Spectral Density Estimation and Its Applications
Spectral density reveals the power spectrum of a stationary time series. It characterizes the second-moment properties of a stationary time series. By inspecting an estimated spectral density, we may identify the frequency ranges that contribute the most variation of data. It also helps to identify an appropriate family of models that possess the key correlation features of the underlying process. In particular, when an estimated spectral density is nearly a constant, one may infer that an underlying process is a white noise process. This is useful for model diagnostics; after fitting a certain family of models, one wishes to verify if the family of models adequately fits a given time series by checking whether or not the residual series is a white noise process. The latter can be done by inspecting whether the estimated spectral density based on residuals is nearly a constant.
KeywordsWhite Noise Spectral Density Stationary Time Series White Noise Process Generalize Likelihood Ratio Test
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