Time series: how to determine the interval of a relatively stable time? I have time series data, it's about the wind speed and direction at each time (minute, or hour).

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

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. 
 A: Let's talk about speed only first.
I suggest you model this with a lognormal distribution.
log(wind_speed) ~ normal(mean, variance)

This would give you fixed mean and variance for all the years. Now what you can do is make mean and variance depend on the years.
log(wind_speed) ~ normal(avg_mean + trend_mean * t, avg_variance + trend_variance * t)

This is the basic idea. Already some problems, you need variance to be positive so you should use
exp(avg_variance + trend_variance * t)

Now this is a very crude model, that would allow you to say things like

*

*"wind speed hasn't increased on average" (trend_mean = +- 0)

*"wind speed has become more extreme" (trend_variance > 0)

And from here, it gets more interesting. How do you model the relative stability? Well you could go into splines or Gaussian processes, however, for now, I think you have plenty of measurements each your to estimate these and it's not really necessary to go into anything that fancy.
Instead, first just estimate a separate mean and variance per year.
log(wind_speed) ~ normal(avg[year], variance[year])

Then you can plot the estimate of the mean and variance over the years.
So the trick here is to parametrize the distribution and then use something to model the time. Above, two examples are a linear trend, and a  completely separate coefficient for each year.
In between solutions would be splines, gaussian processes, or piecewise linear things like used in Prophet (Facebook prediction framework). But you have many samples (many hours in a year) for few parameters (only two).
Now for the wind direction, this is not just a simple lognormal distribution. The speed isn't either, but you can probably model it that way as a first step. But for this one, not that easy. The main obstacle is that it is periodic. I would suggest periodic splines for this. (just a random google link http://www.mosismath.com/PeriodicSplines/PeriodicSplines.html).
Then, increasing the sophistication (and the number of parameters), you can start looking into correlation between the two. For example, wind from the east could be particularly speedy, but this trend can reverse over time.
Also, by the way, I wouldn't trust the spikes in wind direction that are more prominent especially in 2005-2009. Wind direction is one thing I would trust to be completely smooth in distribution, so this is almost certainly an artifact of measurement or rounding somewhere in the process.
A: 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.
