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I am trying to model 3 hour wind speed for Melbourne, Australia. After reading a lot of literature it seems that a subset of auto-regressive models are popular and preferred.

My data does not have any drift or trends and appears to be stationary in mean and variance. So this means I do not have to difference, and will look to use an ARMA model. However there is a strong pattern across days, (3 hourly data, 8 data points for each day, 0:00, 03:00, 06:00....21:00). So The 6th hour of one day is highly correlated with the 6th hour from the last day. The ACF and PAC for 40 (3 hour time intervals is below).

enter image description here

enter image description here My question is what auto-regressive terms to select for the seasonal component? Should I use seasonal differencing (where the season is the day?)?

ARIMA(p, d, q) × (P, D, Q)S

What is the best way of going about this? I know for the non seasonal terms I can refer to the ACF and PAC but how does this interact with seasonal factors?

ARIMA(p, d, q) × (?, ?, ?)S

I will continue to search these forums but would love some input from forum on this matter.

I hope this is clear. Any help or comments would be highly appreciated!

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