Parrots are noisy animals. It is not normal, however, for a parrot to scream incessantly for hours on end. This is not a happy bird (and it will not have a happy family.)
Causes of excessive screaming
Screaming by unhappy birds can usually be traced back to an underlying problem that is stressing the bird. These stresses include:
A change in the family makeup
Loneliness or boredom
A change in the environment
Fear
Jealousy
Remember that some screaming is normal behavior for a parrot. Your goal should NOT be to eliminate all screaming and loud squawking, but to reduce the screaming to a tolerable level.
Make sure its basic needs are being met
Reestablish the humans as higher ranking
Keep track of the occurance of all screaming episodes, including the moods of the people and the bird before, during, and after the episode. With this information, hopefully the cause of the screaming can be identified and eliminated.
From the parrot's perspective, getting any attention while it is screaming will be a reward. Yelling, hitting the bird or the cage, leaving the bird isolated, spraying it with water, or withholding food will only increase the stress on the bird and either make the screaming worse, or the bird will turn to another unacceptable behavior such as feather picking. Some parrots may actually like you to yell back since they love drama and the yelling becomes a reward.
Give positive reinforcement, i.e., giving something good to the bird when it behaves correctly. This could be a special toy, a food treat, and verbal praise. These are rewards. Do NOT use them to bribe the bird into better behavior.
Teach the bird to substitute the desired behavior for the undesired one. For instance, teach the bird to talk instead of scream. Then reward the desired talking behavior. Consistency is absolutely necessary
If the bird is screaming due to loneliness it may be helpful to provide an alternative outlet for the bird's energy. Flapping sessions, showers, a new toy, or leaving the television or radio on can all help relieve pent-up energy.
Remember, parrots use vocalizations as warnings and as ways to find the rest of the flock when separated from it. Screaming can often be prevented from starting by simply answering the parrot when it calls to you, and letting the bird know when you are leaving and have returned.