Since in the ?rst-order autoregressive scheme ut = ρut-1 + εt
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 trans- forming 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:
Σu^t2 . Hildreth and Lu suggest choosing that ρ which minimizes the RSS (hence maximizing the R2 ). If further re?nement is needed, they suggest using smaller unit intervals, say, 0.01 unit 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 Σuˆ t2 ?