PL/pgsql: use cursor to update next record based on a condition from current record
What you want is something this this with lag() and lead()

UPDATE mytble
SET ownby_ctc = false
FROM (
    SELECT
      id_y_q,
      lead(ownby_ctc) OVER () AS lead_ownby_ctc,
      lead(ownby_ftc) OVER () AS lead_ownby_ctc,
    FROM mytbl
    ORDER BY id, year, qrtr;
) AS t2
WHERE t2.id_y_q = id_y_q
  AND t2.id = id
  AND ownby_ctc = 1
  AND ownby_ftc = 0


I'm not sure your copy works and you don't provide an environment but something like this is what you're after.