What is the primary characteristic of a variable exhibiting autocorrelation?

The primary characteristic of a variable exhibiting autocorrelation is that it correlates with itself over time. Autocorrelation occurs when the value of a variable at one point in time is related to its values at previous points in time. This relationship indicates a patterned relationship in the data, meaning that knowing the value of the variable at one time can give information about its past values. This is especially important in time series analysis, where understanding these dependencies can be crucial for forecasting future values or understanding the dynamics of the time series.

In contrast to this, other options do not capture this essential feature. A variable with stationary variance refers to the statistical property of variance rather than the presence of correlation over time. Following a random walk implies that past values do not predict future values, which contradicts the concept of autocorrelation. Being unrelated to other variables suggests independence rather than the self-relation characteristic brought forth by autocorrelation. Therefore, the correct answer correctly identifies the key nature of autocorrelated variables.