Nonparametric and parametric methods of spectral analysis

Spectral Analysis is one of the most important methods in signal processing. In practical application, it is critical to discuss the power spectral density estimation of finite data sampled from some stationary time series. A spectral estimator is expected to have good statistical properties such as consistency, high resolution and small variance. For one spectral estimation method, there exists a trade-off between high resolution and small variance. The paper provides a comparison of several popular spectral methods from both theoretical properties and practical applications. We first address several basic nonparametric methods, whose statistical characters are analysed. Then we explain the connections and differences between temporal windowing and lag windowing. Thereafter, the confidence intervals of both windows are given and used to evaluate the estimated results. Besides, several different parametric estimation methods of autoregressive time series are compared, and whose properties and effects are also introduced. Building on our understanding of these studies, we then apply parametric and nonparametric spectral estimation methods on the data of ocean surface wave height.