Spectral Representation of Univariate Time Series

Abstract

$$\displaystyle{X_{t}\text{ second order stationary, } E\left ( X_{t}\right ) =0\text{, } \gamma _{X}\left ( k\right ) =\int _{-\pi }^{\pi }e^{ik\lambda }dF_{X}\left ( \lambda \right )}$$

$$\displaystyle\Rightarrow \text{additive decomposition of }X_{t} \text{ into periodic components?}$$