Estimation of the Sampling Autocorrelation ρ _z

Abstract

This chapter describes how under some regularity conditions the sampling autocorrelation coefficient ρ _z can be estimated in practice. The basic idea of the estimation procedure is that the fixed value Z _j can be decomposed numerically into two components: (i) a part Ф _j that is linear in the powers of p _j and (ii) an uncorrelated remainder Ω _j (j = 1,...,N). Or to say it in a more intuitive way, we assume that Z _j can be split up according to

$$\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{{Z}_{j}} \equiv \frac{{{{Y}_{j}}}}{{{{p}_{j}}}} = f({{p}_{j}}) + {{\Omega }_{j}}} & {(j = 1, \ldots ,N)} \\ \end{array} } \\ { \approx \sum\limits_{{k = 0}} {{{\beta }_{k}}p_{j}^{K} + {{\Omega }_{j}}} } \\ { = {{\Phi }_{j}} + {{\Omega }_{j}},} \\ \end{array}$$