In Chapter 7 we gave three basic procedures for parameter estimation:
1. The prediction-error approach in which a certain function VN(θ, ZN) is minimized with respect to θ.
2. The correlation approach, in which a certain equation fN(θ, ZN) = 0 is solved for θ.
3. The subspace approach to estimating state space models.
In this chapter we shall discuss how these problems are best solved numerically.
At time N, when the data set ZN is known, the functions VN and fN are just ordinary functions of a finite-dimensional real parameter vector θ. Solving the problems therefore amounts to standard questions of nonlinear programming and numerical analysis. Nevertheless, it is worthwhile to consider the problems in our parameter ...