tutorial1_1.md

title	author	subtitle	output	email
Time Series Course 2020/2021	Emilia Wisnios	Tutorial 1	html_document pdf_document keep_md true default	e.wisnios@student.uw.edu.pl

Apply Holt-Winters filtering to the Mauna Loa data. Plot the original data and the one-step fitted values. Plot the Holt-Winters predictors for the next four years. Try this with both additive and multiplicative seasonal models. Which is best (i.e. which gives better prediction)?

www = "https://www.mimuw.edu.pl/~noble/courses/TimeSeries/data/atmospheric-carbon-dioxide-recor.csv"
carbon = read.csv(www)
carbon = carbon[-611,]
y = carbon$MaunaLoaCO2
MaunLoaCo2 = ts(data = y, frequency = 12)
plot(MaunLoaCo2)

output.stl = stl(MaunLoaCo2, s.window = "periodic")
plot(output.stl)

MaunLoaCo2 = ts(data = y, frequency = 12)
output.stl = stl(MaunLoaCo2, s.window = "periodic")
plot(output.stl)

a <- output.stl$time.series
acf(a)

apply(a,2,sd)

##   seasonal      trend  remainder 
##  2.0402413 21.0085895  0.2735003

MaunLoaCo2_mult.hw <- HoltWinters(MaunLoaCo2,seasonal="mult")
plot(MaunLoaCo2_mult.hw)
legend("topleft",c("observed","fitted"),lty=1,col=1:2)

MaunLoaCo2_mult.predict <-predict(MaunLoaCo2_mult.hw,n.ahead=4*12)
ts.plot(MaunLoaCo2,MaunLoaCo2_mult.predict,lty=1:2)

MaunLoaCo2_add.hw <- HoltWinters(MaunLoaCo2,seasonal="additive")
plot(MaunLoaCo2_add.hw)
legend("topleft",c("observed","fitted"),lty=1,col=1:2)

MaunLoaCo2_add.predict <-predict(MaunLoaCo2_add.hw,n.ahead=4*12)
ts.plot(MaunLoaCo2,MaunLoaCo2_add.predict,lty=1:2)