I applied quantile regression on some data and did it for tau = 0.25, 0.5, 0.75. After i got the estimates of each model, i did some cross validation on my hold out data. When i used the estimates for my hold out data i calculated in what quantile each of my independent variables lie, 25%, 50% or 75%. For instance if my x-values (independent variable) looks as follows,
x -> 1 2 3 4 5 6 7 8 9 11 10 12 13 14 15
I calculated my quantiles using the R function
cut(x,4) and got the following quantile ranges (0.986; 4.49], (4.49; 8], (8; 11.15], (11.15; 15]. I then divide the x vector into the correct quantile range and depending on what range it falls determine what quantile regression estimates i use, either 0.25, 0.5 or 0.75. So for the x-values 1 to 4 i will use the estimates of the 0.25, 5 to 8 i use the estimates of 0.5 and the rest i used 0.75.
I do get very accurate results, i.t.o. forecast accuracy, but can someone please tell if this is the correct way to do my quantile cross validation.