }
REGARMA simulation proof
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