Rinse the pork shoulder under cold water and pat dry with paper towels. Place skin-side up in a large roasting pan and score several slits into the fat using a sharp knife
In a small bowl, combine the achiote paste, olive oil, salt, onion powder, paprika, pepper, garlic, rosemary and thyme.
Using your hands, rub the paste all over the pork shoulder, working the mixture into the slits and under the skin, along with the olives. Cover with plastic wrap and let marinate for a minimum of 3 hours and up to 2 days.
When ready to begin cooking, remove the meat from the refrigerator and let it sit for up to 30 minutes to bring to room temperature. Adjust an oven rack to the lowest position and remove the other racks if needed. Preheat the oven to 350 degrees F.
Pour the chicken stock or water into the pan so that it goes about an inch up the side of the pork. Roast, uncovered, until the meat is tender and the skin is dark brown and crisp, about 4 hours. Allow the meat to rest a minimum of 15 minutes before slicing. Transfer the slices to a serving platter.