If the sweater was an apparition, how was your grandfather able to throw it out?
Let me be clear here. I really, honestly lived in a "haunted" house. If there weren't other witnesses to what happened, I would never tell it. I'm predisposed to believe you. But something is wrong in your story. Were you very young when all of this happened? Perhaps you're forgetting some of the details.
Let me tell you one story of mine. My brother Mike was spending the evening at a mutual friend's house, named Kelly. I was in bed when I was awakened by headlights shining on the wall above my bed. I got up, looked out into the driveway, and saw my Mike get out of his friend Rick's car. I heard Mike and Rick talk, say goodbye, and saw Rick leave. I then heard my mother say, "Mike's home, I'll let him in." Mom then went and unlocked the front door. Mike came in without speaking (normal for him) and started up the stairs, where I was waiting for him. Mike climbed 3 or 4 stairs, looked up at me, and disappeared. I thought I must have been still asleep and dreaming and went back to bed.
Next morning, when I woke up, I remembered what happened and went across the hall to see if Mike was really home or not. Mike was not in the room and his bed wasn't slept in. I then went downstairs and began helping my mom with breakfast. I set 4 places at the table. My mother said, no, set 5 places. I said, no, it's you, me, Dad, and James. Mom said, and Mike. I said, Mike's not here. Mom said, yes he is and you know he is here. You were waiting for him at the top of the stairs when I let him in last night.
Now, at this point my mother went upstairs and checked Mike's room to no avail. My dad also was confused because he watched Mom let Mike in the door. Mom called the house of the person who dropped Mike off the night before and he and his mother both confirmed that Mike never left their house, neither did Rick, and that Rick did not drop Mike off at home. The mother confirmed numerous times that Mike had spent the night at her house.
This kind of stuff happened all the time. Even the neighbors had experiences at our house with Mike~when he wasn't really there. It all stopped when Mike moved out.
Now, our family had experiences when I was little and my grandfather lived with us. The experiences stopped after he died.
So, as I say, I'm predisposed to believe you but your story isn't specific enough. It just doesn't make a lot of sense. Tell it again, from the beginning, and don't leave anything out.
And I'm not going to say what it was re: my brother or my grandpa, i.e., demons or ghosts, what have you, because I simply don't know. I do believe that someday we will discover perfectly natural explanations for all of this stuff.