Tests for error correlation in the functional linear model

Abstract

In this chapter, we consider two tests for error correlation in the fully functional linear model, which we call Methods I and II They complement the tools described in Section 8.6 and the graphical goodness of fit checks used in Chapter 9. To construct the test statistics, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distribution are chi–squared with known numbers of degrees of freedom (different for the two forms). The test statistics can be relatively easily computed using the R package fda.