#R : R 3.4.1
# Ex1_interest_rates_R.txt

# source("Z:/LV/QF_FinancialEconometrics/CHP1_GARCH_DF_Endo_Caus_IV/EXERCISES/Ex1_interest_rates_R.txt")
# setwd("C:/LVs/QF_FinancialEconometrics/R_Test")  
# setwd("C:/MH/LV/Daten/")
 
library("tseries")
library("urca")

# lending rate. Switzerland. 1981-2015, World Bank

li <- c(5.56, 6.22, 5.52, 5.49, 5.49, 5.46, 5.24, 5.07, 5.85, 7.42, 
        7.83, 7.80, 6.40, 5.51, 5.48, 4.97, 4.47, 4.07, 3.90, 4.29, 
        4.30, 3.93, 3.27, 3.20,	3.12, 3.03, 3.15, 3.34, 2.75, 2.73,
        2.72, 2.69, 2.69, 2.69, 2.68)

li   <- ts(li, frequency=1, start=1981);    nli   <- length(li)
d_li <- ts(diff(li), start=1982);           nd_li <- length(d_li)

### Plotting univariate data
plot( li , main = "lending rate, CH")  # plot interest rate 
plot(d_li , main = "change of lending rate, CH")  # plot diff(li) 

### Testing for white noise 
acf(li);                     # acf: very slow decay nonstat?
acf(d_li);                   # acf: white noise ?

Box.test(li, lag =  1, type = "Ljung-Box", fitdf = 0)  # Ljung-Box tests
Box.test(li, lag =  5, type = "Ljung-Box", fitdf = 0)
Box.test(li, lag = 10, type = "Ljung-Box", fitdf = 0)

Box.test(d_li, lag =  1, type = "Ljung-Box", fitdf = 0)
Box.test(d_li, lag =  5, type = "Ljung-Box", fitdf = 0)
Box.test(d_li, lag = 10, type = "Ljung-Box", fitdf = 0)


##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

# li
summary( ur.df(li,  type="none",  lags=5, selectlags="AIC")  )
summary( ur.df(li,  type="drift", lags=5, selectlags="AIC")  )
summary( ur.df(li,  type="trend", lags=5, selectlags="AIC")  )

# diff(li)
summary( ur.df(d_li,  type="none",  lags=5, selectlags="AIC")  )
summary( ur.df(d_li,  type="drift", lags=5, selectlags="AIC")  )
summary( ur.df(d_li,  type="trend", lags=5, selectlags="AIC")  )

## Testing for GARCH for diff(interest rate)
d_li2 <- ( d_li-mean(d_li) )^2
d_li2_v <- as.vector(d_li2)

plot(d_li2)

acf(d_li2);                   # (d_li)^2 autocorrelated ?

Box.test(d_li2, lag =  1, type = "Ljung-Box", fitdf = 0)  # Ljung-Box tests
Box.test(d_li2, lag =  5, type = "Ljung-Box", fitdf = 0)
Box.test(d_li2, lag = 10, type = "Ljung-Box", fitdf = 0)

# GARCH 
summary( garch(d_li, order=c(0,1) ) ) # ARCH(1)
summary( garch(d_li, order=c(1,1) ) ) # GARCH(1,1)

## more elaborate and comprehensive GARCH estimation in pakage rugarch