R/Kasa.ComT.R

In CommonTrend: Extract and plot common trends from a cointegration system. Calculate P-value for Johansen Statistics.

Kasa.ComT <- function (data,rank,k)
{ 
  
  begin= k+1
  max= length(rownames(data))
  width=length(colnames(data))
  length=max-k

  cotest = ca.jo(data, type = "trace", ecdet = "none", K=k,    spec="transitory")
  equation = cajorls(cotest, r = rank , reg.number = NULL)

  alpha=matrix(NA,width,rank)
  alpha [,1:rank] = t(equation$rlm$coefficients[1:rank,1:width])####otherwise, when rank is one, the data structure will change 
  oalpha <- qr.Q(qr(alpha),complete=TRUE) [ ,(rank+1):width] #### (width-rank) is the number of common trends

  beta= equation$beta
  obeta <- qr.Q(qr(beta),complete=TRUE)[,(rank+1):width] ### beta's structure is variable*rank
   
  loading=obeta%*% ginv(t(obeta)%*%obeta) #  Kasa's method and GG's method are different here.
   
  Pure.T= matrix(NA,(width-rank),(max-k) )
  Pure.T[1:(width-rank),]= t(obeta) %*% t (data[begin:max,]) #  Kasa's method and GG's method are different here.
  Com.T= loading%*%Pure.T
  
  station.p = beta%*% ginv ( t(beta)%*%beta )%*% t(beta)   %*% t (data[begin:max,])

  result = list (method="Kasa(1992)",length = length,lag.chosen=k,
                 beta = beta, othog.beta = obeta,alpha=alpha,
                 othog.alpha=oalpha,
                 common.trend=Com.T,pure.trend=Pure.T,
                 loading.vector= loading,  
                 stationary=station.p, data.used=t(data[(k+1):max,])  ) 
  class(result)<-"ComT"
  return(result)
  }