Hildreth-Lu Search Procedure:

Since we know that p lies  between 1 and - 1, this procedure  searches  over  this  range, i.e., using values of p say between -0.9 and 0.9  in intervals of 0.1. For each ρ we compute  the  regression  in (7.3) and report  the  residual sum of squares  corresponding to that ρ.  The minimum residual sum of squares gives us our choice of ρ and the corresponding  regression gives us the estimates of β₁,β₂ and σ².  We can refine this procedure around the best ρ found in the first stage of the search. For example, suppose  that ρ=0.6  gave the-minimum residual sum of squares. We can search  next between 0.5 1 and 0.69 in intervals of 0.01. This search  procedure guards against a local minimum.