Testing nonparametric and semiparametric hypotheses in vector stationary processes

摘要: We propose a general nonparametric approach for testing hypotheses about the spectral density matrix of multivariate stationary time series based on estimating integrated deviation from null hypothesis. This covers many important examples interrelation analysis such as tests noncorrelation or partial noncorrelation. Based central limit theorem quadratic functionals matrix, we derive asymptotic normality suitably standardized version test statistic under hypothesis and fixed well sequences local alternatives. The results are extended to cover also parametric semiparametric matrices, which includes goodness-of-fit separability.