are you having these ids in the activity which holds this fragment ?
R.id.timerStartDown,
R.id.timerStopDown,
R.id.chronometerDown
Else if it thr in ur R.layout.fragment_timer_countdown, try this
countdownStart = (TextView) view.findViewById(R.id.timerStartDown);
countdownStop = (TextView) view.findViewById(R.id.timerStopDown);
countdownChronometer = (Chronometer) view.findViewById(R.id.chronometerDown);
since u r inflating the layout in view as
View view = inflater.inflate(R.layout.fragment_timer_countdown, container, false);