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

At lag $h$, the plot shows the sample autocorrelation functionUnder a white noise process, each fixed nonzero-lag sample autocorrelation is approximately $N(0,1/n)$, so the dashed pointwise $95\%$ reference lines are approximately $\pm 1.96/\sqrt{n}$.

The first nonzero-lag bar is well above the upper line, which contradicts the zero autocorrelation expected from white noise. Since the plot then largely cuts off, an moving-average process of order one is a plausible model; with the sampling interval as the time unit this is an $\mathrm{ARMA}(0,1)$ model.