A <weakly stationary process> has a constant finite mean and covariance $\operatorname{Cov}(X_t,X_{t+h})$ depending only on lag $h$. The plotted process is not stationary: it has a declining trend and a pronounced oscillation of period about $25$, so its mean depends on time.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 218 / 6 / a / Solution

A process $(X_t)_{t\in\mathbb Z}$ is <weakly stationary process>[weakly stationary] when it has finite second moments, a time-independent mean $\mathbb E X_t=\mu$, and an <autocovariance function>
$$
\operatorname{Cov}(X_t,X_s)=\gamma(t-s)
$$
that depends only on the lag.

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 218 / 2 / a / Solution

A weakly stationary process has constant finite mean and covariance depending only on lag.


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