You are given observational/experiment-like panel data as three equal-length arrays: - `period[i]`: an integer time period label for observation `i` (e.g., -2, -1 are pre; 0, 1 are post). - `group[i]`: 1 if the unit is in the treatment group, 0 if in control. - `outcome[i]`: numeric outcome. Tasks: 1) **Difference-in-differences (DiD)**: compute the DiD estimate using: - pre period = the **latest** pre period (`max{period < 0}`) - post period = the **earliest** post period (`min{period >= 0}`) Define: - \(\bar{Y}_{T,post}\), \(\bar{Y}_{T,pre}\), \(\bar{Y}_{C,post}\), \(\bar{Y}_{C,pre}\) as the mean outcomes for Treatment/Control at the chosen post/pre periods. - \(\text{DiD} = (\bar{Y}_{T,post}-\bar{Y}_{T,pre}) - (\bar{Y}_{C,post}-\bar{Y}_{C,pre})\). 2) **Parallel trends / pre-trend validation**: given a numeric `threshold`, validate that treatment and control follow similar trends in the pre period by checking: - For each pre period \(t\), compute \(d_t = \bar{Y}_{T,t} - \bar{Y}_{C,t}\). - The pre-trend is considered valid if `max(d_t) - min(d_t) <= threshold` across all pre periods. Output: - Return the DiD estimate (float) and a boolean indicating whether the pre-trend validation passes. Assumptions: - There is at least one pre period and one post period. - Means are computed over all rows matching the period/group filters.