Goodness-of-Fit Tests for Testing the Hypothesis About the Spectrum of Linear Processes

Abstract

In this chapter the problem of testing the hypothesis H₀ concerning the form of spectral density f of a linear process X_t of the form (II.6.1) is considered. Unlike in the preceding chapter more general assumptions on the nature of the process X_t are imposed. Namely, it is assumed that the coefficients g₁, g₂, … and the sequence of identically distributed random variables ε_t, t = …,-1,0,1, …, satisfy the following conditions which are more stringent than those in Chapter II, Subsection 6.1: for some $\delta > 0,{\text{ }}\sum _{{j = 1}}^{\infty }{{j}^{{1/2 + \delta }}}\left| {{{g}_{j}}} \right| < \infty$ and for some r > 4, E(∣ε_t∣^r) < ∞.