ACF and PACF provide tests of a single autocorrelation coefficient. The Ljung-Box is a joint test for all autocorrelation coefficients up to the lag m. There is no clear rule on how to select the number of lags. You have to keep in mind that the power of the test goes down as you increase the number of lags. On the oder hand, you don't want to choose too few either. It also depends on the sample size. I prefer to look at all lags from (p+q) (because it is chi-square m-(p+q) ) to some max lags instead of 1, 12, 24, say. If you reject at 6 lags you may not see it because the power at 12 may be low. I like to see how the test evolves as we increase m. ACF and PACF are useful if we reject because it helps choosing a better process.

Pierre

On 31/03/11 05:10 AM, Sam Sam wrote:

Dear all:

Afer estimating ARIMA, It is convenient to test if residual is white noise in Gretl.
But I have two questions:
1. Gretl provide Ljung-Box Q statistic, residual acf and pacf.
   Some paper test lag of 1 to 24,
   Some only test lag of 6, 12, 18, 24.
   Some only test lag of 1, 12, 24.
I am confused about the lag of Q statistic, acf and pacf.

2. Some paper test ARIMA residual by Q statistic, residual acf and pacf.
   But some just test by Q statistic. Ignoring residual acf and pacf.
  Are residual acf and pacf necessary when testing ARIMA residual ?

Thanks a lot
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