Estimating : The HildrethLu scanning or search procedure.* Since in the first order autoregressive scheme u t = u t 1 + t

Estimating ρ: The Hildreth–Lu scanning or search procedure.* Since in the first order autoregressive scheme

u_t = ρu_t−1 + ε_t

ρ is expected to lie between −1 and +1, Hildreth and Lu suggest a systematic “scanning’’ or search procedure to locate it. They recommend selecting ρ between −1 and +1 using, say, 0.1 unit intervals and transforming the data by the generalized difference equation (12.6.5). Thus, one may choose ρ from −0.9, −0.8, . . . , 0.8, 0.9. For each chosen ρ we run the generalized difference equation and obtain the associated

RSS:Σû²_t. Hildreth and Lu suggest choosing that ρ which minimizes the RSS (hence maximizing the R²). If further refinement is needed, they suggest using smaller unit intervals, say, 0.01 units such as −0.99, −0.98, . . . , 0.90, 0.91, and so on.

a. What are the advantages of the Hildreth–Lu procedure?

b. How does one know that the ρ value ultimately chosen to transform the data will, in fact, guarantee minimum Σû²_t?