Stationary time series has its own definitions; it's either "strong" or "weak" stationary. Therefore, if the time series has a trend, deterministic or stochastic, it's "NOT" stationary.
In mathematics and statistics, a stationary process (or strict(ly) stationary process or strong(ly) stationary process) is a stochastic process whose joint probability distribution does not change when shifted in time. Consequently, parameters such as the mean and variance, if they are present, also do not change over time and do not follow any trends.
上述是关于 strictly stationarity 的定义，通俗易懂。weak stationarity 就更好懂了，简单的讲就是 mean 和 covariance 不变。
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