Decomposition

We will consider two examples of decomposition. The first an example where the time series is additive and the second where the time series is multiplicative.

Example from OTexts Forecasting: principles and practice fpp

What is white noise? The term white noise means the Irregular part of the time series is Normally distributed with mean zero and it has constand variance.

x.error <- as.ts( rnorm(100) )
plot(x.error)

So when we decompose a time series the Irregular part should look like white noise.

Additive decomposition

Consider the beer production data.

library(fpp)
class(ausbeer)

[1] "ts"

data("ausbeer")

Plot the data.

plot(ausbeer, type="o", xlab="Year")

plot(decompose( ausbeer, "additive" ), xlab="Year")

Example from ts4

Mutliplicative decomposition

Consider the Johnson & Johnson data.

library(astsa)
class(jj)

[1] "ts"

data(jj)

Plot the data

plot(jj, type="o", xlab="Quarter", ylab="Quarterly Earnings per Share")

We see the seasonal component increasing in time. So we should consider a multiplicative decomposition.

plot(decompose( jj, "multiplicative" ), xlab="Quarter")

What if we use an additive model.

plot(decompose( jj, "additive" ), xlab="Quarter")

The Irregular part does not look like white noise.

Using piping from dplyr

jj %>% decompose("multiplicative") %>% plot()

jj %>% decompose() %>% plot()

Using a different R function that also does decomposition. stl()

ausbeer %>% stl("periodic") %>% plot()

jj %>% stl("periodic") %>% plot()

log(jj) %>% stl("periodic") %>% plot()