R/YZ.R

In InfoTrad: Calculates the Probability of Informed Trading (PIN)

YZ_class <- function(a,d,m,eb,es,lk,pin) {
  value <- list(alpha=a, delta=d, mu=m, epsilon_b=eb, epsilon_s=es, LKval=lk, PIN=pin)
  attr(value, "class") <- "YZ_class"
  value
}

print<-function(obj){
  UseMethod("print",obj)
}

# S3 Method for print
print.YZ_class <- function(obj) {
  cat("Alpha:", obj$alpha, "\n")
  cat("Delta:", obj$delta, "\n")
  cat("Mu:", obj$mu, "\n")
  cat("Epsilon_b:", obj$epsilon_b, "\n")
  cat("Epsilon_s:", obj$epsilon_s, "\n")
  cat("Likelihood Value:", obj$LKval, "\n")
  cat("PIN:", obj$PIN, "\n")
}

YZ<-function(data, likelihood=c("LK","EHO")){
  
  # User can choose to run LK or EHO whereas default is "LK"
  choice <- match.arg(likelihood)
  
  #Separating buy values from sell values  
  Bt<-data[,1]
  St<-data[,2]

  #Replace NA's with zero to allow the existence of zero order days.
  Bt[is.na(Bt)]=0
  St[is.na(St)]=0
  
  #Defining variables for the mean buy and sell orders and the max amount of order
  mean_b=mean(Bt)
  mean_s=mean(St)
  maxim=max(c(max(Bt),max(St)))

  #Setting the input parameter panel
  alpha_in<-c(0.1, 0.3, 0.5, 0.7, 0.9)
  delta_in<-c(0.1, 0.3, 0.5, 0.7, 0.9)
  gamma_in<-c(0.1, 0.3, 0.5, 0.7, 0.9)

  #Creating a matrix for estimates driven through all combinations of initial values
  #Output matrix contains estimates of alpha, delta, mu, eb, es and the likelihood value for all initial combinations.
  output=matrix(nrow=125,ncol=6)
  
  #A dummy is created for moving in out matrix. 
  dum=1
  for (i in (1:5)){
    for(j in (1:5)){
      for(k in (1:5)){
      
        alpha=alpha_in[i]
      
        delta=delta_in[j]
      
        epsilon_b=gamma_in[k]*mean_b
      
        mu=(mean_b-epsilon_b)/(alpha*(1-delta))
      
        epsilon_s=mean_s-(alpha*delta*mu)
        
        #YZ indicates that es cannot be negative
        #In addition this part forces to provide initial values for mu that are less maximum value for order.
        if (epsilon_s<=0 | mu>=maxim){
          dum=dum+1
          next
        }
      
        par0<-c(alpha,delta,mu,epsilon_b,epsilon_s)
        
        if(choice=="LK"){
          nLL<-LK(data) #Negative log likelihood in Lin and KE form
        }
        if(choice=="EHO"){
          nLL<-EHO(data) #Negative log likelihood in Easleyetal form
        }
  
        #The boundary constraints
        low=c(0,0,0,0,0)
        up=c(1,1,Inf,Inf,Inf)
        
        model<-neldermead(par0,nLL,lower=low,upper=up)
        
          output[dum,1]=model$par[1]# alpha_hat
          output[dum,2]=model$par[2]# delta_hat
          output[dum,3]=model$par[3]# mu_hat
          output[dum,4]=model$par[4]# eb_hat
          output[dum,5]=model$par[5]# es_hat
          output[dum,6]=model$value*(-1)

        dum=dum+1
      }
    }
  }
  
  #Sorts the output matrix such that the last term will provide the estimates that maximize LK
  output_s<-output[order(output[,6],na.last=FALSE,decreasing=FALSE),]
  
  # Give column names
  colnames(output_s) = c('Alpha','Delta','Mu','Eb','Es','LKVal')
  
  # Remove rows with Alpha=0
  output_s = output_s[output_s[,"Alpha"]!=0,]
  
  #Final output file 
  fin_output<-matrix(nrow=1,ncol=7)
  #Collects the parameter estimates
  fin_output[1]=output_s[nrow(output_s),1] #alpha_h
  fin_output[2]=output_s[nrow(output_s),2] #delta_h
  fin_output[3]=output_s[nrow(output_s),3] #mu_h
  fin_output[4]=output_s[nrow(output_s),4] #eb_h
  fin_output[5]=output_s[nrow(output_s),5] #es_h
  fin_output[6]=output_s[nrow(output_s),6] #Fval
  
  #Calculates the probability of informed trading 
  fin_output[7]=(fin_output[1]*fin_output[3])/((fin_output[1]*fin_output[3])+fin_output[3]+fin_output[4])
  ret=YZ_class(fin_output[1],fin_output[2],fin_output[3],fin_output[4],fin_output[5],fin_output[6],fin_output[7])
  
  return(ret)
  
}