# 1.2 Linear Filtering of Time Series

# Example 1.2.1. (Unemployed Females Data). The series of monthly
# unemployed females between ages 16 and 19 in the United States
# from January 1961 to December 1985 (in thousands) is
female <- read.table("female.txt")
temp <- data.matrix(female) # Start making a ts object
temp <- t(temp)
female <- ts(temp[1:length(temp)],start=c(1961,1),freq=12) # End making a ts object
plot(female)
female.ma.17 <- filter(female,filter=rep(1/17,17))
lines(female.ma.17,col="red")


# Example 1.2.2
unemployed1 <- read.table("unemployed1.txt")
colnames(unemployed1) <- c("month","t","unemplyd")
unemployed1
unemp <- ts(unemployed1$unemplyd,start=c(1975,7),freq=12)
unemp.star <- filter(unemp,filter=c(0.5,rep(1,11),0.5)/12)
d <- unemp - unemp.star
d
decompose(unemp)

# Example 1.2.3. (Temperatures Data). The monthly average temperatures
# near Wuerzburg, Germany were recorded from the 1st of
# January 1995 to the 31st of December 2004
temperature <- read.table("temperatures.txt")
temperature <- ts(temperature[,1],start=c(1995,1),freq=12)
plot(temperature)
decom <- decompose(temperature)
lines(decom$trend,col="red")

# Example 1.2.3a (Unemployment1 Data) Applying X-12 to the data
unemployed1 <- read.table("unemployed1.txt")
unemployed1 <- ts(unemployed1[,3],start=c(1975,7),freq=12)
plot(unemployed1)
decom.unemp <- decompose(unemployed1)
lines(decom.unemp$trend,col="red")


# Try after installing X-12-ARIMA from http://www.census.gov/srd/www/x12a/
# and istalling the package x12
library(x12)
x12()

# Local Polynomial Fit
stl(unemployed1,s.window="periodic")
plot(stl(unemployed1,s.window="periodic"))

# Example 1.2.7. (Electricity Data). The following plots show the
# total annual output of electricity production in Germany between 1955
# and 1979 in millions of kilowatt-hours.
electric <- read.table("electric.txt")
temp <- data.matrix(electric[,-(1:2)]) # Start making a ts object
temp <- t(temp)
electric <- ts(temp[1:length(temp)],start=c(1955,1),freq=12) # End making a ts object
plot(electric)

electric.sum <- read.table("electric.txt")[,-(1:2)]
electric.sum <- data.matrix(electric.sum)
electric.sum <- rowSums(electric.sum)

plot(electric.sum,type="l")
plot(diff(electric.sum),type="l")
plot(diff(diff(electric.sum)),type="l")

elec <- ts(electric.sum,start=1955)
plot(elec)
plot(filter(elec,side=1,filter=c(1,-1)),ylab="diff.elec")
plot(filter(elec,side=1,filter=c(1,-2,1)),ylab="diff.diff.elec")