1. A character input prediction apparatus comprising: a first operation input unit configured to obtain information of a first character input operation that is performed by a user using a character key layout display in which a plurality of character keys are arranged; a dictionary storage unit configured to store a dictionary including a plurality of candidate character strings; a character key layout management unit configured to store a character key layout showing the arrangement of the plurality of character keys in the character key layout display; a first indication movement detection unit configured to detect a first indication position and a first indication direction in the character key layout display from the information of the first character input operation, the first indication position showing a position of the first character input operation, and the first indication direction showing a movement direction of the first character input operation; a first filter generation unit configured to determine a vector having the first indication position as a base point using the first indication position and the first indication direction, and determine a first character range using the character key layout, the first character range including a plurality of character keys located in an extending direction of the vector; and a dictionary search unit configured to search the plurality of candidate character strings included in the dictionary, for a predictive character string that includes a character corresponding to any one of the plurality of character keys included in the first character range.