Using self-organizing maps to adjust for intra-day seasonality

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.