I am working with an ARIMA model using data with hourly resolution and a 24 hour cyclical pattern. When I run an ACF on the data I can see a peak at a lag of 24. Does this mean I set p to 24 or am I missing something. I have found this slow to run.
Hourly data is best handled by incorporating daily sums as a predictor series into an ARMAX model. See https://stats.stackexchange.com/search?q=user%3A3382+daily+data for some very powerful examples and interesting discussions
Simple ARIMA models get confused when weekends are different from weekdays and holidays/events have an effect what is often useful is a combined model containg both deterministic structure and memory i.e. exogenous and endogenous . The problem with simple ARIMA or SARIMA models for hourly/daily data is that the model structure is all endogenous (autoregressive).