Computational Aspects of Data Transformations and Ansley’s Algorithm

Abstract

In Section 5 of the previous chapter a simple recursive algorithm was given for an appropriate transformation of the disturbances and the data of a regression model when the disturbances follow an MA(1) process. In the Sections 2 and 3 of this chapter auxiliary recursive formulae are derived in order to transform the disturbances u_t as well as the data when the disturbances follow an arbitrary MA or ARMA process, and where the number of multiplications involved only increases linearly with the number of observations. Furthermore, it will be shown in this chapter in Section 4 how the method of Ansley (1979) in the case of ARMA(p,q) disturbances can be put in the framework of the previous chapter and how this leads to an algorithm for calculating |Γ_u| as well as v=L⁻¹z where L is the lower triangular matrix such that LL’=Γ_z, i.e., the Cholesky decomposition; z is defined in Section 7 of the previous chapter.