"Warning! This post is mathematical. Disinterested readers beware!
One of the goals of time series analysis is to model the signal underlying the data. If the data have some random element to them, they’ll follow some probability distribution. The distribution might be dependent on external variables (like time), in which case we usually create a model in which the mean of the distribution is time-dependent. Suppose, for example, we model a variable as following a straight line time trend, plus random noise..."
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