How many lags in Q-statistic?

Question

How many lags should one use a Ljung-Box test for the returns on 1320 daily price quotes? Is there a rule of thumb? What is exactly the impact in the end result of misuse of lag number?

Answer 1

To the first part of your question there is no general answer I think, because it's a question about the "correct" null hypothesis of a test. Maybe you would be interested only in a short-run effect, so just one lag might do. Or you suspect a yearly/seasonal correlation, then you might need the 250th lag, too. So it depends.

As a rule of thumb for this sample size and for such financial data I would personally view anything above lag 20 as awkward, but it's a matter of taste.

With respect to the consequences of misuse, if you include too many lags the test loses power. So it might not reject the null of no correlation if only the first lag is relevant but you include 250 lags. On the other hand, if you only test the first lag(s) but the action is in the 20th, then the chosen hypothesis itself might not be adequate or reasonable (also inducing non-rejection).

Answer 2

There are a couple of thumb rules. Matlab's lbqtest help doc cites:

• Tsay's log(1320) rule
• Box-Jenkins' min[20,1320-1] rule

References:

• Tsay, R. S. Analysis of Financial Time Series. 2nd Ed. Hoboken, NJ: John Wiley & Sons, Inc., 2005.
• Box, G. E. P., G. M. Jenkins, and G. C. Reinsel. Time Series Analysis: Forecasting and Control. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.