Example 13.4

EXAMPLE 13.4 Lagging Disney Returns

disney

Consider again the 238 weekly Disney returns of Example 13.1. By using the established system of notation, the time series can be denoted as , where . To compare observations with prior observations, we create new variables that take on earlier values of the original variable. This is accomplished by a process known as lagging.

lagging

By lagging a variable, we are creating another variable by arranging the data so that original observations are lined up with prior observations from a certain number of periods back.

Here, for example, are the return data along with lagged variables going one and two periods back:


1	−4.01	*	*
2	−2.04	−4.01	*
3	−1.41	−2.04	−4.01
4	−0.04	−1.41	−2.04
5	1.79	−0.04	−1.41
⋮	⋮	⋮	⋮
236	−1.24	0.06	1.81
237	0.49	−1.24	0.06
238	−0.99	0.49	−1.24

652

The variable is called a lag one variable, and the variable is called a lag two variable. For any given time period, notice that the lag one variable takes on the value of the immediately preceding observation, while the lag two variable takes on the value of the observation from two periods back. The asterisk symbol () denotes a missing value. For example, there is a missing value for the lag one variable in period one because there is no available observation prior to period one.

lag variable