Lag operator
Operator for offsetting time series elements / From Wikipedia, the free encyclopedia
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"Backshift" redirects here. For the linguistic sense, see Sequence of tenses.
In time series analysis, the lag operator (L) or backshift operator (B) operates on an element of a time series to produce the previous element. For example, given some time series
This article includes a list of general references, but it lacks sufficient corresponding inline citations. (January 2011) |
then
- for all
or similarly in terms of the backshift operator B: for all . Equivalently, this definition can be represented as
- for all
The lag operator (as well as backshift operator) can be raised to arbitrary integer powers so that
and