Seasonal long memory in intraday volatility and trading volume of Dow Jones stocks

It is well known that intraday volatilities and trading volumes exhibit strong seasonal features. These seasonalities are usually modeled using dummy variables or deterministic functions. Here, we propose a test for seasonal long memory with a known frequency. Using this test, we show that deterministic seasonality is an accurate model for the DJIA index but not for the component stocks. These still exhibit significant and persistent periodicity after seasonal de-meaning so that more evolved seasonal long memory models are required to model their behavior.