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.
This is a part of the course
“Time Series Analysis in R”
Exercise instructions
- Apply the
diff()
function toz
, saving the result asdz
. - Use
ts.plot()
to view a time series plot of the transformed seriesdz
. - Use two calls of
length()
to calculate the number of observations inz
anddz
, respectively.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Generate the first difference of z
dz <-
# Plot dz
# View the length of z and dz, respectively