I think there are several approaches to this:
1) Latent variable growth models: A psychometric approach that uses the concept of "latent variables" (in this case, most probably some idea of "confidence") that explains some extent of variability that is introduced by the discrete event and the subsequent trends in stock, since these trends are easily conceptualized as "self-effecting" (that is perturbations in variance can cause long term ascending or descending trends).
2) Regression analysis: There are a number of approaches here: lagged effects, mixed modeling with ARIMA, cumulative effects, etc. etc. Understanding specification of covariance structure in mixed models is essential to capturing ongoing trends in the outcome.
3) Granger causality: similar to the latent variable approach, this is a method of causal inference similar to a dag approach that tries to isolate specific causal pathways.
4) Marginal Structural Models can be deployed when you are longitudinally measuring other markers for a company's performance over time, such as staffing turnover and layoffs, etc. This is because some exposures vary with time and intensity and their lasting affects modify exposures causing a "cascading" effect in the outcome which may be biased.
Personally, I favor 2. I think that the naive approach for detecting a difference in means in a carefully adjusted regression model, especially in the presence of a well identified control group (such as companies of similar stature in the same country not affected by the earthquake) will provide: 1-easily interprettable effects, 2-high power, and 3-greater generalizability. What some may call a bias in estimates of efficacy in-vitro (such as foolish business leadership mistakes causing a decrease in profitability after the earthquake), are actually unbiased in estimates of effectiveness or in-vivo, because you can't tell whether the foolish business decision would have been made had the earthquake not happened. This highlights the importance of having a well identified control group in any analysis you intend to do.