0.50 4 
(ne 
0.00 0.06 0.12 0.19 0.25 0.31 0.37 0.44 0.50 
Fig. 5.5c. Estimated by nonparametric method. 
Fig. 5.5. (Continued) 
5.2.2 Autoregressive Process of the First Order, AR(1). 
When X, follows the relation 
X,=aX,i+€;, (5.7) 
where a is a constant and {e,| is a stationary pure random process, 
2 ets 
then GEG ee ees SO Gig.) = GB) 
0 otherwise. 
{X,} is called an autoregressive process of the first order AR(1). Equation 5.7 means that 
1. X, has a linear regression on X;_) as in Fig. 5.6 
2. €, plays the role of error in the above relations of regression 
3. X, is dependent on one step back value of the same process X;_1. 
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