If the value of y at time t relates to its value at time t - 1, what type of autocorrelation is present?

When we discuss autocorrelation in the context of time series data, we are essentially looking at how the value of a variable at a certain point in time is related to its past values. In this case, if the value of y at time t is directly related to its value at time t - 1, we are identifying a first-order autocorrelation.

First-order autocorrelation specifically refers to the correlation between observations that are one time period apart. For example, if we consider a sequence where each term is influenced or dependent on the term that immediately preceded it, this creates a first-order relationship. In various fields such as economics or finance, modeling this first-order autocorrelation can capture trends or patterns that occur from one period to the next.

In contrast, zero-order autocorrelation would not involve any time-dependent relationships beyond a single observation. Second-order autocorrelation would concern relationships between values that are two periods apart. Non-linear autocorrelation suggests a more complex relationship that isn't strictly linear and would involve different statistical modeling techniques. Thus, the mention of time t and time t - 1 clearly points to a first-order relationship, validating that the choice made is indeed correct.