# Differencing and Log Transformation

### 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.

```
> 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.

```
> 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.

```
> 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.

#### Course Downloads

LESSONS

- Financial Time Series Data
- Exploring Time Series Data in R
- Plotting Time Series in R
- Handling Missing Values in Time Series
- Creating a Time Series Object in R
- Check if an object is a time series object in R
- Plotting Financial Time Series Data (Multiple Columns) in R
- Characteristics of Time Series
- Stationary Process in Time Series
- Transforming a Series to Stationary
- Time Series Transformation in R
- Differencing and Log Transformation
- Autocorrelation in R
- Time Series Models
- ARIMA Modeling
- Simulate White Noise (WN) in R
- Simulate Random Walk (RW) in R
- AutoRegressive (AR) Model in R
- Estimating AutoRegressive (AR) Model in R
- Forecasting with AutoRegressive (AR) Model in R
- Moving Average (MA) Model in R
- Estimating Moving Average (MA) Model in R
- ARIMA Modelling in R
- ARIMA Modelling - Identify Model for a Time Series
- Forecasting with ARIMA Modeling in R - Case Study
- Automatic Identification of Model Using auto.arima() Function in R
- Financial Time Series in R - Course Conclusion

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