People on the autism spectrum tend to have sensory processing differences. Some are highly sensitive to loud noises, colors, textures, or other sensory stimuli and are called "sensory avoiders" because they try to get away from stimuli that are too disturbing. Others on the spectrum are called "sensory seekers" because they pursue high levels of sensory input by, say, eating spicy foods or running around and crashing into things. Sensory seekers seem to need proprioceptive feedback in order to calm down and re-equilibriate.
***EDIT: I should probably post this information here. Most children with sensory differences have some sensory seeking and some sensory avoiding behavior. See discussions in the comments for more information.***
There are places that sell compression vests and jackets, sometimes with weights. Those can run about $50-150. Compression vests are more for long term wear, say during the school day to help sensory seekers feel secure and able to concentrate.
This is a quick fix that works for us when my 3 year old can't seem to calm himself. I can't always drop everything and give him deep pressure massage for 20 minutes if he's freaking out, and this is another option.
Note: if you feel the urge to leave a comment or send me a note about how you heard that autism is caused by vaccines, poor nutrition, gluten intolerance, food additives, or poor parenting... just don't.