Your parakeet might be bored or lonely. If you can't afford a bird-cage sized mirror, you might be able to use one from a cosmetics compact. My mom's parakeet, a lifetime ago, chirped happily to his reflection all day!
It seems as though you only have one bird which can be a problem because birds in nature will preen (pluck feathers) from other birds. A solution for this is to put a feather duster in the cage. Your bird should preen the duster instead of over-preening itself. A dollar store duster should work well especially if you can find one a similar color to your bird.
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