What is a true statement about autoregressive models of order one, AR(1)?

In an autoregressive model of order one, commonly denoted as AR(1), the model is represented as expressing the current value of a time series as a linear combination of its immediately preceding value and a random error term. A key aspect of AR(1) models is their reliance on a single lagged value, which influences the current outcome.

A notable property of a stationary AR(1) process is that it converges towards a mean over time, often indicating that the autocorrelations diminish as the lag increases. Specifically, the autocorrelation function of a stationary AR(1) model is given by a formula that expresses it in terms of the parameter of the model, which typically implies that the lag k autocorrelation declines exponentially with increasing k.

In the context of the choices presented:

• A true AR(1) model is indeed not characterized as a meandering process, as it implies a steady convergence rather than random wandering.

• While a stationary AR(1) model is a set of specific conditions, it does not encompass the behaviors exhibited by white noise or random walk models; instead, these models represent distinctly different statistical behaviors.

• The statement about the lag k autocorrelation being always non-negative is also incorrect; the values