Autocorrelation, definition, estimation, and the returns puzzle
Define the autocorrelation function of a stationary time series and its sample estimate. How would you test whether a return series is serially correlated? And what does it mean that stock returns show near-zero autocorrelation while their absolute values show strong, slowly decaying autocorrelation?
Show a hint
Under the null of white noise, sample autocorrelations at each lag are approximately . For the puzzle: does zero correlation imply independence?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.