matlab - Measure the STD of RMSE -

i'm working on time series forecasting problem , confirm if makes sense compute standard deviation of root mean squared error. if so, correct way?

std_test = std(sqrt((y_real-y_pred).^2)) 

also, imagine output of model 100, rmse 20 , std 10. means real value between [70,120] ?

the term y_real-y_pred vector of errors. expression squares each element of it, , sqrts each element of it, having effect of abs(). std() run on vector of errors. thus, computing s.d. of (absolute) error. meaningful metric, unlikely after. try:

e = y_real-y_pred; mse = mean(e.^2); rmse = sqrt(mse); sd = std(rmse); 

that compute want. however, since rmse scalar value, value sd zero, answer first part of question, no not meaningful. meaningful @ s.d. of error itself:

sd = std(e); 

rmse , s.d. related distinct.