INTRADAY VOLATILITY OF A STOCK INDEX: CONDITIONAL PERSISTENCE AND SPECTRAL DECOMPOSITION OF VARIANCE BY TIME SCALES

Abstract

This study investigates intraday volatility regularities and their distribution across temporal scales by combining conditional variance modeling with frequency-domain decomposition. A one-minute intraday time series is employed, collected between November 3 and December 12, 2025, standardized to the regular trading session (10:00–18:00), totaling 24 trading days with 481 observations per day after time validation and duplicate removal. Returns are computed as one-minute logarithmic differences. In the econometric stage, estimated models indicate high persistence and slightly superior informational adjustment, with no statistical evidence of sign-based asymmetry. In contrast, a statistically significant response to shock magnitude and elevated persistence in volatility dynamics are observed. Diagnostics on standardized residuals show no remaining autocorrelation in the standardized series, but suggest residual heteroskedasticity at intraday horizons of 20–60 minutes.In the spectral stage, the intraday variance distribution is estimated for each trading day in the frequency domain using a smoothed periodogram, after controlling for intraday patterns and mitigating extreme observations. Subsequently, relative power is computed for predefined periodicity bands (2–8, 8–16, 16–32, 32–64, and 64–128 minutes), with daily normalization. Results indicate a systematic predominance of fast components (2–8 minutes), with secondary and variable contributions at intermediate scales (8–32 minutes) and occasionally higher participation of slow scales (above 32 minutes).The findings suggest that, within the analyzed window, intraday risk is primarily concentrated in rapid fluctuations, while conditional modeling points to high persistence and responsiveness to shock magnitude, without sign asymmetry.