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:

[4.44]

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

[4.45]

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.