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I'm studying weakly stationary stochastic processes, and I'm confused by the title of the "moving average" representation of such a process.

Suppose that $y_t$ is a weakly stationary stochastic process, so that it can be written in the following form: $$y_t=\epsilon_t+c_1\epsilon_{t-1}+c_2\epsilon_{t-2}+...$$

where the epsilons are following a white noise distribution. This is supposedly referred to as the MA($\infty$) representation of a weakly stochastic process, but because it is referred to as a moving average, I am inclined to interpret the $c$ coefficients as being weights, in which case I believe they should add up to one. Is this correct?

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    $\begingroup$ No, they do not add to one. The term is simply misleading. $\endgroup$ – Richard Hardy May 10 at 16:13
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    $\begingroup$ Because the (common) variance $\sigma^2$ of the $\epsilon_t$ is unspecified, the sum of the coefficients (including the initial $1$) has no meaning. Without any loss of generality, then, the sum could be constrained to be in the set $\{0,1,-1\}$ through a suitable choice of $\sigma.$ This slightly generalizes the sum-to-unity ("average") case. Thus, maybe the terminology is not that misleading. $\endgroup$ – whuber May 10 at 16:40

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