Nonparametric and Robust Approach in Time Series Analysis

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This research is concerned with the estimation of the autocorrelation of a stationary Gaussian process by nonparametric and robust method without assuming a specific parametric model, and the tests based on nonparametric spectral estimators in time series analysis.We discuss the estimation of the autocorrelation based on limiter estimating functions for a stationary Gaussian process having the representation of an infinite moving average. Several new estimators are proposed and their asymptotic distributions are obtained. The estimation of the autocorrelation of a stationary Gaussian process with additive outliers is discussed. The biases of several estimators of the autocorrelation based on limiter estimating functions are compared.We consider to test whether the integral of appropriate function of the spectral density is equal to a given constant or not. For this problem a test based on a nonparametric spectral estimator is proposed, and the asymptotic power evaluation under a sequence of nonparametric contiguous alternatives is given. We discuss to test whether the integral of appropriate function of the spectral density of a process, is equal to that of the other process, or not.