Differencing and Log Transformation

Removing Linear Trend

We will now perform the first difference transformation [z(t) - z(t-1)] to our series to remove the linear trend.

1> sp_linear_diff <- diff(sp_linear)
2> plot.ts(sp_linear_diff, main="Daily Stock Prices (log)", ylab="Price", col=4)
3>
4

Removing Seasonal Differencing

Let's take another example to understand how we can use the diff() function to remove seasonal differencing from data. We will use the John Deer's Quarterly earnings data we used earlier as it exhibits seasonality.

1> par(mfrow = c(1,2))
2> de_earnings_diff <- diff(johndeere_earnings,lag=4)
3> plot.ts(johndeere_earnings, main="Earnings (Quarterly)")
4> plot.ts(de_earnings_diff, main="Earnings (Differenced, lag=4)")
5

The chart on the left shows the original earnings. The chart on the right shows the difference in earnings with a lag of 4.