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Yes, it is possible to create such chart with 4 xAxis headings. For the Quarter and Months you just have to set tickInterval property to months and change labels to desired format. Take a look at this demo:https://jsfiddle.net/BlackLabel/p8nyL2d1/.
As for custom defined time frames for xAxis, you can check out this example:https://jsfiddle.net/BlackLabel/mfjt4gab/. You could use this code to customize it for your case, since I'm not aware what are the exact time frames and what are they supposed to indicate.