Is it my imagination or do pets really give a sign that they are near you after death?

2 of my closest cats died suddenly about a year apart. At the time they died I was attached to each one the most. They both died tragically. I was distraught and didn't sleep or eat for weeks. I went on a guilt trip both times and I felt they deserved better lives and I failed them. About a week after each died I had signs they came back. I was thinking these signs were to ease the bad experience I was having. Perhaps a sign they were still with me and cared. I know people have the same real life experiences with family members,etc.. So my question asks whether this has been known to happen. Did any one else or do other people have the same experiences? The signs I received were usually at night. I felt small movements on my couch and on my shoulder. Something was walking right on me and brushed up against me. It also happened on my bed and on my feet. Each time I felt the movement I thought it was one of my other (living) cats. I turned around and looked to see which cat came into the room. There was nothing there though! The day after each experience was strange or significant. also. A really dramatic thing happened. A current problem suddenly ended. There were 2 other very obvious signs but I think that explains enough to understand the question.