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I have time series data, it's about the wind speed and direction at each time (minute, or hour).

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If I plot the histogram of the data by grouping in years, the histograms would look like this

enter image description here

It can be seen that the distribution is not stable across the years. And recent year is a little bit more smoother and more stable.

Question: How can I determine the interval?

For example, maybe year 2005 - 2013 is more stable.


My thoughts: The wind data has a 1-year period. So for each year, I can define a metrics for the wind speed, direction and their correlation, for their stablity (maybe simply mean and std). Then I can plot the year-stability, and by defining a proper limit, I can get the time in which the data are more stable.

Question: Are there standard approaches for this kind analysis?

I don't want to re-invent the wheel.

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  • $\begingroup$ Why would you expect wind speeds to be stable across the years? Climate change would suggest there won't be stability across the years. You could potentially control for this however by including temperature as a Xreg in an ARIMAX model. Why do you need stability across the years? What are you trying to achieve? (Also you have 4 yearly effects such as el Nino and el Nina who's exact impact depends on the time they last for) $\endgroup$ – Morgan Ball Mar 24 '17 at 12:31
  • $\begingroup$ @MorganBall Well, for one thing, it doesn't have to be extremely very stable. However, as you see from the data above, it is relatively stable across these years. 1. Given the assumption that the distribution is weakly stable, the unstability may arise from observation error, surrounding changes, equipment changes etc, which makes the data useless. I want to exclude this data, so I want to know the effective time span for the data. 2. If the climate did change systemtically, the approach that I'm asking for, may help me to seperate them into different stages. $\endgroup$ – cqcn1991 Mar 24 '17 at 14:59
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I have not enough reputation to comment it. So I write an answer, maybe help you.

What you want is the stability, or stationary. There are mean stationary, variance stationary and covariance stationary. You can find this in time series book. If i have more time, i will describe it for you. Wait for another day to add it.

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  • $\begingroup$ Thanks! I'm reading a time series book now, but I'm not very good at this topic. $\endgroup$ – cqcn1991 Mar 24 '17 at 14:50
  • $\begingroup$ You can visit this site:people.duke.edu/~rnau/411diff.htm, It defines the stationary time series, trend-stationary and difference-stationary. $\endgroup$ – wolfe Mar 25 '17 at 0:04

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