A method performed by a pen or a pen detection apparatus that detects the pen, the method includes: acquiring a pen pressure level according to a force applied to a pen nib of the pen; generating a pen-down event or a pen-up event based on a result of comparing the pen pressure level and a pen pressure determination threshold; acquiring a proximity value indicating a positional relationship between the pen and the pen detection apparatus from a proximity detector provided on one of the pen and the pen detection apparatus; and updating the pen pressure determination threshold based on the pen pressure level when the proximity value indicates that the positional relationship between the pen and the pen detection apparatus satisfies a predetermined relationship.