Time-Varying Periodicity in Intraday Volatility

We develop a nonparametric test for deciding whether return volatility exhibits time-varying intraday periodicity using a long time-series of high-frequency data. Our null hypothesis, commonly adopted in work on volatility modeling, is that volatility follows a stationary process combined with a constant time-of-day periodic component. We first construct time-of-day volatility estimates and studentize the high-frequency returns with these periodic components. If the intraday volatility periodicity is invariant over time, then the distribution of the studentized returns should be identical across the trading day. Consequently, the test is based on comparing the empirical characteristic function of the studentized returns across the trading day. The limit distribution of the test depends on the error in recovering volatility from discrete return data and the empirical process error associated with estimating volatility moments through their sample counterparts. Critical values are computed via easy-to-implement simulation. In an empirical application to S&P 500 index returns, we find strong evidence for variation in the intraday volatility pattern driven in part by the current level of volatility. When market volatility is elevated, the period preceding the market close constitutes a significantly higher fraction of the total daily integrated volatility than is the case during low market volatility regimes.