Analysis of Exchange Rates as Time-Inhomogeneous Markov Chain with Finite States

Pseudocode 1

R-Codes.

Transition frequency and limiting closeness index transitional probabilities.

d5<-c(NA,NA,NA,NA,NA)

X<-datad4<-c(NA,NA,NA,NA)

N<-nrow(N)-1 d3<-c(NA,NA,NA)

Y<-c(rep(NA,N)) d2<-c(NA,NA)

D<-c(rep(NA,N)) euclidean<- function(a, b) sqrt(sum((a- )^2))

for (i in 1:N) {euclidean(SM[1,],SM[2,])

Y[i]<-X[i+1]-X[i] for (j in 2:6) {

}                        a=j-1

for (i in 1:1592) {d5[a]<-euclidean(SM[1,],SM[j,])

if (Y[i] <=0) D[i]<-0 else D[i]<-1}

}for (j in 3:6) {

A<-c(rep(NA,1592)) a=j-2

B<-c(rep(NA,1592))                d4[a]<- euclidean(SM[2,],SM[j,])

for (i in 1:N) {                   }

A[i]<-D[i]                  for (j in 4:6) {

B[i]<-D[i+1]                  a=j-3

M<-table(A,B)                 d3[a]<- euclidean(SM[3,],SM[j,])

}                        }

SM<-matrix(M, nrow =6,ncol=4)         for (j in 5:6) {

SMa=j-4

Q<-matrix(data, nrow=30, ncol=2) d2[a]<- euclidean(SM[4,],SM[j,])

for (j in 1:30) {}

A<-SM[sample(3, siz =1, replace = FALSE), ]d<- euclidean(SM[5,],SM[6,])

AA<-matrix(A, nrow =2,ncol=2) v<-c(d5,d4,d3,d2,d)

P<-matrix(c(NA,NA,NA,NA),nrow =2,ncol=2) exp(mean(log(v)))

for (i in 1:29) {

Y<-c(0,0,0,0)

Y<-SM[sample(3, size = 1, replace = FALSE), ]

YY<-matrix(Y,nrow =2,ncol=2)

for (j in 3:6) {

AA<-P

}

Q[j,]<-AA[1,]

{

Col.Means(Q)

## SM is a data matrix with i^th row elements

  being i^th year transition probabilities arranged

in the order , and .

closeness index

Similar procedure for index with second line after each “for” line replaced correspondingly by d5[a]<-mean(SM[1,]/SM[j,]), for example, for the first “for” line.