Since your degrees of freedom is low, I would be a bit worried.  Further the Jarque-Bera test is an asymptotic test, so with your small sample, it might be giving you the wrong outcome.  Maybe do a second test for normality or check with a histogram?

Wooldridge explains that one can assume asymptotic normality when the OLS  assumptions about the error term are valid, but I don't think you can invoke asymptotic anything when you only have 16 observations (maybe I misread your comment and you have quarterly or daily data?)

Hi Mary, I have annual data and after applying the optimal lags, I have a total of 33 observations (not 16) and my degree of freedom is mostly 1. I thought the Jarque-Bera test is a normality test, or which second one are you suggesting? Any help will do at this point....or do you use Stata?

Dear Ngo,

Normality is not a big issue in ARDL because even if normality is solved the estimates does change that much. You know this of course from your elementary statistics that JB is for a large sample n=100 so if you try to add dummy using standardized residual to identify the outlying data point and the results do not improve just go ahead a use Newey-west  estimator (ignore mentioning JB) since all the nonspherical errors have been contained

@Ngo 

Am glad that you understood my write-up despite my typing errors. You are good in typing, and I suffer when my GA's are not available. I dictate, and they handle the rest. I will attempt to forward to you a link or a summary from Monte Carlo studies and a dissertation by a Nigerian in London concerning ARDL. Hopefully, my next week!! 

Thanks Prof. Arinze!

diagnostic checks for single-equation error-correction and autoregressive distributed lag models

Could you please share how you went about testing for ARCHLM and JB normality test after ardl estimation. I have stata 14. Thank you.