Frequency-Dependent Order Flow Information:High-Frequency Foreign Dominance and the Retail Swing Puzzle

Standard analysis of daily order flow conflates distinct groups of market participants operating on radically different time horizons---from high-frequency algorithmic reaction to multi-week institutional rebalancing. This paper deconstructs the temporal architecture of market cap-normalized order flow in the Korean stock market using three complementary methodologies. First, applying Maximal Overlap Discrete Wavelet Transform (MODWT), we decompose investor flows into distinct frequency scales, revealing that foreign investors exhibit maximum predictive power at high frequencies (2--4 days, Sharpe ratio = 9.24), while individual investors show normalization-sensitive medium-frequency patterns (8--16 days) that reflect a mixture of volatility exposure and genuine predictive content. Second, cross-spectral analysis uncovers frequency-dependent lead-lag relationships that collapse during market stress: foreign investors lead retail by 0.31 days during calm periods, but this advantage vanishes entirely when volatility exceeds the 75th percentile. Third, we document a striking small-cap turn-of-month anomaly---foreign buying surges 219\% in the smallest quintile versus declining 39\% in large caps---that directly contradicts the index arbitrage hypothesis. Our findings challenge conventional wisdom about ``patient'' foreign capital and ``noisy'' retail traders, demonstrating that time is the missing dimension in order flow analysis.