## A Conceptual Vocalubary of Time Series Analysis

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### M

#### mean function

The mean function of a time series process is defined as  $$\mu_{xt}=E[X_t]$$ provided that it exists.

Example 1: If $$w_t$$ denotes a white noise series, then If $$E(w_t)=0$$  for all $$t$$.

Example 2:Consider the random walk with drift model $$x_t= \delta _t+ \frac{1}{n} \sum\limits_{j = 1}^t {{w_j}}, t=1,2, ...$$

Because$$E(w_t)=0$$  for all $$t$$ and  $$\delta _t$$ is a constant we have $$\mu_{xt}=E[X_t]=\delta _t+\sum\limits_{j = 1}^t {{w_j}}=\delta _t\$$which is a straight line with slope $$\delta$$.