Sort cranberries, discarding any bruised or decayed fruit. Rinse berries.
In a 3- to 4-quart pan over medium-high heat, bring 1 cup water, cranberries, sugar, apricots, currants, raisins, and vinegar to a boil, stirring often. Reduce heat and simmer, stirring occasionally, until cranberries begin to pop, 5 to 8 minutes.
Meanwhile, pull off peel and white membrane fibers from tangerines; discard peel and fibers. Separate segments and coarsely chop, discarding seeds. Add tangerines and juice to pan; simmer to blend flavors, 2 to 3 minutes.
Stir in pecans. Serve at room temperature or chilled.
Nutritional analysis per 1/4 cup.