Heidegger's Bible Handbook: Haggai: Chronology

3.  An account of the time in which he prophecied.

Haggai prophesied בִּשְׁנַ֤ת שְׁתַּ֙יִם֙ לְדָרְיָ֣וֶשׁ, in the second year of Darius, in which to him the word of the Lord concerning Zerubbabel and Joshua or Jesus the High Priest, came three times, Haggai 1:1; 2:1; 2:20.  Which Darius that was is not evident to all.  That it was Darius I, the Mede, the son of Ahasuerus, of whom mention is made in Daniel 6:1, not all are agreed.  That it was Darius II, the son of Hystaspes, Josephus, and after him Jerome, and other learned men think.  But, since, after the return and prohibited building of the Temple, the Jews are said to have fasted in the land שָׁנִים, many years, even indeed seventy years, Zechariah 7:3, 5, and for seventy years God is said to have dealt rigidly with them, that is, most recently, Zechariah 1:12; the seventy years have not expired from Cyrus to the second year of Darius II, the son of Hystaspes.  Hence Sulpicius Severus,[1] Junius, Drusius, Piscator, Tarnovius, and others think that Darius III, called Nothus, is probably indicated.  Who are also supported by this, that, by a comparison with Ezra 4:5, 6, 24; 5:1, 7; 6:1, that Darius plainly succeeds Artaxerxes.  But Darius Nothus succeeded Artaxerxes Longimanus.

[1] Sulpicius Severus (c. 360-425) was a member of the Roman senatorial aristocracy, who renounced all for the monastic life.  He wrote the first biography of Martin of Tours and the Chronicorum Libri Duo (or Historia Sacra), providing a history from the creation to 400 AD.  Drusius produced an annotated edition of his works.