Unless your supporting parent who can be claimed as your dependent, you can only get HOH status if a child is living with you.
I'm single, live alone, and have no dependents. Can I file as head of household?
No. To use this filing status, you must have paid over half the cost of keeping up a home for you and a child or other qualifying person for over half the year. For detailed information, refer to Tax Topic 353, What is Your Filing Status, or Publication 501, Exemptions, Standard Deduction, and Filing Information.