Removing seasonal trends with seasonal differencing

For time series exhibiting seasonal trends, seasonal differencing can be applied to remove these periodic patterns. For example, monthly data may exhibit a strong twelve month pattern. In such situations, changes in behavior from year to year may be of more interest than changes from month to month, which may largely follow the overall seasonal pattern.

The function diff(..., lag = s) will calculate the lag s difference or length s seasonal change series. For monthly or quarterly data, an appropriate value of s would be 12 or 4, respectively. The diff() function has lag = 1 as its default for first differencing. Similar to before, a seasonally differenced series will have s fewer observations than the original series.

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Time Series Analysis in R

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Instrucciones del ejercicio

The time series x has already been loaded, and is shown in the adjoining figure ranging below -10 to above +10. Apply the diff(..., lag = 4) function to x, saving the result as dx.
Use ts.plot() to show the transformed series dx and note the condensed vertical range of the transformed data.
Use two calls of length() to calculate the number of observations in x and dx, respectively.

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# Generate a diff of x with lag = 4. Save this to dx
dx <- 
  
# Plot dx
  

# View the length of x and dx, respectively

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