How is the autocorrelation function evaluated?

How is the autocorrelation function evaluated?

• A. Corr(Y_t, Y_{t-k}) for various lags k.
• B. Cov(Y_t, Y_{t-1}) only.
• C. Var(Y_t) across time.
• D. E(Y_t) across time.

Answer: (A)

The autocorrelation function measures how a time series relates to its own past values at different time gaps. For a given lag k, you look at how Y_t and Y_{t-k} move together, which is quantified by the correlation Corr(Y_t, Y_{t-k}). By evaluating this correlation for a range of lags, you obtain the whole autocorrelation function, often using a standardized value between -1 and 1 (and, at lag zero, it equals 1). This approach captures the persistence and patterns in the data over time. The other options focus on a single lag, or on variance or mean over time, none of which describe how the series relates to its past values across different gaps.

The autocorrelation function measures how a time series relates to its own past values at different time gaps. For a given lag k, you look at how Y_t and Y_{t-k} move together, which is quantified by the correlation Corr(Y_t, Y_{t-k}). By evaluating this correlation for a range of lags, you obtain the whole autocorrelation function, often using a standardized value between -1 and 1 (and, at lag zero, it equals 1). This approach captures the persistence and patterns in the data over time. The other options focus on a single lag, or on variance or mean over time, none of which describe how the series relates to its past values across different gaps.