As an adjective it can mean periodical, but in a sentence like above, it is impossible for someone to mean our periodical, that's why it is not accepted. Περιοδικό in greek actually means periodical (because magazines come out periodically e.g. once a month) but saying το περιοδικό μας always refers to a magazine, not just any other periodical thing.
pe·ri·od·i·cal ˌpirēˈädək(ə)l/ noun 1. a magazine or newspaper published at regular intervals. synonyms: journal, publication, magazine, newspaper, paper, review, digest, gazette, newsletter, organ, quarterly, annual, weekly; More adjective 1. occurring or appearing at intervals; occasional. "she took periodical gulps of her tea"
Magazine and periodical can be synonymous and interchangeable in English. Not only is it not impossible but it is very frequently used in English in this exact context (as a noun of course).