Empirical spectral processes and their applications to time series analysis
Let X(t) be an r-dimensional strictly stationary Gaussian time series with a matrix \(F=(F_{ab})\) of spectral distribution functions (SDF's). Let \(F^{(N)}\) be the matrix of empirical SDF's. Let \[ E_ N(g)=(N^{1/2}\int^{\pi}_{- \pi}g_{ab}(\lambda)\{dF_{ab}^{(N)}(\lambda)- dF_{ab}(\lambda)\})_{a,b=1,...,r}. \] The author proves weak convergence and equicontinuity of \(E_ N(g)\) for some classes of functions used as index sets for empirical processes. Some applications of general results to the theory of time series are indicated.
strictly stationary Gaussian time series
scientific article; zbMATH DE number 4069935
scientific article