## A Conceptual Vocalubary of Time Series Analysis

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### C

#### Cauchy–Schwarz inequality

The Cauchy–Schwarz inequality states that for all vectors x and y of an inner product space it is true that $$|\langle x,y\rangle| ^2 \leq \langle x,x\rangle \cdot \langle y,y\rangle$$  where $$\langle\cdot,\cdot\rangle$$ is the inner product, also known as dot product. Equivalently, by taking the square root of both sides, and referring to the norms of the vectors, the inequality is written as$$|\langle x,y\rangle| \leq \|x\| \cdot \|y\|.$$

#### cross-correlation function

The cross-covariance function scaled to live in [-1, 1] is called cross-correlation function and given by$$\rho_{xy} (s,t)=\frac{ \gamma_{xy}(s,t)}{\sqrt{\gamma_x(s,s)\gamma_y(t,t)}}.$$

#### cross-covariance function

The cross-covariance function between two series, $$x_t$$ and $$y_t$$ , is$$\gamma_{xy} (s,t)=cov(x_s,y_t)=E[(x_s- \mu_{xs})(y_t- \mu_{yt})].$$