Rinse kumquats; cut in half and remove seeds. Place in a food processor; process until coarsely chopped., In a Dutch oven, combine kumquats and water. Stir in pectin. Bring to a full rolling boil over high heat, stirring constantly. Stir in sugar; return to a full rolling boil. Boil and stir 1 minute., Remove from heat; skim off foam. Ladle hot mixture into seven hot half-pint jars, leaving 1/4-in. headspace. Remove air bubbles and adjust headspace, if necessary, by adding hot mixture. Wipe rims. Center lids on jars; screw on bands until fingertip tight., Place jars into canner with simmering water, ensuring that they are completely covered with water. Bring to a boil; process for 10 minutes. Remove jars and cool.