## R Ue6.1 at_17 "Business Cyle" im GDP, AT, 1976 -- 2009 
## gdpn, gdpr, gdp per capita AT, Mrd €, 1970 - 2017

## tt       ... Linearer Trend 1976=1

#setwd("C:/MH/WU/LV/OEKONOMETRIE_BA/Oe1_WS23/Chp6/EXERCISES/")
setwd("C:/Users/hoersaal/Downloads/")
source("BasicStatistics_R.txt")

# Daten einlesen (nicht ganz einfach)
dat <- read.table("at_17.csv", sep=";", dec=",", header=TRUE, na.strings = "#NV", fill = TRUE, comment.char="")

## Daten anschauen
#head(dat)
#tail(dat)
#dim(dat)   # Zeitreihen n=48 k=5 (Variablen)  von 1970 bis 2017
names(dat)  # Namen der Variablen

gdpr  <- ts(dat$gdpr, start=1970, end=2017)
n     <- length(gdpr)
tt    <- ts(c(1:n), start=1970, end=2017)                   # (Linearer) Trend
const <- ts(rep(1,n), start=1970, end=2017)
year  <- ts(c(1970:(1970 + n - 1)), start=1970, end=2017)

df <- as.data.frame(cbind(year,gdpr,tt,const))
head(df)
tail(df)                # es gibt keine NAs

df1 <- df[df$year %in% c(1976:2009),]           # 1976 -- 2009   n=34

## plot von gdpr
plot.ts(gdpr, ylab="gdpr")
## plot von log(gdpr)
plot.ts(log(gdpr), ylab="log(gdpr)")
## plot von tt
plot.ts(tt, ylab="Linearer Trend")
   
## Modell: log(gdpr) = a + b tt + u   bzw  gdpr = exp(a)*exp(tt)^b*v
## Exponentieller(!) Trend in gdpr mit konstanter Wachstumsrate b
mod <- lm(log(gdpr) ~ tt + 1, data=df1)   
summary(mod) 
#
lgdpr <- log(df1$gdpr)
plot_ser_fit_res.ts(lgdpr,mod,"log(gdpr)",1976,lab_main="Exponentieller Trend")

## AT business cycle
n1       <- length(df1$gdpr)
null     <- ts(rep(0,n1), start= 1976, end= 2009)
bc       <- ts(mod$residuals, start= 1976, end= 2009)
#
plot.ts(bc, col="red")
lines(null, xlab="", ylab="", lty=3)
title("AT Business Cycle 1976 -- 2009")
#