Exercise

# Removing trends in level by differencing

The first difference transformation of a time series \(z[t]\) consists of the differences (changes) between successive observations over time, that is \(z[t] - z[t-1]\).

Differencing a time series can remove a time trend. The function diff() will calculate the first difference or change series. A difference series lets you examine the increments or changes in a given time series. It always has one fewer observations than the original series.

The time series `z`

has already been loaded, and is shown in the figure on the right.

Instructions

**100 XP**

- Apply the
`diff()`

function to`z`

, saving the result as`dz`

. - Use
`ts.plot()`

to view a time series plot of the transformed series`dz`

. - Use two calls of
`length()`

to calculate the number of observations in`z`

and`dz`

, respectively.