2011/09/23 by Yizao Wang, Wang, Yizao
Economics, Econometrics and Finance · Mathematics · Decision Sciences · #Financial Risk and Volatility Modeling #Stochastic processes and statistical mechanics #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.1109.5160
We establish a central limit theorem for partial sums of stationary linear random fields with dependent innovations, and an invariance principle for anisotropic fractional Brownian sheets. Our result is a generalization of the invariance principle for fractional Brownian motions by Dedecker et al. (2011) to high dimensions. A key ingredient of their argument, the martingale approximation, is replaced by an m-approximation argument. An important tool of our approach is a moment inequality for stationary random fields recently established by El Machkouri et al. (2011).