There is nothing to stop you renting a permanent (long-term) apartment in Spain from legal point of view, but most landlords only let to people with Spanish job, or with residence permit such as TIE with income such as pension.
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Economic means may be accredited by presenting cash, traveller's cheques, a credit card accompanied by a bank account statement, an up-to-date bank book, or any other resource that accredits the amount available, such as a credit statement regarding the card or bank account.