What can we predict from the follow ACF and PACF plots? This is a time series of a wind speed data collected every hour for a month. What can you interpret from the ACF and PACF plots about the trends and seasonal components? Are there any? And which model would be the best fit for this data?
From what I understand is that there is a bit of a trend (looking at the ACF) but no significant seasonal components. And it seems like the ACF is decaying exponentially and the PACF cuts off at lag 3. So the best fit would be the AR(3) model.
But I am not sure at all. Can you please offer your insight as I am a student trying to learn.
Thank you!


 A: The plots have been made on hourly wind speed readings.
Most weather phenomenon like wind, temperature, humidity are continuously changing with time and do not occur spontaneously. This is also seen from the ACF plot you've shared. If the wind speed was 100 km/hr right now, it was 80 km/hr an hour ago and 70 km/hr 2 hours ago; thus indicating that speed picked up gradually and didn't just shoot up to 100 km/hr from still air conditions.
So, in a way the ACF chart does help you by improving your understanding of how current wind conditions can help predict the wind speed after 1 hour. But tha ACF and PACF do not provide sufficient information to be able to deduce which type of time series model will be the best for the problem you're trying to solve.
For trends and seasonality, you need observations that span longer time periods.
A: this is consistent with AR(1) process with weak 24hrs seasonality.
it has a cut off at lag 1 in PACF as well as smooth decline in ACF. There should be some 24hr seasonality too, logically. ACF's wavy shape around 24 hrs and a little bump in PACF around 25 lag are evidence. It's probably not very strong effect-size wise, but should be statistically significant.
