### Removing Variability Using Logarithmic Transformation

Since the data shows changing variance over time, the first thing we will do is stabilize the variance by applying log transformation using the `log()`

function. The resulting series will be a linear time series.

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> sp_linear<-log(sp_ts) > plot.ts(sp_linear, main="Daily Stock Prices (log)", ylab="Price", col=4) |

### Removing Linear Trend

We will now perform the first difference transformation `[z(t) - z(t-1)]`

to our series to remove the linear trend.

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

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

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

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