Central limit theorem for linear processes

Random central limit theorems for linear processes with weakly dependent innovations

“…Under the ψ-weak dependence, Coulon-Prieur and Doukhan (2000) provided a CLT for triangular arrays with applications for linear arrays. As in Peligrad and Utev (1997), the CLT result for the linear triangular arrays of Coulon-Prieur and Doukhan (2000) can yield an ordinary CLT for the partial sums of the linear processes with ψ-weakly dependent innovations. Here we consider random CLTs for the partial sums under Assumption 2(a) or Assumption 2 …”

“…Juodis and Rackaukas (2007) established a CLT for self-normalized sums of a linear process, while Mynbaev (2009) dealt with a CLT for weighted sums of a linear process. For dependent innovations, Peligrad and Utev (1997) studied CLTs of linear processes under several well-known mixings and associated sequences, and their results were extended to ψ-weakly dependent processes by Coulon-Prieur and Doukhan (2000). Wu and Min (2005) and Wu and Woodroofe (2004) considered CLTs of linear processes under a wide class of dependent innovations whose dependence structure involves conditional moments.…”

Central limit theorems for LS estimators in the EV regression model with dependent measurements

“…Let X k,n := (x k −x n ) σ n √ S n (ε k − βδ k ) =: a k,n Z k , then the proof of this theorem is on the basis of Theorem 2.2 in Peligrad and Utev (1997).…”

Estimation of the variance for strongly mixing sequences

“…This lemma directly follows from Lemma 2.2 and the following observation. Var(2Z~) < Var( E EzG+,) <l: • maxVar( EZi, +,).The following theorem is a variant of Theorem 2.1 from[10].…”