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  "body": "\n## Definition\n\nLet $T$ be a set of time points, usually $T = \\Z$, $T = \\set{1, \\dots, n}$ or an interval of $\\R$.\nA *time series* is a family of observations $(x_t)_{t \\in T}$ indexed by time, together with the order of $T$.\nAs a statistical model, a time series is a realization of a [[stochastic process|0QH5ENKZM1]] $(X_t)_{t \\in T}$.\nThe same name is often used for the process itself.\nThe series is in *discrete time* when $T$ is a subset of $\\Z$, and in *continuous time* when $T$ is an interval of $\\R$.\n\n## Remarks\n\nExample: the yearly maximum temperatures $x_{1990}, \\dots, x_{2020}$ at one weather station form a discrete-time series with $T = \\set{1990, \\dots, 2020}$.\nNon-example: the heights of $30$ pupils, listed in alphabetical order of their names, are not a time series.\nThe index is not time, and its order carries no meaning.\nA discrete-time series is a finite or infinite [[sequence|0G9EKM0E15]] of real numbers or vectors; when its values are vectors it is called multivariate.\nMany methods assume that the underlying process is stationary, possibly after removing a trend or a seasonal component.\n",
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