# R 3.0.1
#     Ex4_Pepper_R.txt
rm(list=ls())
library("tseries")  
library("zoo")
library("dynlm")
library("urca")
library("vars")
library("AER")
data("PepperPrice")

# Plots
plot(PepperPrice, plot.type= "single", col =1:2 )     # series
legend("topleft", c("black", "white"), bty = "n" , col =1:2, lty = rep(1,2) )

plot(PepperPrice[,"black"],PepperPrice[,"white"])      # scatter

#adf.test( log(PepperPrice[, "white"]))
#adf.test( diff( log(PepperPrice[, "white"]) ) )

##Dickey-Fuller Unit root test: level and 1st difference
# tau* test for  H0:                (1-rho) = 0   in various models
# phi1  test for H0: const=0   and  (1-rho) = 0   in model w const/drift
# phi3  test for H0: no trend  and  (1-rho) = 0   in trend model
## type = "none" or "drift" or "trend"
## selectlags= "Fixed" or "AIC", ... 
## relevant statistic: tau

w.df <- ur.df( log(PepperPrice[, "white"]) , type="drift", lags=5, selectlags="AIC")    
summary(w.df)
dw.df <- ur.df( diff(log(PepperPrice[, "white"])) , type="drift", lags=5, selectlags="AIC") 
summary(dw.df)   

b.df <- ur.df( log(PepperPrice[, "black"]) , type="drift", lags=5, selectlags="AIC")    
summary(b.df)
db.df <- ur.df( diff(log(PepperPrice[, "black"])) , type="drift", lags=5, selectlags="AIC") 
summary(db.df)  


##Cointegration  - test
# spec="transitory"  is our specification: Delta x_t = ... Pi x_(t-1) ...
# const in Delta x always included
# help("ca.jo-class")   reference: ci_test@Z0
## type = c("eigen", "trace"),  ... tests
## ecdet = c("none", "const", "trend")   ... deterministic part
## (K-1) no of lags of Delta x included

pepper.jo <- ca.jo( log(PepperPrice) , ecdet = "none", type = "trace", K=2, spec="transitory")  # with ecdet="none" r=1 signif
summary(pepper.jo)
pepper.jo <- ca.jo( log(PepperPrice) , ecdet = "none", type = "eigen", K=2, spec="transitory")  # with ecdet="none" r=1 signif
summary(pepper.jo)



 ## CI VAR
pepper.civar <- cajorls(pepper.jo, r = 1)         # r ... chosen coint rank
summary(pepper.civar$rlm)                         # No t-values for beta, AIC    
pepper.civar$beta                                 # ect error correction term 


#pix <- pepper.jo@ZK %*% t(pepper.jo@PI)       # Pi * x(t-1)
#varlevel <- vec2var(pepper.jo, r=1)       # coeff matrices of the lagged endogenous vars

## EXERCISE: 
# (1) Repeat all single steps and comment.
# (2) Write down the estimated CIVAR.