Project without external funding

Autoregressive error processes and cubic splines


Project Details
Project duration: 01/200112/2003


Abstract
Consider the linear model y = X beta + u, where u = (u1,...,uT)' and ut = rho ut-1 + varepsilont, varepsilont idependent N(0, sigma2) and |rho| < 1. The covariance-matrix of u is proportional to Omega = (p|i-j|; i,j = 1,...,T) and processes an explicit tridiagonal inverse Omega-1. This allows the computation of the aitken-estimator in a very simple way. Equidistant cubic spline interpolation requires the inversion of a tridiagonal matrix Omega0 whose diagonal elements are equal to 4, while the elements in the side-diagonals are equal to 1. If turns out that thix matrix is of the form a (Omega-1 + DD'), a = 2 squart 3, rho = -2 + squart 3. The inverse of this matrix can be easily computed by using Omega and the Törnquist-Egervary formula. Moreover, it turns out that the elements of this inverse matrix are functions of ai, bi; i = 2,...,n+1, where rhon = an + bn rho.

Last updated on 2017-11-07 at 13:45