A Conceptual Vocalubary of Time Series Analysis




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W

white noise

The time series generated from uncorrelated variables \( w_t \) with mean 0 and finite variance \( \sigma^2_w \) is called white noise and denoted as \( w_t \sim wn(0, \sigma^2_w). \)  The designation white originates from the analogy with white light and indicates that all possible periodic oscillations are present with equal strength.

If uncorrelated variables \( w_t \)s are further independent and identically distributed (iid) the process is a white independent noise and denoted as \( w_t \sim iid(0, \sigma^2_t). \)

If \( w_t \) are independent normal random variables, with mean 0 and variance \(\sigma^2_w\), the process \( w_t \sim N(0, \sigma^2_t)\) is called Gaussian white noise.