An unbiased autoregressive conditional intraday seasonal variance filtering process

We develop a new autoregressive conditional seasonal variance (ARCSV) process that captures both the changes in and the persistency of the intraday seasonal (U-shape) pattern of volatility. Unlike other procedures for seasonality, this approach allows for the intraday volatility pattern to change over time, resulting in an increase in the filtering performance over the extant deterministic filtering models. We quantify the gains in the filtering performance by comparing our model with the flexible Fourier form (FFF) model of Andersen and Bollerslev [ J. Empir. Finance , 1997a, 4 , 115--158]. Moreover, the ARCSV model does not create any statistical distortion in the filtered series, as occurs with other de-seasoning processes. We prove that the ARCSV model satisfies the spectral criteria required to be judged as a good filtering process. Monte Carlo simulation results show that the performance of the ARCSV model is superior to the FFF model. In particular, the seasonal adjustment performance of the ARCSV model is robust under the condition that the innovation of the underlying seasonal variance process is large and the daily non-seasonal variance process is misspecified.