In among time series data, Methods of ARDL is the most appropriate method for short times of data. But 15 years for 11 variable is very short time to estimate ARDL method. I suggest you to change your data from time series to panel data.
Obviously you have no theoretical model for your problem. It seems that you want to explain an economic variable and took (by accident) 10 variables which may have an influence on that variable. Then you want to throw these variables into an econometric method which is modern. But econometrics is called so because it is connected to economics. Without economics the method is nothing. Therefore, one should always have an economic model (hypothesis) before applying a statistical method. This model need not be from a text-book, you can create it yourself by carefully thinking through the problem. So you could find out which variables are likely to be most relevant and if it is reasonable to assume lags (and which lags). One should also try to find out which relations (functions) and transformations are appropriate. Then it may be possible to test at least parts of your model - even with 15 data only.