What exactly is meant by "constant autocorrelation structure" in the definition of stationarity of a time series? I have come across the term "constant autocorrelation structure" in every definition of stationarity but I have not been able to find an explanation of this phrase. I know that autocorrelation refers to present values being dependent on past values but can anyone please elaborate on what a "constant" autocorrelation structure looks like?
Secondly, can I say that seasonality and trends are all conceptually subsets of autocorrelation? Can there be a situation where there is a trend and seasonality but zero autocorrelation?
 A: "Constant" refers to the requirement that the pattern of autocorrelation does not change over time. So the strength of the dependence of, say, 2020 and 2014 is the same as that between 1990 and 1984. When you for example have an AR(1) process
$$
y_t=\phi y_{t-1}+e_t,$$
the autocorrelation coefficient of $y_t$ and $y_{t-j}$ is well-known to be $\phi^j$. This depends on the lag $j$, but not on when we look at that lag. If $\phi$ were to change over time, as in $\phi=\phi_t$, the condition would be violated.
For the second question, consider $y_t=\delta t + u_t$, a trending process of time $t$ with slope $\delta$ and an error term $u_t$ which we assume to be iid. The autocorrelation function does not show any autocorrelation, as
\begin{eqnarray*}
Cov(y_t,y_{t-j})&=&E[(y_t-E(y_{t}))(y_{t-j}-E(y_{t-j}))]\\
&=&E[(\delta t + u_t-\delta t)(\delta (t-j) + u_{t-j}-\delta (t-j))]\\
&=&E[u_tu_{t-j}]\\
&=&0
\end{eqnarray*}
You could run the following code to get such a "trend-stationary" process.
T_end <- 100
t <- 1:T_end
delta <- 2
u <- rnorm(T_end)
y <- delta*t+u
plot(t, y, type="l")

