# R 3.4.1 
require(moments)
require(tseries)

####################################
###  script for basic statistics ###
####################################

basic_stats <- function(ts0) {
     ts <- as.numeric(ts0)
     hh <- c("Basic Statistics: "," Nobs=", formatC( length(ts), digits = 5, width=8) )
     print.noquote(hh)
     hh <- c("Min=     ", formatC(  min(ts), digits = 5, width= 8, format = "fg") , 
             "Max=     ", formatC(  max(ts), digits = 5, width= 8, format = "fg")  )
     print.noquote(hh)
     hh <- c("Mean=    ", formatC( mean(ts), digits = 5, width= 8, format = "fg") , 
             "StDev=   ", formatC(  sd(ts) , digits = 5, width= 8, format = "fg")  )
     print.noquote(hh )                  
     hh <- c("Skewness=",formatC( skewness(ts), digits = 5, width= 8, format = "fg") ,
             "Kurtosis=",formatC( kurtosis(ts), digits = 5, width= 8, format = "fg")  )
     print.noquote(hh) 
     
     jbt <- jarque.bera.test(ts);      jb  <- as.numeric( jbt[1:3])
     hh <- c("Jarque Bera Test:");  print.noquote(hh)
     cat("    Chi2 =",jb[1], " df =", jb[2], " p-value =", jb[3], "\n")
                           }  
#####################################
   
plot_ser_fit_res.ts <- function(ser,model,ser_name,start_year,lab_main="") {
## PLOT - Datenreihe (ser) , Fitted, Residuen: 
# Period is determined by the model. 
# If lags you loos obs at the beginning!

res      <- ts(model$residuals, start= start_year)
n_res    <- length(res)
end_year <- start_year + n_res - 1
observed <- ts(ser, start= start_year, end= end_year)
fitted   <- ts(model$fitted, start= start_year)

null     <- ts(rep(0,n_res), start= start_year, end= end_year)

max_y <- max(fitted,observed); min_y <- min(fitted, observed)
#
op <- par(mfrow=c(2,1))
par(mar=c(0, 4, 4, 2) +0.1) 
plot.ts(observed, ylab= ser_name, xlab="", ylim= c(min_y, max_y) )
par(new=TRUE) 
plot.ts(fitted, xlab="", ylab="", col="blue", axes=FALSE, ylim= c(min_y, max_y) )
lab_title <- paste("observed and fitted, residuals:",lab_main, sep=" ")
title(lab_title)
#
par(mar=c(5, 4, 2, 2) +0.1) 
plot.ts(res, col="red")
lines(null, xlab="", ylab="", lty=3)
par(op)
#
                                }

#######################################