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 \( \delta \).