From reading the help file of did_imputation, I saw that
pretrends(integer): if some value k>0 is specified, the command will performs a test for parallel trends, by a separate regression on nontreated observations only: of the outcome on
the dummies for 1,...,k periods before treatment, in addition to all the FE and controls. The coefficients are reported as pre1,...,prek. The Wald statistic, pvalue, and
degrees-of-freedom as reported in e(pre_chi2), e(pre_p), and e(pre_df) resp.

- Use a reasonable number of pre-trends, do not use all of the available ones unless you have a really large never-treated group. With too many pre-trend coefficients, the power
of the joint test will be lower.

- The entire sample of nontreated observations is always used for pre-trend tests, regardless of hbalance and other options that restrict the sample for post-treatment effect
estimation.

- The number of pretrend coefficients does not affect the post-treatment effect estimates, which are always computed under the assumption of parallel trends and no anticipation.
I am wondering about how we should conduct a pre-trend testing. Is it that after having pre1,...prek, we conduct a joint null test for the coefficient of pre1 to prek by using
Code:
test (pre1=0) (pre2=0)....(prek=0)?