= Solution
A <nonstationary process> has a statistical law that changes with the time origin. In the weak sense, this includes a time-dependent mean or <variance>, or a <covariance> that depends on the two times separately rather than only on their lag. A <strictly stationary process> requires invariance of every <finite-dimensional distribution> under a common time shift.
In the preceding plots, series $1$ suggests a stochastic trend or changing level, and series $4$ suggests a deterministic seasonal mean. These are the intended nonstationary examples. A plot alone cannot prove either conclusion: in particular, a stationary random-phase <sinusoid> can have a seasonal-looking trace and an oscillatory ACF. The interpretation of series $4$ as nonstationary concerns a seasonal mean tied to calendar time.
Three standard responses are to remove a fitted deterministic trend or seasonal mean; to use regular or seasonal <differencing> for an appropriate trend or seasonal component; and to stabilize a changing <variance> by a transformation or explicit seasonal scale model. For example, logarithms or a <Box–Cox transformation> can address level-dependent <variance>. The operation should match the source of nonstationarity; <differencing> a varying <variance> does not generally make it stationary.
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