Autocorrelation and What It Reveals About a Return Series

A return series can be unpredictable in direction and highly predictable in the size of its moves, and these are separate claims.

Autocorrelation measures how strongly a series is correlated with its own past values at a given lag, and in a return series it separates two very different questions: whether the direction of the next move is predictable, and whether the size of the next move is. Daily equity returns generally answer the first question close to no, while the second question, about the size of moves, has a clear and persistent answer.

The autocorrelation function computes the correlation between a series and itself shifted by one lag, two lags, and so on, producing a full profile of how the series relates to its own recent history rather than a single number. The Ljung-Box test checks a set of lags jointly, asking whether any meaningful serial correlation exists across the whole group rather than testing each lag in isolation, which avoids inflating the false positive rate that comes from testing many individual lags one at a time.

This distinction, a full profile of correlation across many lags rather than a single number, is why the ACF is typically presented as a plot rather than a table, and why the Ljung-Box statistic built on it is the standard first test run before deciding a return series has no exploitable serial structure at any horizon worth checking.

Autocorrelation in raw daily returns at short lags is typically close to zero, a result broadly consistent with the weak form of the efficient market hypothesis, which holds that past price data alone should not predict future direction once the market has absorbed it. This does not mean every return series is perfectly unpredictable at every horizon or in every regime, but the baseline finding across liquid, widely traded instruments is a direction that is very hard to forecast from lagged returns alone.

Interviewers use this as a check on candidates who claim to have found a simple return-predicting signal from lagged prices: the burden is on the candidate to explain why their signal survives where decades of similar attempts on liquid instruments generally have not, rather than assuming novelty.