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

• K. Dzhaparidze
Chapter
Part of the Springer Series in Statistics book series (SSS)

## Abstract

In this chapter the problem of testing the hypothesis H0 concerning the form of spectral density f of a linear process Xt of the form (II.6.1) is considered. Unlike in the preceding chapter more general assumptions on the nature of the process Xt are imposed. Namely, it is assumed that the coefficients g1, g2, … and the sequence of identically distributed random variables εt, 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(∣εtr) < ∞.

## Keywords

Spectral Density Random Vector Critical Region Linear Process Autoregressive Process
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