Either your wife is playing a prank or you have a very real problem of a grave order. This wasn't done by cats, and I think the number 13 is important.
I think arson is inferred.
Have you ever even seen green-headed wooden matches? I think I have, but many, many years ago. A crime lab may be able to identify the source and the age.
Someone wants you out to get the house or something in it, or they are targeting you, as a killer of probable insane mentality.
Have there been any recent mysterious fires in your area? Have you had any quarrels? Testified in any court cases? Filed any complaints?
I'd get a security camera and not tell anyone but your wife. And I'd tell the sheriff about the intrusion and see if he's had any similar reports.
Did you photograph the match arrangement?
I won't rule out a ghost, but usually doubt such things without added evidence. I think this is human activity. And it isn't funny. Be very careful. Keep us posted.
And ghost/poltergeist or not, I'd offer up very sincere prayers for your safety. This is really not funny, and I hope the usual jokers will respect that.
Be especially careful around the 13th day/night after the matches were left. Is there any police patrol activity at all in your area? Can tney increase the frequency of those for awhile? Stake out your house at a distance?
Check your roof and basement for signs of entry and the attic.
Go armed for awhile and watch your cats when you're awake. They'll tell you if they detect anything they find unusual, via body language. If it's spiritual, they may wail, hunch their backs, come to you for comfort, etc. May do that for an ordinary intruder, too. Or, hide.
This isn't cats or coyotes, and I don't think anyone is going to blame it on George W. Bush, either.

The cats probably limit the liklihood of pack rats, too. Do your cats ever bring you dead mice they've killed? My late mother used to have a cat that did that, for admiration and approval. I don't think she ever ate the rats or mice. Probably just sport hunted.
Do keep us posted. I'm very interested.