The Brains Trust - 2016, page-13392

Yes no problem. You can open an account in Australia with a bank that does online broking. As you are a non-resident, the only tax you have to pay is withholding tax of 10% on interest earned, not on capital gains. You don't need to submit an Australian tax return. You should double check this information, perhaps with the bank you use for the service, as this is my just my honest opinion, and the Australian Tax Office does not like to spell out clearly their own rules. Good luck!