4.6.4 Differencing

4.6.4  Differencing

One technique is to take differences of one or more components of the time series. With differencing, we transform a time series x into a time series  by replacing suitable components txi with differences:


Not all components may need to be differenced. For those components txj that don’t require it, we merely set


Although differencing is widely used in economic applications, it may fail to address nonstationarities in financial time series.

For example, differences in a stock’s price tend to be proportional to the stock price. If the unconditional mean of a stock’s price increases with time, so will the unconditional mean of differences in the stock’s price. We may solve this problem by taking returns instead of differences.