Asymptotics for moving average processes with dependent innovations (Q5953876): Difference between revisions

The authors consider a linear process \(X_t=\sum_{k=0}^\infty \psi_k \varepsilon_{t-k}\) with centered random variables \(\varepsilon_k\). Functional limit theorems for suitably normalized partial sums of \((X_t)\) are investigated in two cases. On one hand, the long memory case where \(\psi_k=k^{-\alpha} \ell(k)\) with \(\alpha \in (1/2,1)\) and a slowly varying function \(\ell(.)\) is studied. In contrast to known results from the literature with independent innovations \((\varepsilon_k)\), it is assumed in this paper that they form a martingale difference sequence. On the other hand ordinary linear processes with \((\psi_k) \in \ell_1\) and innovations \((\varepsilon_k)\) forming a martingale difference sequence or satisfy some mixing conditions are considered.