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).

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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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