Lag Operator - Difference Operator

Difference Operator

In time series analysis, the first difference operator Δ is a special case of lag polynomial.

$\begin{array}{lcr} \Delta X_t & = X_t - X_{t-1} \\ \Delta X_t & = (1-L)X_t ~. \end{array}$

Similarly, the second difference operator works as follows:

$\begin{align} \Delta ( \Delta X_t ) & = \Delta X_t - \Delta X_{t-1} \\ \Delta^2 X_t & = (1-L)\Delta X_t \\ \Delta^2 X_t & = (1-L)(1-L)X_t \\ \Delta^2 X_t & = (1-L)^2 X_t ~. \end{align}$

The above approach generalises to the ith difference operator

Read more about this topic: Lag Operator

Famous quotes containing the word difference:

“The difference between human vision and the image perceived by the faceted eye of an insect may be compared with the difference between a half-tone block made with the very finest screen and the corresponding picture as represented by the very coarse screening used in common newspaper pictorial reproduction. The same comparison holds good between the way Gogol saw things and the way average readers and average writers see things.”
—Vladimir Nabokov (1899–1977)