The existence of an intra-day seasonality component in financial market variables (volatility, volume, activity, etc.) has been highlighted in many previous studies. To remove this cyclical component from raw data, many researchers use the intra-day average observations model (IAOM) and/or some smoothing techniques (e.g. the kernel method). When the seasonality is related to the first moment (the conditional expectation) and involves only a deterministic component, the IAOM method succeeds in estimating the periodicity almost perfectly. However, when seasonality affects the first or the second moment (the conditional variance) of the data and contains both deterministic and stochastic components, both IAOM and the kernel method fail to capture it. We introduce self-organizing maps (SOM) as a solution. SOM are based on neural network learning and nonlinear projections. Their flexibility allows seasonality to be captured even in the presence of stochastic cycles.

Event studies are an important tool for empirical research in Finance. Since the seminal contribution of Fama et al. [Fama, E., Fisher, L., Jensen, M., Roll, R., 1969. The adjustment of stock prices to new information. International Economic Review 10, 1–21], there have been many enhancements to the classical test methodology. Somewhat surprisingly, the estimation period has attracted less interest. It is usually routinely determined as a fixed window prior to the event announcement day. In this study, we propose a test that reduces the impact of potentially unrelated events during the estimation period. Our proposition is based on a two-state version of the classical market model as a return-generating process. We present standard specification and power analyses. The results highlight the importance of explicitly controlling for unrelated events occurring during the estimation window, especially in the presence of event-induced increase in return volatility.