Pulse cranberries in a food processor just until roughly chopped; transfer to a clean glass container. Add vodka, simple syrup, lemon peel, orange peel, cinnamon stick, and allspice to cranberries; stir until well mixed. Seal container with a lid and store in a cool dark area, 3 to 5 days, stirring several times a day. Strain through a fine mesh strainer into a glass bottle and refrigerate.